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This coding, including for assessments, is not visible to students in the printed student edition of the book.


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PHYSICS OF THE

UNIVERSE Meet the Writing Team

Benjamin

Benjamin J. Westleigh I have a BSc from the University of Miami and a Masters in Teaching and Learning from Waikato University. I have taught high school science and mathematics since 2009 and was based in Maine, in the USA, before moving to New Zealand.

PR E O V N IE LY W Author

Kent Pryor I have a BSc from Massey University majoring in zoology and ecology and taught secondary school biology and chemistry for 9 years before joining BIOZONE as an author in 2009.

Kent

Contributing author

Tracey Greenwood I have been writing resources for students since 1993. I have a Ph.D in biology, specialising in lake ecology and I have taught both graduate and undergraduate biology.

Cover photograph

Black Holes: Monsters in Space (Artist's Concept)

Tracey

PHOTO: NASA/JPL-Caltech

Senior Author

This artist's concept illustrates a supermassive black hole, with a mass millions to billions times that of our Sun. It is surrounded by an accretion disk, which forms as the dust and gas in the galaxy falls onto the hole, attracted by its gravity. The artist has also drawn an outflowing jet of energetic particles. These are believed to be powered by the black hole's spin.

Lissa Bainbridge-Smith I worked in industry in a research and development capacity for 8 years before joining BIOZONE in 2006. I have a MSc from Waikato University.

Lissa Author

David

Consulting editor

For more information visit: https://photojournal.jpl.nasa.gov/catalog/PIA16695

David Sole (consulting editor) I have a degree in physics, mathematics, and psychology and have been teaching physics and electronics for over 40 years. I have also worked as a physics and science advisor for the Education Department and have published and edited a number of science texts.

Thanks to:

The staff at BIOZONE, including Mike Campbell for design and graphics support, Paolo Curray for IT support, Anu Chauhan for logistics, Felix Hicks for assistance with illustration, Allan Young for office handling, , and the BIOZONE sales team.

ISBN 978-1-927309-75-9 First Edition 2019 Second printing

Copyright Š 2019 Richard Allan Published by BIOZONE International 441345Ltd Milford

Printed by THOMSON PRESS (INDIA) LTD

Even_Odd A41A Mid Year Diary.pdf

1

25/09/19

Next Generation Science Standards (NGSS) is a registered trademark of Achieve. Neither Achieve nor the lead states and partners that developed the Next Generation Science Standards were involved in the 2:05 PM production of this product and do not endorse it.

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All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electrical, mechanical, photocopying, recording or otherwise, without the permission of BIOZONE International Ltd. This book may not be re-sold. The conditions of sale specifically prohibit the photocopying of exercises, worksheets, and diagrams from this book for any reason.

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Purchases of this book may be made direct from the publisher:

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Re-order Code 441345


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Contents

IS1 Forces and Motion

IS4 Nuclear Processes and Earth History

29 30 31 32 33 34 35 36

Student Questions ........................................ 144 ANCHORING PHENOMENON Powering a 15 Billion km Journey .................. 145 A Bit more on Atomic Structure........................ 146 Inside the Nucleus............................................ 150 Radioactivity..................................................... 153 Radioactive Decay and Half Lives.................... 163 The Age of the Earth........................................ 168 Powering a 15 Billion km Journey Revisited.......................................................... 186 Summative Assessment................................... 187

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Physics of the Universe: A Flow of Ideas ........... iv Using This Book ...................................................v Using BIOZONES's Resource Hub .................. viii Using the Tab System ......................................... x

Student Questions ............................................ 1 ANCHORING PHENOMENON Start Your Engines .............................................. 2 Motion................................................................. 3 Forces .............................................................. 11 Newton's Laws of Motion.................................. 15 Building Bridges................................................ 23 Momentum......................................................... 28 Engineering and Forces..................................... 36 Forces of the Earth .......................................... 40 Start Your Engines Revisited.............................. 43 Summative Assessment..................................... 44

IS2 Forces at a Distance

Student Questions .......................................... 48

11 ANCHORING PHENOMENON Let's Go Climbing.............................................. 49 12 Exploring Gravity................................................ 50 13 Planetary Motion................................................ 55 14 Electrostatic Force............................................. 70 15 Atomic Structure and Bonding........................... 75 16 Magnetism.......................................................... 83 17 Applications of Electromagnetic Forces............. 89 18 Let's Go Climbing Revisited ............................. 98 19 Summative Assessment..................................... 99

IS3 Energy Conversion and Renewable Energy

20 21 22 23 24 25 26 27 28

Student Questions ........................................ 103 ANCHORING PHENOMENON The Winds of Change .................................... 104 Electricity in Daily Life...................................... 105 How do Power Plants Work?............................ 117 Generating Electricity....................................... 124 Converting Light to Electricity.......................... 129 Evaluating Renewable Power Plants................ 134 Engineering Energy Conversion Devices........ 136 The Winds of Change Revisited....................... 139 Summative Assessment................................... 140

IS5 Waves and Electromagnetic Radiation

37 38 39 40 41 42 43

IS6 Stars and Origins of the Universe

44 45 46 47 48 49 50

Activity is marked:

to be done

Student Questions ........................................ 231 ANCHORING PHENOMENON Hidden in Plain Sight ...................................... 232 Star Light, Star Bright....................................... 233 The Sun............................................................ 240 The Life of Stars............................................... 246 Origins of the Universe..................................... 253 Hidden in Plain Sight Revisited ...................... 266 Summative Assessment ................................. 267

Basic Skills for Physics Students

Student Questions ........................................ 271 The Nature of Science..................................... 272 Systems and Models........................................ 274 Observations and Assumptions....................... 275 Measurement and Units................................... 276 Useful Concepts in Physics.............................. 279 Accuracy and Precision.................................... 281 Working With Numbers.................................... 282 Graphical Analysis........................................... 284 Describing the Data......................................... 286 Periodic Table................................................... 288

51 52 53 54 55 56 57 58 59 60

CODES:

Student Questions ........................................ 189 ANCHORING PHENOMENON I'm Still Standing ............................................ 190 The Nature of Waves........................................ 191 Earthquake Waves........................................... 202 The Nature of Light.......................................... 209 Waves and Technology.................................... 220 I'm Still Standing Revisited............................... 227 Summative Assessment................................... 228

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1 2 3 4 5 6 7 8 9 10

Appendix: Equipment List................................. 289 Appendix: Units and Formulae......................... 291 Image Credits................................................... 292 Index................................................................ 293

when completed

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Physics of the Universe: A Flow of Ideas

This concept map shows the broad areas of content covered within each Instructional Segment of Physics of the Universe. Anchoring phenomena are indicated in red boxes and dashed red arrows show conceptual connections between topics. Green boxes show some of the crossing cutting concepts linking some of the topics. Can you find other connections?

1

Forces

Newton’s laws

Inverse square law

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To IS4

Forces and Motion

SYSTEMS AND SYSTEM MODELS

Motion

CAUSE AND EFFECT

Collisions

Let’s Go Climbing!

Orbits

Life cycle of stars

Inverse square law

The origin of the universe

Coulomb’s law

Atomic structure

Energy in stars

Molecular properties

The color of stars

Stars and the Origins of the Universe

ENERGY AND MATTER

Non-renewable energy sources

Properties of light

Radioactivity and decay

CAUSE AND EFFECT

PATTERNS

The nature of light

4

Nuclear reactions

5

Waves and Elecgtromagnetic Radiation

I’m Still Standing Waves and technology

Dating geological features

STABILITY AND CHANGE

Earth’s structure

E = mc2

Nuclear Processes and Earth History

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ENERGY AND MATTER

Efficiency of electricity generation

SCALE, PROPORTION AND QUANTITY

Health effects

Nuclear energy

Energy Conservation and Renewable Energy

The Winds of Change

Renewable energy sources

Environmental impact

Electromagnetic spectrum

Applications

3

ENERGY AND MATTER

Health effects

Magnetism

Electricity generation

Hidden in Plain Sight

CAUSE AND EFFECT

PATTERNS

PATTERNS

Powering a 15 Billion km Journey

Stratigraphy

ENERGY AND MATTER

Earthquake waves

Conservation of energy and mass

To IS1 To IS6

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Electrostatic force

Kepler’s Laws

STRUCTURE AND FUNCTION

The Big Bang

To IS4

Planetary motion

Tectonic plates

Expanding universe

Forces at a Distance

PATTERNS

Design safety

Mountain building

2

Gravity

Start Your Engines


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Using This Book

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Activities make up most of this book. These are presented as integrated instructional sequences over multiple pages, allowing you to build a deeper understanding of phenomena as you progress through each chapter. Each chapter begins with an anchoring phenomenon. This is something you would have seen or experienced (e.g. comparing the performance of race cars and ordinary cars) but may not necessarily be able to explain. The anchoring phenomenon is revisited at the close of the chapter. Most of the other activities in a chapter are designed to lead you an understanding of that phenomenon. Each activity begins with a task to engage your thinking, asking you to review your current understanding of a phenomenon and setting the scene for the content to follow. The activity then allows you to explore related content through modeling, experimentation, or data analysis. You can then explain phenomena described through models, simulations, data, descriptions, or photographs. Many activities will also require you to elaborate (expand) on what you have explored and then to evaluate your understanding of the material.

Chapter introduction

Structure of a chapter

Identifies the activities relating to the guiding questions.

Summative assessment

This can be used as a formal assessment of one or more of the NGSS performance expectations addressed in the chapter.

Anchoring phenomenon

Anchoring phenomenon revisited

The first activity is always an anchoring phenomenon. It introduces a phenomenon that can be explained by the rest of the activities in the chapter.

Once you have completed the activities in the chapter should be able to explain various aspects of the anchoring phenomenon more fully.

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Activity pages


Chapter Introductions

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vi

This identifies the Instructional Segment to which this chapter applies.

1

Forces and Motion

Instructional Segment 1

Activity number

Guiding questions These are the guiding questions outlined for the Physics of the Universe course.

Anchoring Phenomenon 1 9

Start your engines! Race cars are designed for high speed cornering.

How can Newton's laws explain how and why things move? 2 10

1

The study of motion is an important part of physics. How do you describe the motion of objects around you? Identify the three main aspects of motion and construct diagrams to describe these different aspects of movement. Distinguish between speed and velocity. Use and interpret mathematical representations of the relationship between distance and time to determine velocity. Working in groups, investigate this relationship for yourselves and plot your results.

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2

What do we mean when we say something is accelerating? Use a mathematical expression (equation) to calculate the acceleration for an object traveling in a particular direction. Given a known acceleration, time, and final velocity, how would you calculate distance traveled?Draw and interpret graphs of displacement versus time and velocity versus time.

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3

What do you understand by the term force? What happens when unbalanced forces are applied to an object? Weight is a specific kind of force caused by gravity but forces can act on objects from any direction. Draw a simple model to show the effect of a constant force being applied to objects of increasing mass. Interpret data on the effect of friction on motion. Explain why friction is an important consideration in the design and operation of moving objects.

3 10

c

4

You now understand the difference between mass and weight and can analyze the motion of objects subjected to a constant force (gravity). Interpret data from investigations of the effect of increasing mass on acceleration and explain the relationship between the force on an object, its mass, and its acceleration. Draw and analyze free body diagrams to calculate the net forces on known masses and thus determine their acceleration.

4 10

c

5

Extend your study of forces and motion to include collisions and momentum. Investigate the momentum of objects of different mass using marbles on a ramp. Use your results to explain how momentum affects the distance the marbles roll.

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Analyze the results of investigations of the effect of collisions on the momentum of the colliding objects in an isolated system. Explain the results in terms of conservation of momentum. Extend your analysis to explain the effects of collisions between real objects (e.g. motor vehicles). What happens when the force of a colliding object is spread out over a longer (or shorter) period of time? Use a mathematical model to demonstrate this and explain its significance to how much damage occurs during a collision.

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7

Use Google Earth to identify places on Earth where there is evidence of Earth's constructive and destructive forces. Recognize the different time scales over which these forces operate. Use or interpret models of tectonic activity made using a squeeze box to explain how Newton's three laws of motion apply to the movement of tectonic plates and continents. Communicate your findings about one geomorphic feature (e.g. mountain range) to the class.

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Use your understanding of Newton's laws to design the strongest bridge you can given certain equipment and test conditions. Working in groups, discuss your bridge design. You can test possible designs first using a digital bridge builder program. Evaluate your design and explain if and how it could be improved on the basis of your research. How do (or might) different materials influence the strength of your bridge?

5

c

9

Use your understanding of changes in momentum and impulse to analyze the design of modern safety equipment, e.g. crash helmets for different sports and air bags and crumple zones in cars. Use mathematical thinking to explain how these safety devices reduce the force delivered during a collision.

7

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10

Demonstrate your understanding of forces and momentum by designing a landing device to protect a raw egg from a fall of at least 5 meters. Working in groups, discuss how you will make the lander and the different designs you could use to cushion the egg at impact and/or slow its descent. Justify your design choice in terms of Newton's laws of motion.

7

c

2 3 10

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Mark the check boxes to indicate the outcomes you should complete. Check them off when you have finished.

A red number indicates the summative assessment for this chapter where an NGSS performance expectation is addressed.

6

6 10

8

How can mathematical models of Newton's laws be used to test and improve engineering designs?

36

7

The activity in the book related to these questions or statements. Some activities contribute to you meeting the NGSS performance expectations.

37

Engineering and Forces

INVESTIGATION 1.7: Building a lander ``

1. Consider the two photographs below. The car on the left was built in about 1960, the car on the right was built in 2018. Imagine the cars were both travelling at 80 kmph and were involved in a head on crash into a power pole. In which of these vehicles would the occupants experience the greater impact force and why?

2. The conditions: You will build a landing device that will protect a raw egg from a fall of at least 5 m. Your are free to use the equipment (below) in any way but there may be no platform for the lander to fall onto (landers don't have convenient foam landing pads to fall onto when they reach their destination).

3. (a) Explain why the Curiosity rover used a sky crane to lower it to the surface:

(b) The acceleration due to gravity of Mars is 3.71

See appendix for equipment list.

1. You will now have the opportunity to put your knowledge of forces and momentum to the test. The objective of this investigation is to build a device that will protect a lander from descent of at least five meters.

(b) Would these methods work on the Moon or Mercury?

m ⁄ s2. What

39

ELABORATE: Designing to meet specifications

2. (a) What are the two main methods used by NASA to land its rovers or landers on Mars?

ENGAGE: Crash!

3. The equipment: 1 egg, 60 cm of tape, 5 rubber bands, 1 small garbage or plastic bag, 10 paper clips, 1 m string, 20 plastic or paper straws, 1 plastic egg or similar sized object for testing. Your teacher may modify this equipment as they wish. 4. Building time will be determined by your teacher.

is the weight of the Curiosity rover on Mars?

5. Before you begin, discuss with your group how you will construct the lander and in what ways you could cushion the egg at impact or slow its descent to reduce the shock of landing.

(c) What equivalent mass on Earth would produce this weight?

4. Why was reducing the force experienced during landing so important for these rovers?

EVALUATE: Lander design

10. Now that you have built and tested your egg lander you must evaluate its structure and performance. (a) Describe the structure of your lander:

EXPLAIN: Crumple zones

`` Of all the space agencies that have tried to land probes and rovers on Mars, NASA is by far the most successful. NASA has devised two main ways of landing its probes and rovers on to the surface safely: using parachutes and retro-rockets, or parachutes and air bags.

`` Is this thinking actually practical when it comes to a crash? From your studies on force, momentum, and impulse, would you rather be in a car that crumpled up when it had a crash or was rigid and kept its shape?

`` The first of NASA's Mars landers to successfully touch down was Viking 1 in 1976. The lander used parachutes to slow its descent from 250 m ⁄ s to 60 m ⁄ s. It then used retro-rockets to slow its descent below 2.4 m ⁄ s before touch down. Shock absorbers in the legs reduced the final force on landing to a slight jolt.

`` Cars today have sophisticated safety systems that in many cases allow the car to avoid a collision. However these do not prevent all crashes and in the case of an actual crash the frame of the car is designed to crumple up.

ETS1.B ETS1.C

(d) Recall the landing devices designed used by other groups in your class. Which of these where the most effective? Can you explain why?

Mars Pathfinder lander

5. Why do cars have crumple zones?

6. What other safety devices do modern cars regularly have installed to protect the occupants in the event of a crash?

7. Motorbikes have little capacity for crumple zones (although this is performed to a degree by the front wheel and steering system). Bicycles have virtually no capacity for a crumple zone. How do riders protect themselves in a crash? Curiosity rover and sky crane

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Group discussions, informative articles, simple practical activities, and modeling are used to engage with and explore material related to the activity.

©2019 BIOZONE International ISBN: 978-1-927309-75-9 Photocopying Prohibited

You will need to use your knowledge and the evidence presented to explain trends in data or how a particular system works.

(e) Given enough material, it would be easily possible to design a lander than would protect the egg from a much higher fall than 5 m. The same applies to planetary landers. However, there are numerous constraints on the development of these devices, one of which is cost. Discuss with your group what other constraints there might be on the design on a lander for Mars:

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PS2.A

(c) If your egg cracked, what could have been done to keep it from cracking if you repeated the test?

`` The crumpling effect increases the time the force of the crash is applied and so reduces the impact force felt by the occupants.

`` Both the Spirit and Opportunity rovers, which landed in 2004, used similar landing devices as the Mars Pathfinder. `` The Curiosity rover, which landed in 2012, used a particularly advanced retro-rocket package. Because the rover was so heavy (899 kg), it was not feasible to use parachutes and air bags to land. NASA therefore developed a sky crane (right) which lowered the rover to the ground. The huge 16 m diameter parachute, deployed after entry into the atmosphere, produced up to 289 kN of drag. At 1.8 km in altitude, the powered descent stage was released. Using retro-rockets, this hovered above the surface and lowered the rover 7.6 m to the ground before detaching and flying away far enough not to interfere with the rover. It later crashed into the Martian desert.

(b) On a scale of 1-5, how did your egg survive the fall? (1= completely scrambled, 5 = safe and sound):

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You can elaborate on the skills and understanding developed during the activity and evaluate your understanding using further modeling and data analysis.

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`` The Mars Pathfinder lander, which touched down in 1997, used a slightly different landing technique. After entering the atmosphere, the lander also deployed a parachute to slow its descent. Air bags around the lander's frame were inflated. At just 98 meters above the ground, retro-rockets were fired to bring the lander to a sudden halt. The lander was then cut loose from the parachute and fell to the ground, using the inflated air bags to cushion its landing. When it hit the ground, it bounced up to 15 m high and experienced a maximum force of 18 G.

"Cars today, they're just not built tough. A small crash and they're just wrecked". Have you heard this before? Or how many times have you heard someone say "I like being in a SUV or four wheel drive, they're solid, tough, and can take a crash."

NHTSA: National Highway Traffic Safety Administration

EXPLORE: Landing on Mars

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Practical Investigations

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An important part of physics involves carrying out investigations and carefully observing and recording what occurs during them. Throughout the book you will notice green investigation panels (like the ones shown below). Each investigation has been designed using simple equipment found in most high school laboratories. The investigations provide opportunities for you to investigate phenomena for yourself. The investigations have different purposes depending on where they occur within the chapter. Some provide stimulus material or ask questions to encourage you to think about a particular phenomenon before you study it in detail. Others build on work you have already carried out and provide a more complex scenario for you to explain. The investigations will help you develop:

``Skills in observation

``Skills in critical analysis and problem solving

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``Skills in mathematics and numeracy

``Skill in collecting and analyzing data and maintaining accurate records ``Skills in working independently and collaboratively as part of a group ``Skills in communicating and contributing to group discussions

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`` In 1798 Henry Cavendish demonstrated it is possible to observe the gravitational attraction between objects. A modern representation of his experiment is shown below:

Reflecting the laser beam "amplifies" the movement by doubling the angular deviation.

Wire thread

Mirror

Laser light

Small masses hang from a thread so they can pivot.

Light source / laser

Large masses fixed in place.

70

14 Electrostatic Force

`` Originally Cavendish was able to measure the force of gravity between masses by precisely measuring the twisting force on the wire thread used to suspend the smaller masses. The twisting was produced by the movement of the smaller masses towards the larger fixed masses.

ENGAGE: Zap!

`` Gravity is the weakest of the universe's four fundamental forces. Its effects are only noticeable when there is aEver huge `` got out of a car, gone to close the door and received an amount of mass in one place. Even so, the force of gravity can be measured using the simple experiment below. electric shock? What about taking off a polar fleece sweater or jacket? Try it in a darkened room and you will see sparks flash aslist. the jersey rubs against the material of your shirt. What about See appendix for equipment INVESTIGATION 2.1: Cavendish's experiment lightning? What causes that? Study the photo of the little girl's hair (right) What's causing that to happen? 1. Construct a torsion bar by fixing two 1 m rulers together using tape or rubber bands (or just use one 2 m long piece of (thin) wood). 2. Loop nylon fishing line around the center of the torsion bar to produce a torsion balance. Don't worry if the bar doesn't balance perfectly.

3. Hang the torsion balance from a ceiling beam or hook using the fishing line so that the bar hangs a few centimeters over the ground or a table and swings freely.

1. What do you think is causing these phenomena? Where does the

Large masses electricity come from? Discuss your ideas with others in your class (5 - 10 kg)

and write down a summary of these ideas:

Fishing line

4. Hang 1 kg masses on each end of the torsion bar. Adjust their placement until the torsion bar is horizontal (carefully measure the height at each end). Make sure the bar still swings freely. Allow the balance to come to a rest before going on to the next step.

Torsion balance

Small masses (1 kg)

Plan view of investigation

5. Place large masses several centimeters away from each end of the torsion bar in clockwise positions to the small mass (as in the diagram above).

EXPLORE: Balloon electrostatics 6. Set a video recorder (e.g. your device's camera) so it can view the experiment, close all windows and `` Balloons are well known for producing some interesting electrostatic effects: doors, and cover any vents and openings into the room to prevent air flow. 7. Predict how the balance will behave:

INVESTIGATION 2.5: Balloon electrostatics

See appendix for equipment list.

1. In a still, warm room, fully inflate a balloon and hang it from the ceiling or an insulated support with nylon thread or fishing line.

8. Everyone should now leave the room (very carefully and quietly!) for a few minutes to allow the torsion balance to settle. 9. After 10 minutes reenter the room and turn off the video recorder.

10. Watch the video in 5-10x speed and observe what happens to the torsion balance.

2. Rub the balloon with a piece of wool/synthetic material or a sweater so that it becomes charged. 3. Predict what will happen if you bring the material or sweater used to rub the balloon near the balloon.

11. Move the large masses away from the torsion bar and repeat the investigation from step 5. This time place the large masses in counterclockwise positions.

4. Carry out step 3 and record your observations:

5. Fully inflate a second balloon and hang it from the ceiling with more nylon fishing line near the first balloon.

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6. Rub both balloons with the same material (wool/synthetic fabric or a sweater). This should give the balloons a charge of the same sign and a similar amount. 7. Predict what will happen to these similarly charged balloons as they hang near each other.

8. Carry out step 7 and record your observations:

9. Leave the balloons hanging near each other for a few minutes. Record any changes that take place:

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Using BIOZONE's Resource Hub ``BIOZONE's Resource Hub provides links to online content that supports the activities in the book. From this page, you can also check for any errata or clarifications to the book since printing.

``The external websites are, for the most part, narrowly focused animations and video clips directly relevant to some aspect of the activity on which they are cited. They provide great support to help your understanding.

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www.BIOZONEhub.com

Then enter the code in the text field

Search for an activity here.

Instructional segment (IS) and chapter title.

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Click on an activity title to go directly to the resources available for that activity.

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ix Search for an activity here.

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Activity

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Activity you are viewing

Resources available for this activity. Hyperlink to an external website.

Teacher-only resources are identified. These may be scientific papers containing original data or resources to enhance teaching (e.g spreadsheets or simulations).

The Resource Hub icons

Weblink

Video

Weblink

MS Word file

Video

Word

MS Excel spreadsheet

Excel

MS Powerpoint file

Powerpoint

PDF

PDF

3D Model

Explore videos

Explore spreadsheet modeling

Video

Explore web based resources

Video Excel

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Excel Video

Powerpoint Word

Explore 3D models

Word Powerpoint

Excel PDF

Powerpoint 3D Model

PDF

3D Model

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Weblink Word

Word Weblink

Excel

PDF

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Weblink

Video

3D model

3D Model Powerpoint


(b) Try the experiment above right. What happened to the level of the water after it froze to density of the ice compared to the water? Does it tell you anything about the structure x

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Using the Tab System

The tab system is a useful way to quickly identify the crosscutting concepts, disciplinary core ideas, and science and engineering practices embedded within each activity. The tabs also indicate whether or not the activity is supported online.

3. What kind of energy exchanges do you think are happening here?

The orange disciplinary core idea tabs indicate the core ideas that are covered in the activity. These are covered in the introduction to each chapter, under the guiding questions. The code itself is just a guide for your teacher.

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The gray hub tab indicates that the activity has online support via the BIOZONE RESOURCE HUB. This may include videos, animations, articles, 3D models, and computer models.

A hub icon in the margin shows which part(s) of the activity have a hub resource.

PS1.A

The blue science and engineering practices tabs use picture codes to identify the science and engineering practices (SEPs) relevant to the activity. You will use science and engineering practices in the course of completing the activities.

Science and Engineering Practices

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The green crosscutting concepts tabs indicate activities that share the same crosscutting concepts. You will become familiar with the concepts that connect all areas of science.

Cross Cutting Concepts

Patterns We see patterns everywhere in science. These guide how we organize and classify events and organisms and prompt us to ask questions about the factors that create and influence them.

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Cause and effect A major part of science is investigating and explaining causal relationships. The mechanisms by which they occur can be tested in one context and used to explain and predict events in new contexts.

SPQ

Scale, proportion, and quantity Different things are relevant at different scales. Changes in scale, proportion, or quantity affect the structure or performance of a system.

SSM

Systems and system models Making a model of a system (e.g. physical, mathematical) provides a way to understand and test ideas.

Constructing explanations (for science) and designing solutions (for engineering) Constructing explanations for observations and phenomena is a dynamic process and may involve drawing on existing knowledge as well as generating new ideas.

EM

Energy and matter Energy flows and matter cycles. Tracking these fluxes helps us understand how systems function.

Engaging in argument from evidence Scientific argument based on evidence is how new ideas gain acceptance in science. Logical reasoning based on evidence is required when considering the merit of new claims or explanations of phenomena.

SF

Obtaining, evaluating, and communicating information Evaluating information for scientific accuracy or bias is important in determining its validity and reliability. Communicating information includes reports, graphics, oral presentation, and models.

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Developing and using models Models can be used to represent a system or a part of a system. Using models can help to visualize a structure, process, or design and understand how it works. Models can also be used to improve a design.

Planning and carrying out investigations Planning and carrying out investigations is an important part of independent research. Investigations allow ideas and models to be tested and refined. Analyzing and interpreting data Once data is collected it must be analyzed to reveal any patterns or relationships. Tables and graphs are just two of the many ways to display and analyze data for trends. Using mathematics and computational thinking Mathematics is a tool for understanding scientific data. Converting or transforming data helps to see relationships more easily while statistical analysis can help determine the significance of the results.

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Structure and function The structure of an object or living thing determines many of its properties and functions.

Stability and change Science often deals with constructing explanations of how things change or how they remain stable.

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Asking questions (for science) and defining problems (for engineering) Asking scientific questions about observations or content in texts helps to define problems and draw valid conclusions.

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Forces and Motion

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Instructional Segment 1

1 Activity number

Anchoring Phenomenon Start your engines! Race cars are designed for high speed cornering.

1 9

How can Newton's laws explain how and why things move? The study of motion is an important part of physics. How do you describe the motion of objects around you? Identify the three main aspects of motion and construct diagrams to describe these different aspects of movement. Distinguish between speed and velocity. Use and interpret mathematical representations of the relationship between distance and time to determine velocity. Working in groups, investigate this relationship for yourselves and plot your results.

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2

What do we mean when we say something is accelerating? Use a mathematical expression (equation) to calculate the acceleration for an object traveling in a particular direction. Given a known acceleration, time, and final velocity, how would you calculate distance traveled? Draw and interpret graphs of displacement versus time and velocity versus time.

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3

What do you understand by the term force? What happens when unbalanced forces are applied to an object? Weight is a specific kind of force caused by gravity but forces can act on objects from any direction. Draw a simple model to show the effect of a constant force being applied to objects of increasing mass. Interpret data on the effect of friction on motion. Explain why friction is an important consideration in the design and operation of moving objects.

3 10

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4

You now understand the difference between mass and weight and can analyze the motion of objects subjected to a constant force (gravity). Interpret data from investigations of the effect of increasing mass on acceleration and explain the relationship between the force on an object, its mass, and its acceleration. Draw and analyze free body diagrams to calculate the net forces on known masses and thus determine their acceleration.

4 10

c

5

Extend your study of forces and motion to include collisions and momentum. Investigate the momentum of objects of different mass using marbles on a ramp. Use your results to explain how momentum affects the distance the marbles roll.

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6

Analyze the results of investigations of the effect of collisions on the momentum of the colliding objects in an isolated system. Explain the results in terms of conservation of momentum. Extend your analysis to explain the effects of collisions between real objects (e.g. motor vehicles). What happens when the force of a colliding object is spread out over a longer (or shorter) period of time? Use a mathematical model to demonstrate this and explain its significance to how much damage occurs during a collision.

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7

Use Google Earth to identify places on Earth where there is evidence of Earth's constructive and destructive forces. Recognize the different time scales over which these forces operate. Use or interpret models of tectonic activity made using a squeeze box to explain how Newton's three laws of motion apply to the movement of tectonic plates and continents. Communicate your findings about one geomorphic feature (e.g. mountain range) to the class.

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1

NASA

2 3 10

6

6 10

8

How can mathematical models of Newton's laws be used to test and improve engineering designs?

5

8

Use your understanding of Newton's laws to design the strongest bridge you can given certain equipment and test conditions. Working in groups, discuss your bridge design. You can test possible designs first using a digital bridge builder program. Evaluate your design and explain if and how it could be improved on the basis of your research. How do (or might) different materials influence the strength of your bridge?

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9

Use your understanding of changes in momentum and impulse to analyze the design of modern safety equipment, e.g. crash helmets for different sports and air bags and crumple zones in cars. Use mathematical thinking to explain how these safety devices reduce the force delivered during a collision.

7

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10

Demonstrate your understanding of forces and momentum by designing a landing device to protect a raw egg from a fall of at least 5 meters. Working in groups, discuss how you will make the lander and the different designs you could use to cushion the egg at impact and/or slow its descent. Justify your design choice in terms of Newton's laws of motion.

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NASA

2 10

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2

Start Your Engines

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1

ANCHORING PHENOMENON: Race cars are designed for high speed cornering Compare a standard domestic car (below left) with a Formula 1 (below right) or IndyCar. Notice any difference?

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Wing

Wing

`` Clearly there are important differences in the appearance of the cars (much of which is related to function), but which car could travel the fastest around a tight bend?

`` Notice all the wings around the car on the right, what do they do?

`` Notice also the angle (camber) of the race car's wheels. Why are they angled outwards at the bottom? How does this affect its ability to corner?

`` It has been shown in simulations that a formula 1 car would be able to drive upside down along a tunnel when moving a top speed. How is this possible?

1. What keeps both the cars above pressed down on the road?

2. The car on the left has a mass of about 1,100 kg and a engine output of about 177 kilowatts. The car on the right has a mass of about 760 kg with an engine output of about 710 kilowatts. How will this affect the acceleration of each car?

3. Wings produce down force. Why would this be useful to a race car?

4. The car on the left produces a lot of drag. How would this affect its ability to accelerate?

5. The diagram below shows a rear view of a domestic car (left) and a race car (right). Each car is making a tight left turn at very high speed.

Explain why in this situation the domestic car is likely to slide off the track, while the race car will continue on round the corner:

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Turning direction

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Motion

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2

3

ENGAGE: Describing motion

Where's she going?

`` Take a moment to observe the movement of objects around

you. The movement could be of the tip of your finger, or your classmate wandering around the room, or your teacher walking to the other side of the desk. How would you describe the motion of these things?

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1. Describe the motion or movement of three things in your classroom in terms of their speed and direction: (a)

(b)

(c)

2. The image below shows two trucks racing in straight lines. Write down how the motion of these trucks could be described:

3. (a) This morning you left your house or apartment and went to school. Using Google Maps (or a similar web based mapping program) locate your home and your school. Find the route you used to get to school. This will work best in the map view rather than the satellite view. (b) On graph paper set a grid with x and y axes extending in both positive and negative directions. The point where the axes cross define your home. Call this the origin, the point at which your journey began.

(c) Map your journey on the grid, starting from the origin. Make sure you use a uniform scale throughout.

(d) Use the mapping program to find out the total distance of your journey.

(e) Draw a straight line from the origin to the end point of your journey (the school). Using the measurements of your x and y axes, you can work out the length of this line. This is the actual distance from your house to your school ("as the crows flies", as the saying goes). How much further is your total distance traveled compared to the actual distance to school?

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EXPLORE: Displacement and distance

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`` An important part of physics is the study of motion. Motion is the movement of an object from one point to another. Two important aspects of motion are the distance moved and the direction traveled.

`` Distance is how far an object moves. It is measured in meters (m). Distance belongs to a group of variables called scalars. The common feature of scalars is that they have size (also called magnitude) only.

`` Displacement is the straight–line distance from the initial position to the final position and includes direction.

Displacement therefore belongs to a group of variables we call vectors. All vectors have size (also called magnitude) and direction. In other words, displacement is an object's overall change in position. Using notation, you can use d for distance and d or d or d for displacement.

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4. Imagine a man walking along a flat straight street. He starts at home (0) and walks 10 m. Realizing he's walking in the wrong direction he turns around and walks 50 m to the store. Plot the two stages of the walk on the number line below:

–45

–40

–35

–30

x (m)

–25

–20

(a) What is the total distance the man walked?

(b) What is man's the displacement?

–15

–10

–5

0

5

10

15

5. (a) On the grid below plot the following motion. A person walks 10 m west, then 10 m north, then 20 m east, and

finally 20 m south.

North

Meters

0

South

0 Meters

(b) What is the total distance the person walked?

(c) What is the person's displacement at the end of the journey? Hint you might need to use Pythagoras a2 + b2 = c2 to find the distance.

EXPLORE: The role of time

East

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West

`` Time is important when describing motion. If another person traveled the same route in the journeys above, but took more or less time, then the motion would be different because they would have moved faster or slower.

`` The number line and the grid above simply showed an object’s position in one dimension and two dimensions

respectively. We can show the effect of time by plotting a distance versus time graph or a displacement versus time graph. Distance and displacement are usually plotted along the y-axis whereas time is plotted along the x-axis.

`` For motion in one dimension, distance traveled will always be positive as it is cumulative. Displacement can be

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positive or negative depending on whether the object is going away from the starting point or going back towards the starting point. Time always runs forward and so is always positive.

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5

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6. A horse trots at a steady speed 20 m to a water trough in 4 seconds. It drinks for 10 seconds. It then trots 30 m back the way it came, taking 6 seconds. Finally it turns around again and trots 20 m in 5 seconds.

(a) Plot the movement of the horse on the displacement-time graph below: 40

30

Displacement (m)

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20

10

0

–10

–20

0

5

15

10

25

20

Time (s)

(b) What is the horse's displacement at the end of its movement?

(c) What is the total distance the horse moves?

EXPLORE: Speed and velocity

`` Speed describes how fast something is moving. It is the rate at which an object covers a certain distance. In physics, speed is measured in meters per second (m ⁄ s).

Dd

`` Like distance, speed is considered to be scalar, meaning it is only described by its magnitude, and no direction is included.

v

Dt

`` Velocity takes into account an object's speed and direction. Thus like

displacement, it is a vector. Constant velocity means that the object is moving at a constant speed and in a constant direction. A change in speed or direction results in a change in velocity. Like speed, velocity is measured is meters per second but will have direction, e.g. +5 m ⁄ s indicates movement in one direction whereas -5 m ⁄ s indicates movement in the opposite direction. Velocity is therefore a vector.

`` We can use velocity to determine how much distance is traveled in a

The relationship between distance, velocity, and time is shown in the triangle above. When calculating an unknown value, cover that value's symbol in the triangle. The remaining symbols will shown you how to calculate the unknown.

certain amount of time using the equation:

Change in distance (Dd) = velocity (v) x change in time (Dt)

30

`` Velocity can be found on a distance-time graph (or a displacement-

(a) Calculate Δd/Δt (= v) for X and Y (include units):

(b) How is v different for X and Y? ©2019 BIOZONE International ISBN: 978-1-927309-75-9 Photocopying Prohibited

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20 15

Y

10

5

0

0

1

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7. The axes opposite show the motion graphs for two people, X and Y:

Distance (meters)

time graph) from the gradient, since gradient = rise/run, and rise/run = Δd/Δt, and Δd/Δt = v. This is demonstrated in the next question.

X

25

2 3 4 Time (seconds)

5


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INVESTIGATION 1.1: Distance, displacement, and velocity

See appendix for equipment list.

1. Set out a straight line (one-dimensional) course with 9 markers at 10 m intervals as shown below. The starter and the runner are at the middle of the course. 2. On the right side of the course, each marker has 2 timers, one for the outward journey and one for the return journey. Starter

Timers

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Timers

10m

10m

10m

10m

10m

10m

10m

10m

Runner

3. On the starter’s signal (they should use a large visual signal): (a) The runner runs from the middle of the course to one end and then back to the opposite end. (b) All the timers start timing at the starter's signal and stop when the runner reaches their marker. 4. Complete the tables below:

Table 2

Table 1

Table 3

d= distance traveled (m)

t = time elapsed (s)

d= displacement (m)

t = time elapsed (s)

Dd = dfinal – dinitial (m)

0

0

0

0

10 – 0 = 10

10

10

20 – 10 = 10

20

20

20 – 10 = 10

30

30

30 – 20 = 10

40

40

40 – 30 = 10

50

30

30 – 40 = -10

60

20

20 – 30 = -10

70

10

10 – 20 = -10

80

0

0 – 10 = -10

90

-10

-10 – 0 = -10

100

-20

-20 – -10 = -10

110

-30

-30 – -20 = -10

120

-40

-40 – -30 = -10

Dt = tfinal – tinitial (s)

v = Dd/Dt (m/s)

t = mid interval time (s)

NOTE: tmid interval = (tfinal + tinitial) ÷ 2

5. Use Table 1 to plot a graph of distance versus time on grid 1 opposite. Use the plotted points to make a smooth trendline. 6. Use Table 2 to plot a graph of displacement versus time on grid 2 opposite. Use the plotted points to make a smooth trendline.

8. Why is it necessary for the starter to use a visual signal?

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7. Use the last two columns of Table 3 to plot a graph of velocity versus time on grid 3 opposite. Make a smooth trendline.

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9. Why was it necessary to use the mid-interval times for the third table and third graph?

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Graph 1: Distance versus time

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Graph 3: Velocity versus time

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Graph 2: Displacement versus time


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10. Describe the shape of the distance-time graph:

11. Describe the shape of the displacement-time graph:

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12. Describe the shape of the velocity-time graph:

13. How can you tell what kind of velocity is occurring on a distance-time or displacement-time graph?

14. How is constant velocity shown on a distance-time or displacement-time graph?

15. How is direction shown on a displacement-time graph?

16. How is direction shown on a velocity-time graph?

40

40

30

30

Displacement (m)

20 10

20

40

60

10 0

80

20

80

40

Velocity (m ⁄ s)

40

Velocity (m ⁄ s)

60

Time (s)

Time (s)

30 20 10 0

40

20

40 Time (s)

60

80

30 20 10 0

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0

20

40

60

80

Time (s)

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Distance (m)

17. Study the graphs below and state the type of motion they are showing:

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9

EXPLORE: Acceleration

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Acceleration occurs when velocity changes. Acceleration can be changed by altering speed or direction (or both). It is defined as the change in velocity over the time elapsed.

Dv

Acceleration (a) = change in velocity (∆v) ÷ change in time (Dt)

a

`` In everyday language, we talk about accelerating (speeding up) and decelerating

Dt

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(slowing down) as would describe the skiers below.

`` In physics, acceleration can be positive and negative.

`` Positive acceleration acts in the direction of an object's movement. Negative acceleration acts in the direction

opposite to the object's movement. Thus negative acceleration, if it persists, means that an object will not only slow down, but stop and eventually travel backwards in the opposite direction as shown in the diagrams (1-4) below. v = +2

1

v = +1

a= –1

t=1

2

t=2

v=0

a= –1

3

t=3

v = –1

a= –1

4

t=4

a= –1

`` Acceleration is measured in meters per second per second (m ⁄ s2). A car accelerating from a stationary start at 5 m ⁄ s2 will increase its velocity by 5 meters per second every second.

18. For the car mentioned above, what will its velocity be after:

(a) 1 second:

(b) 2 seconds:

(c) 3 seconds:

Velocity of car 1 (m ⁄ s)

Velocity of car 2 (m ⁄ s)

0

0

0

1

10

7.5

2

20

15.0

3

30

22.5

4

40

30.0

(a) Calculate the average acceleration of car 1:

(b) Calculate the average acceleration of car 2:

(c) Calculate the average velocity of car 1:

(d) Calculate the average velocity of car 2:

(e) How far did car 1 travel in the 4 second race?

(f) How far did car 2 travel in the 4 second race?

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Time (s)

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19. Two cars compete in a straight line race. The velocities of each car are shown in the table below:


10

EXPLAIN: Displacement, velocity, and acceleration

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20. The photograph right shows a jet being launched from an aircraft carrier. The catapult that launches the jet accelerates it at 33 m ⁄ s2 to a final velocity of 70 m ⁄ s from a standing start. (a) Rewrite the equation for acceleration to find Dt:

(b) What is the time taken for the jet to reach its final velocity?

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`` We know distance = velocity x time. Given the initial (Vi) and final (Vf) velocities we can calculate the average velocity and multiply by the time taken to find the distance or:

d = 0.5(vi + vf)Dt

`` We can replace t with your equation from 20(a) to get:

d = 0.5(vi + vf) vf – vi a

`` Which can be rearranged and simplified to give:

d=

vf2 – vi2 2a

21. Returning to the aircraft carrier launching the jet, how far does the jet travel as it launches?

22. In question 19(e) and (f) you were asked to calculate the displacement of two dragsters. Use the equation above to calculate their displacement. Do these answers agree with your initial calculations?

(b) How far does it travel while stopping?

24. What is the average acceleration of a bullet that reaches a speed of 600 m/s in a distance of 0.6 m?

Niel Noorhoek CC3.0

(a) How long does it take the car to come to a stop from a run of 885 km/h (245.8 m/s)?

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23. A land-speed car can decelerate at 9.8 m/s.

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Forces

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3

11

ENGAGE: Moving?

`` Place a ball on the bench or on the ground in front of you so

that it stays still. Don't touch it for 10 seconds. Did it move in that time? Leave it for another 10 seconds? Did it move?

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1. (a) Why didn't the ball move?

(b) How would you get the ball to move?

2. Give the ball a push. What happens to the motion of the ball?

3. Give the ball a harder push. Compare the motion of the ball this time to the first push:

4. Why are these motions different?

EXPLORE: Force, what is it?

`` Force is another important term that you will use a lot in your physics class. It can be simply described as a push or a pull. A example of a push would be you pushing the ball in the activity above. A pull could be the ball being pulled by gravity towards the ground when dropped.

5. What happens to a stationary object when a force is applied to it in one direction?

6. What happens if a greater force is applied to the object?

`` The characteristics of a force include:

• A force is a push or pull acting on an object.

• A force acts on an object. The push or pull of the force must be applied to something (object). • A force requires an “agent” to provide the push or the pull, e.g. a soccer player’s boot kicking a ball, a bungee rope pulling a bungee jumper up from the lowest point of the jump.

• Long-range forces act without physical contact between the agent and the object, e.g. magnetic forces, electrostatic forces, and gravitational forces. 7. Objects accelerate when the forces applied to them are unbalanced or there is a net force. The diagram right shows two balls in a vacuum, one being held by a string, the other string has broken and the ball is falling to Earth. Draw arrows on the balls indicating the direction and size of the forces acting on the balls.

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Hanging ball

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• Contact forces require contact between the agent and an object, e.g. a bat hitting a ball.

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• All forces are vectors as they have size and direction.

Falling ball


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EXPLAIN: Your weight is not your mass

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`` Everyday language often gives meanings to words that are different to what they have in physics. Mass and weight are good examples. When most people talk about weight they actually mean mass.

`` Mass (m) measures the amount of matter (atoms) making up an object. The SI unit for mass is kilogram (kg). Take the stone on the right as an example. If you placed it on an electronic balance, you might get a readout of 50 grams. This is the stone's mass.

`` But how does the scale know how much matter is in the stone? It doesn't count every

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atom, so what it is doing? It is measuring the force due to gravity (weight) in Newtons acting on the stone. Near the surface of the Earth, scales or balances are calibrated so that the force due to gravity they are measuring is divided by 9.8, which gives the result on the readout as the mass in kilograms.

8. (a) What would happen to the scale’s reading if the stone and scale were placed on the Moon where the strength of gravity is 17% of what it is here on Earth?

(b) Would the amount of matter in the stone change if placed on the Moon?

(c) Why then is the reading from the scale different on the Moon compared to the Earth?

`` Gravity is a property of all masses that causes them to pull together. This pull is almost insignificant unless at least one of the masses is extremely large, e.g. the Earth’s gravity pulls all smaller objects near it towards its center.

`` Weight is the measurement of the pull of gravity on an object, so it is also called the force due to gravity. It is a

force, so it is measured in Newtons (N). The mass of an object remains the same (unless it gains or loses atoms) but its weight will depend the strength of gravity at its location. Thus, your weight on Earth is your mass multiplied by the strength of gravity.

`` Gravity has the symbol g. You can think of it as the strength of gravity 9.81 N/kg near the Earth’s surface) or as the acceleration due to gravity (9.81 m/s2 near the Earth’s surface). However you view g, a value of 9.8 is generally accurate enough for most calculations.

9. Write an equation for calculating weight: 10. Complete the table below:

Place

Strength of gravity (N/kg)

Mass (kg)

Earth

9.81

70

Mars

3.71

70

Moon

1.62

70

Jupiter

24.79

70

Weight (N)

Mass (kg) on Earth that has the same weight

11. (a) A person standing in an elevator has mass of 80 kg. The elevator is stationary. Calculate the person's weight:

(b) The elevator starts moving upwards, accelerating upwards to 18 m ⁄ s in 5 seconds. Would the person feel heavier or lighter during the first 5 seconds than when the elevator was stationary?

(c) After 5 seconds, the velocity of the elevator remained at 18 m ⁄ s. Would the person feel heavier or lighter than when the elevator was stationary?

(d) Explain your answers:

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ELABORATE: Calculating the force needed to accelerate an object

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`` Weight (force due to gravity) is just one kind of force. All forces (if they are unbalanced) will cause an object to

accelerate. The equation you produced for weight can be generalized into Isaac Newton’s second law of motion which relates forces in general (F), mass (m), and acceleration (a):

12. Write an equation to calculate force (F):

You should have come up with F = m x a Note the equivalence of the units: N = kg x m/s2 and N/kg = m/s2

13. Calculate the force in newtons of the following: (a) A 2 kg mass is accelerated by 2 m ⁄ s2:

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(b) A 65 kg person has a weight force of:

(c) A 200,000 kg locomotive accelerates at 0.5 m ⁄ s2:

(d) 300 kg accelerates at 5 m ⁄ s2:

14. (a) Draw a simple model to show the effect of a constant force being applied from the left hand side to three objects of increasing mass:

(b) Explain your model in terms of the force equation above:

15. (a) Rearrange the force equation at the top of the page to calculate mass:

(b) Calculate the mass of an American bison with a weight of 9682 N:

16. An 850 kg race car accelerates from 0 m ⁄ s to 27 m ⁄ s in 2.1 seconds.

(a) What is the acceleration of the car?

(b) What force is produced by the car?

17. The gravitational force on Earth is 9.8 N ⁄ kg, but on the Moon it is 1.6 N ⁄ kg. Calculate the weight of an astronaut with a mass of 100 kg when they are walking on: (a) Earth:

(b) The Moon:

(c) The astronaut jumps on the moon. Why would they jump higher on the moon than on the Earth? Explain:

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EXPLAIN: Friction

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Friction is a force that resists motion. It is caused when materials slide past each other. Friction is industrially important as additional force is needed to overcome it before useful work can occur.

`` Certain processes try to minimize or maximize friction

depending on the outcome required. For example, the moving parts of a wheel bearing are oiled to reduce friction and keep the wheel spinning smoothly. On the other hand, braking systems try to maximize friction to bring a moving object to a stop as quickly as possible.

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`` Friction is a "two-edged sword" in motion. Without it, there would be no stopping a moving object and no grip (try running on ice in socks). However friction opposes the rolling of a tire or the spin of a propeller, and even movement through air.

Brake pad

`` Jet planes experience high friction as they move through the

air. This friction causes the fuselage to heat up. The Concorde's

fuselage became 200°C hotter than the outside temperature when cruising at Mach 1.8 (Mach 1 = 1235 km/h). The fuselage of the SR-71 spy-plane reached well over 300°C at Mach 3.2. The outside of the space shuttle reached 1600°C during re-entry.

Rotor

In a car, two high friction brake pads engage the rotor (attached to the wheel) to stop it spinning. The rotational energy of the rotor is converted to heat. The more quickly the rotor can heat up and disperse the heat, the faster it can stop.

18. (a) Describe some occasions where friction needs to be minimized:

(b) List some occasions when friction needs to be increased:

A group of students wanted to study the friction produced by various materials. For any material sitting on a flat surface, the static force of friction (Fs) is equal to the coefficient of friction (µ) multiplied by the normal force (Fn), which is equal to the weight of the material: Fs = µFn.

`` The students set up the equipment shown below:

Material being tested

Force meter

Smooth, level bench top

`` Each material used was loaded with additional mass to give the same total mass each time.

`` The force meter was attached to the material and pulled until the material just started to move. The force required for this was recorded. This step was repeated several times for each material.

`` The results are shown below:

Wood

2

Paper

1.5

Sand paper

3

Plastic

1.5

19. (a) Which material produced the most friction?

(b) The students did not measure the surface area of the material before carrying out the test. How would this affect their results?

(c) Why did the students adjust the mass of the material being tested?

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Average force required to move object

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Material

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Newton's Laws of Motion

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4

15

ENGAGE: Spinning eggs

`` Have you ever hardboiled an egg and put it back in the refrigerator with the

other eggs only to forget which one is hard boiled? Apart from cracking them open until you find the hard one, how can you figure out which egg you want? Try spinning them on a flat surface.

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1. (a) What happens to the movement of the boiled egg if you gently stop it spinning with your finger?

(b) What happens to the movement of the raw egg if you gently stop it spinning with your finger?

(c) Suggest a reason for the observations you saw:

EXPLORE: A thought experiment

Have you heard of the expression "a thought experiment"? Albert Einstein was well known for his use of thought experiments to illustrate concepts that follow a pattern of logic, but are virtually impossible to show practically.

`` Galileo was also well-known for using thought experiments. One of his most important ones was to demonstrate what would eventually happen to a ball rolled down the ramp if there was no friction at the bottom.

`` He started by rolling a ball on ramps which had equal height and angle (below). The ball never quite reached the

top of the second ramp because of friction. Galileo reasoned that if there was no friction, the ball would reach the top of the second ramp.

`` Decreasing the angle of the second ramp would result in the ball taking a longer route to the top of the ramp:

2. (a) Complete the diagram to show the forces acting on the ball at point A and B in the diagram (assuming no friction):

(b) Predict what would happen to the ball if the second ramp was laid out flat:

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B

PS2.A

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A


16 `` Galileo reasoned that if the second ramp was laid flat, then in a frictionless situation the ball would keep rolling.

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3. (a) What force causes the ball to gain speed as it rolls down the first ramp? (b) What force causes the ball to lose speed as it rolls up the second ramp?

(c) Is there any unbalanced force acting on the ball while on the flat surface?

(d) Why would the ball continue to roll forever if the second ramp was laid flat?

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(e) Try writing your explanation as a simple rule of motion:

EXPLORE: Force, mass, and acceleration

You have seen earlier that weight is the effect of the acceleration of gravity on an object. By using string and a pulley, the force of gravity accelerating a falling object can be used to accelerate a trolley horizontally along a bench at the same time.

`` Two students were investigating acceleration. If they keep the force constant, they wondered what effect changing the mass would have on the acceleration:

Load

Loaded trolley

Timer tape

Bench

Pulley

Ticker timer

`` The mass at the bottom of the string was kept at 1.0 kg during the experiment so that the

1 kg

accelerating force stayed constant at 9.8 N. The mass of the trolley plus its load was progressively increased for each trial as follows: 0.5 kg → 0.7 kg → 0.9 kg → 1.1 kg → 1.3 kg → 1.5 kg.

The corresponding increase in the total mass of the system (loaded trolley mass + 1 kg) for each trial is therefore: 1.5 kg → 1.7 kg → 1.9 kg → 2.1 kg → 2.3 kg → 2.5 kg.

`` Before the 1 kg mass was attached to the string, they compensated for friction by squeezing a suitably sized piece of plasticine onto the string, just below the pulley. If the system (loaded trolley, pulley, string, and ticker tape with timer running) moves at near constant speed after being given a slight nudge then, as near as possible, friction within the system has been balanced out.

`` They attached timer tape to the trolley and threaded the tape through a ticker timer.

`` They then started the timer and let the trolley go. The trolley rolled forward as the 1 kg fell to the floor. When it hit the floor, they stopped the ticker timer.

`` The students reset the equipment and repeated the procedure to produce a tape for each different total mass.

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`` By counting the spaces between the dots on the timer tape the students were able to calculate the exact time the 1 kg was falling. Each space is equal to 0.02 seconds (the timer makes 50 dots per second). They multiplied the number of spaces by 0.02 to determine the exact time the 1 kg was falling.

`` Their results are shown in the table on the following page: 4. Explain the physics behind the technique used to compensate for friction:

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`` The distance the trolley rolled was determined by measuring the distance between the first and last dot.

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17 1 

Force causing acceleration (N)

Total time (s)

Distance (m)

1.5

9.8

0.61

1.2

2

1.7

9.8

0.64

1.2

3

1.9

9.8

0.68

1.2

4

2.1

9.8

0.72

1.2

5

2.3

9.8

0.75

1.2

6

2.5

9.8

0.78

1.2

System mass (kg)

1

System mass

Acceleration (m ⁄ s2)

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Trial

5. (a) Complete the column for the 1 / system mass during each trial:

(b) Complete the acceleration column using the equation a = 2d ÷ t2 to calculate the acceleration of the trolley:

(c) Plot acceleration vs 1 / system mass with a line of best fit below. We use 1/system mass so the slope is positive:

See activity 58

6. (a) What was the general effect on the acceleration when more mass was added to the system?

(b) Calculate the gradient of the graph:

(c) The graph is a straight line, so it has the equation a = gradient x 1/m + intercept. From F = m x a we have the equation a = F x 1/m + 0. By comparing these two equations what is the value of F? Comment on its significance.

`` A second group of students used the same equipment to carry out a slightly different investigation. They wanted to keep the mass of the system constant while increasing the force acting on the system. They achieved this by moving masses from the loaded trolley and adding them to the 1 kg at the bottom of the string.

`` Their results are shown in the table below: System mass (kg)

Mass causing the acceleration (kg)

1

2.6

2

Force causing the acceleration (N)

Total time (s)

Distance (m)

1.0

0.70

1.2

2.6

1.2

0.67

3

2.6

1.4

0.65

4

2.6

1.6

0.63

5

2.6

1.8

0.62

6

2.6

2.0

0.60

1.2 1.2 1.2 1.2 1.2

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Acceleration (m ⁄ s2)

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Trial


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7. For the table at the bottom of the previous page: (a) Complete the column for the force causing the acceleration during each trial (in newtons).

(b) Complete the column for the acceleration during each trial using the equation a = 2d á t2

(c) Plot a graph of acceleration versus force, with a line of best fit, on the grid below:

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8. What was the general effect on the acceleration when more force was used?

9. (a) Calculate the gradient of the graph:

(b) The graph is a straight line, so it has the equation a = gradient x F + intercept. From F = m x a we have the equation a = 1/m x F + 0. By comparing these two equations, calculate a value for m. Comment on its significance:

EXPLAIN: Free body diagrams

Free body diagrams are used to show the forces acting upon an object. They do not show the reaction forces of the object upon its environment. Consider the photograph of the jet fighter in level flight below:

FLift

FThrust

Fg (weight)

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FDrag

`` This free body diagram shows the forces acting on the jet. If it is flying horizontally at constant velocity, then the

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forces will be balanced. The force due to gravity acting on the aircraft is balanced by lift force generated by the wings. The thrust force of the engine is balanced by the drag force caused by air resistance.

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`` The diagrams below show the forces acting on the trolley of 0.5 kg at different times: Box 1

Box 2

Fn (normal force)

Thrust 5 N

Fn (normal force)

Friction 1 N

Thrust 1 N

Fn (normal force)

Friction 1 N

Thrust 0 N

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Friction 1 N

Box 3

Fg

Fg

Fg

10. (a) Complete the table below:

Box 1

Box 2

Box 3

F(net)

F(net)

F(net)

m

m

m

a

a

a

(b) Describe the motion of the trolley in box 1:

(c) Describe the motion of the trolley in box 2:

(d) Describe the motion of the trolley in box 3:

11. The battery in Rebekah's car has gone flat. Michael and Eddy are push-starting the car. The diagram below shows the forces applied to the car. The men need to apply enough force to overcome the forces opposing the movement of the car. The mass of the car is 910 kg. Eddy 400 N

Michael 450 N

Internal friction 530 N

Draw a free body diagram showing the net forces applying to the car:

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Friction with road 150 N


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EXPLAIN: Acceleration and force

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12. The graph below shows the velocity of a medium sized passenger plane as it accelerates down a runway and lifts off. The plane has a mass of 70,535 kg:

Velocity of aircraft

100.0 90.0 80.0 60.0 50.0

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Velocity m/s

70.0

40.0 30.0 20.0

10.0 0.0 0.0

5.0

10.0

15.0

20.0

30.0

25.0

35.0

40.0

Time (s)

(a) What was the acceleration of the plane between 10 seconds and 30 seconds?

(b) Assuming there is no friction on the runway, what was the force of the thrust produced by the engines?

(c) In reality, there is friction between the plane's tires and the runway. Use this to explain why the acceleration of the plane suddenly increases at the 35 second mark:

(d) What distance did the plane cover between 6 seconds and 35 seconds?

13. The graphs below show the velocity of various high performance vehicles:

Velocity of high performance vehicles

160.0

Velocity m â „ s

140.0 120.0

Top fuel dragster

100.0 80.0

Indycar Formula 1 car

60.0

Subaru Imprezza WRX

40.0

Lamborghini Diablo

20.0

1.0

2.0

3.0

4.0

5.0

6.0

Time (s)

7.0

8.0

9.0

10.0

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0.0 0.0

(a) Calculate the acceleration of the top fuel dragster:

(b) Given that the dragster has a mass of about 1050 kg, what force does the engine produce?

(c) Why would your answer for (b) be an underestimate of the force provided by the engines?

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21 `` Ion thrusters are a type of spacecraft propulsion system. Unlike chemical rockets, which burn large amounts of

NSTAR ion thruster on the Deep Space 1 spacecraft

Ion thruster. The Dawn spacecraft was launched in 2007 and arrived at Ceres in 2015. Its main propulsion systems was a xenon based ion thruster.

NASA

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fuel to create enormous thrust, ion thrusters accelerate ions through an electrical field, creating very little thrust. However because they use the ion "fuel" slowly the thruster can remain active for very long lengths of time.

14. Ion thrusters produce only small amounts of thrust. The mass of the dawn spacecraft was 1.2177 x 103 kg. It took 96 hours to accelerate from 0 to 96 kilometers per hour. Calculate the force of the ion thruster produced:

EXPLORE: Action reaction

The picture of the near right shows the space shuttle Endeavour on the launch pad, before launch. What are the forces acting on the stationary shuttle? The shuttle presses down onto the Earth because of gravity (we'll ignore the launch pad for simplicity). But the shuttle isn't going down through the ground. Something is stopping it. What?

`` Forces come in pairs. The force of the shuttle pressing

down on the Earth is balanced by the reaction force of the Earth pressing back against the shuttle. These forces are always equal and opposite.

16. At launch, the shuttle's engines provide a force (thrust) to lift the shuttle off the launchpad. What forces are acting on the shuttle now? Draw arrows on the photo to show the forces on the shuttle. Label the forces appropriately.

Both images: NASA

15. Draw arrows showing the two forces mentioned above onto the photo of the space shuttle. Label them FSE (for force of shuttle on Earth) and FES (for force of Earth on shuttle).

(b) Describe how the action and reaction forces act on the ferry:

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17. (a) The image below shows a ferry being driven forward. The engines are providing the action force (thrust). The hull provides another action force (buoyancy). On the photo, draw and label the action and reaction forces on the ferry.


22 `` Recall the free body diagram of the fighter jet on page 18. Are the forces shown (lift/weight and thrust/drag) action-

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reaction "force pairs"? Because they are acting on the same object (the aircraft) they are not. The diagram below shows the force-pairs acting on the aircraft.

Faircraft-Earth

Fair-wings (lift)

Fair-aircraft (drag)

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Faircraft-air

Fexhaust-aircraft (thrust)

FEarth-aircraft (weight)

Faircraft-exhaust

Fwings-air

18. (a) If the aircraft increases its altitude, what are the main forces involved and explain what needs to happen to them:

(b) In the left box below show the force pairs operating as the aircraft gains altitude and in the right box below show the free body forces operating as the aircraft gains altitude: Force-pairs

Free body diagram

19. (a) Form small groups and use at least two reference sources to research one of the laws of motion identified below. Make a visual presentation to the class to include a general description of the law and an example demonstrating application of the principle. (b) Using what you have learned in this activity and from the presentations of your classmates, describe an example of each of Newton's three laws below. Law

Description

Example

Every object in a state of uniform motion tends to remain in that state of motion unless it is subjected to an unbalanced external force.

(a)

Second law: Definition of force

F= ma

(b)

Third law: Law of reciprocity

For every action, there is an opposite and equal reaction. When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

(c)

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An object's acceleration (a) depends on its mass (m) and the applied force (F).

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First law: Law of inertia

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Building Bridges

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5

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ENGAGE: Bridges

What kind of bridges are near your home? They may be very large and carry many vehicles at once, or they may be quite small and barely noticeable as you cross them.

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1. In groups describe the shapes or types of bridges you can think of that are near your home or school. Discuss why the bridges have different shapes and structures.

EXPLAIN: Many kinds of bridge

There are many bridge designs. The type of bridge made must take into account the weight of the traffic it will carry, the type of environment it will be built in, how it can be anchored, the type of material it will be made from, how long it will be, and even how it will look in the environment where it will be built.

`` Humans have been building bridges for hundreds of thousands of years. Early material would have been wood and stone but these would limit the size of the bridge that could be built and the weight that could be carried.

2. The photographs below show several different types of bridge. For each of them explain how the structure supports the weight of the bridge plus the traffic on it:

(a) Suspension bridge

(a)

(b) Cable-stayed bridge

(b)

SF

CE

ETS1.C ETS1.B ETS1.A PS2.A

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(c)

(c) Arch bridge


24

EXPLORE: Pressure

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Pressure plays an important part in the design of many structures. The supports for a bridge must be anchored in solid rock and they must bear the weight of the bridge. All the weight is concentrated on a small area where the supports are anchored. This produces a large amount of pressure and this must be taken into account when designing the support structures.

`` A thumbtack (drawing pin) has a sharp pointed end and a flat head.

When we press on the head with our thumb, we are applying a force. Applying enough force to the head allows the sharp end to penetrate the corkboard.

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3. (a) Imagine we turned the thumbtack around and pressed on the pointed end with our thumb. Describe what would happen:

(b) Why would this happen?

`` When we pushed on the thumbtack, we applied a force to the flat head. That force was then applied to the

corkboard but only over an area covered by the sharp end. This allowed you to overcome the corkboard’s compressive strength (the compressive stress a material is able to withstand before it starts to deform) by applying a force to a very small area. Turning the thumbtack around means you are applying the force to a small area, the sharp end, and overcoming the compressive strength of the skin on your thumb instead of that of the corkboard.

`` When we apply a force to an area, we are applying pressure. If we increase the size of the force or decrease the area to which the force is applied, we increase the pressure. This is shown in the following equation: P=

F A

Where P = pressure (N/m2) , F = force (N), and A = area (m2)

`` The investigation below demonstrates the effect of force and area on pressure:

INVESTIGATION 1.2: Investigating pressure

See appendix for equipment list.

1. You will need a pair of high heels, flat boots/shoes, and an area of sand, mud, soft soil, or wet grass. 2. Trace the outline of the heel of one boot and one high heel on to graphing paper and estimate the area your weight will be applied to the ground by counting the squares each footwear covers.

3. Note the force applied to the ground (your weight) will remain the same, but the area it is applied to will be different. Which piece of footwear will apply more pressure to the ground?

4. Predict what will happen when you step on the sand with the boots?

5. Predict what will happen when you step on the sand with the high heels?

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6. Carry out the investigation by stepping onto the sand, mud, soil, or grass with the boot and high heel. Record your results and compare them to your predictions:

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EXPLORE: Support force

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`` The force of gravity (your weight) is constantly pulling you down towards the Earth’s

center. Since you usually do not move any closer to the center, something must be holding you up. It is an equal upwards force from the ground, called the support force. If you are standing in quicksand, there will not be enough support force to balance the force of gravity, so you will sink. If you are bouncing on a trampoline and have just reached the lowest point, then the support force will be greater than the force of gravity, so you will be accelerated upwards.

Support force (Fs)

Surface

Weight (mass x gravity)

`` Place a book on top of your desk. It just sits there. Gravity is still acting on the book to

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give it weight, but it does not fall because the support force provided by the desk on the book is equal to the force on the desk applied by the book.

4. Imagine if we placed something very massive on your desk, say a tractor. What do you think would happen?

5. Why do you think this would happen?

EXPLORE: Compressive strength

`` Increasing an object’s mass means there will be greater gravity force (weight), so the material that it rests on must provide greater support force if the object is to stay where it is.

`` The maximum support force that a support material can provide to hold up a load

Force due to gravity (weight)

`` Compressive strength is one way to measure the strength of a material. Material

Load

is called its compressive strength. If the load exceeds the compressive strength of the support material it will begin to deform. strength is important when considering the appropriate material to use in different situations. For example a satellite must be able to withstand the vibrations from a rocket launch, a hospital must be able to withstand the shaking from an earthquake, or a toddler’s toy must be able to withstand various stresses from the child’s daily activities (being sat on, chewed on, tossed around, etc).

Support

`` In most cases, it is not practical to do tests on the actual objects (as much fun

as it sounds to build multiple hospitals out of various materials, each one would take years to build and millions of dollars to complete). Instead, engineers do calculations to test their designs before investing the time and materials needed to build the structure.

Support force no longer great enough to balance the gravity force (weight). The support material starts to deform.

`` We can test the compressive strength of materials by measuring the amount of mass that can be placed on a material before it deforms.

INVESTIGATION 1.3: Investigating compressive strength

``

See appendix for equipment list.

1. You will test the compressive strength of tubes made out of various materials. You will need a cardboard tube (e.g. inside a toilet roll), aluminum can, paper cup, styrofoam cup, and a "tin" food can. 2. For the paper cup and styrofoam cup remove the bottom. For the aluminum can and tin food can remove the top and bottom. 3. Stand the object upright then, for each of the objects in turn, place a thin board (e.g. thick card) on top of the object, then place masses on top of the object until it collapses. 4. Record the mass required to compress the object:

Aluminum can Styrofoam cup Paper cup "Tin" food can

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Cardboard tube

Mass added

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Object


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6. (a) Was the investigation a completely fair test? If not, what variables should have been controlled to make it fairer?

(b) Which object appeared to have the highest compressive strength?

(c) Which object appeared to have the lowest compressive strength?

(d) Can you explain why?

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`` It is also worth considering how the shape of an object affects

its strength. For example steel is an extremely strong material. In construction, steel beams normally have an H shape and so are called I-beams or H-beams. This shape is far stronger that a square or circular beam for vertical loads. Steel beams come in various shapes and sizes depending on the task they are to perform (right).

INVESTIGATION 1.4: Shape and compressive strength

See appendix for equipment list.

1. You will test the compressive strength of tubes of cardboard of different shapes and diameters.

2. The cardboard you use can be of any thickness so long as you use the same type for the entire experiment. 3. Cut rectangles of cardboard of the following dimensions: 10 cm x 5 cm, 10 cm x 10 cm, 15 cm x 10 cm, 10 cm x 20 cm (x 3)

4. Roll the first 4 cardboard rectangles into tubes 10 cm high, fixing the edge with tape all the way down the edge. The diameters (d) of the tubes should be 1.6 cm, 3.2 cm, 4.8 cm and 6.4 cm. Fold the last 10 cm x 20 cm rectangles into a 10 cm high triangular tube (sides of 6.6 cm x 3) and a square tube (sides of 5 cm x 4). Again, tape all the way along the edges. 5. For each object in turn, stand it upright and place a thin board on top of the object, then place masses on top of the object until it collapses. Record the mass required to compress the object: Object

Mass added

Cardboard tube d = 1.6 cm Cardboard tube d = 3.2 cm Cardboard tube d = 4.8 cm Cardboard tube d = 6.4 cm Triangular tube Square tube

7. (a) Did the diameter of the cardboard tube affect its compressive strength?

(b) Describe any pattern in the results for the circular tubes:

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8. Compare the results of the tube with diameter 6.4 cm with the triangular and square tubes:

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ELABORATE: Build a bridge INVESTIGATION 1.5: Building bridges

See appendix for equipment list.

1. You will now have the opportunity to put your knowledge of forces to the test. The objective of this investigation is to build the strongest possible bridge given a set of predetermined conditions.

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2. The conditions: The bridge must span a 30 cm gap (and therefore be longer than 30 cm) and be 5 cm wide. It will be tested to destruction by adding masses in sequential cycles to the center of each third of the bridge, starting with the center third (see diagram below), until the bridge collapses. The aim is to be able to support the greatest mass. Masses added here

Masses added here

Masses added here

Bridge span

Order of masses added:

2

1

3

There will be no support allowed below the bridge (i.e. it can not be supported by the floor). Anchor points can only be attached to either side of the gap.

3. The equipment: 18 plastic drinking straws (or 36 dry spaghetti), 1 gram of Blu Tack or similar putty adhesive, 30 cm of string, 4 x 10 g masses, 1/2 sheet of US letter or A4 sized copy paper. 4. Building time will be determined by your teacher. The size of the weights added to the bridge for testing will also be determined by your teacher.

5. You may use the equipment in any way you like. However the straws (or dry spaghetti) must make up the main support structure of the bridge. 6. Before you begin, discuss with your group how you will construct the bridge and how it will support the masses at the locations shown in the diagram. 7. Use the bridge builder program (see the BIOZONE Resource Hub) to test various designs.

EVALUATE: Bridge design

9. Now that you have built and tested your bridge you must evaluate its structure and performance. (a) Describe the structure of your bridge:

(b) What is the maximum mass the bridge supported?

(c) Which part of the bridge failed when tested to destruction?

(d) What could have been done to fix or strengthen the part of the bridge that failed?

(e) Recall the structures used by other groups in your class. Which structures where the most effective? Can you explain why?

(f) If time and materials allow carry out the bridge building again but with another type of material instead of straws. How does the material affect the strength of the bridge?

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6

Momentum

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28

ENGAGE: Straight shot

Ever played snooker, or pool, or gone bowling? All these games operate on the same principle: using the movement of one ball to move or knock over others.

`` In the game of pool (right) the white ball is used to

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maneuver the others around the table. Sometimes when it hits a target ball, the target will move away while the white ball stops moving. Other times, the white ball continues to move but more slowly after hitting the target ball, which also moves but more slowly.

`` A important part of pool, snooker, or bowling, is the

concept of momentum. In pool, momentum for the white ball is transferred to the target ball to make it move. How this is done will determine the way the target ball and the white ball move after colliding.

1. Obtain two balls. Roll one of them into the other. Repeat this in various ways and directions. How do they move when they collide? Can you work out any rules for their motion?

EXPLORE: Marble momentum

`` Marbles (or ball bearings) are great for exploring motion. Because they are made of glass or steel, they are smooth and hard. This means they roll with very little friction on smooth, hard surfaces and convert very little kinetic energy to heat and sound during collisions. When collisions are like this, they are said to be elastic collisions.

INVESTIGATION 1.6: Investigating momentum

``

See appendix for equipment list.

1. You will need a marble and a ball bearing of similar size but different mass. 2. Set up the following equipment: Marble or ball bearing

Ramp

Carpet

h

Tape measure

3. Measure the mass of marble.

4. Start with the marble one half of the way up the ramp.

5. The velocity of the marble at the bottom of the ramp can be calculated by using the equation: v = (10÷7)gh

where g = 9.8 m⁄s2 and h is the height from which the ball is rolled in meters.

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6. Roll the marble down the ramp (from half way) several times and record the distance that it runs along the carpet each time. 8. Move the marble to the top of the ramp and repeat steps 6 and 7. 9. Measure the mass of the ball bearing.

10. Replace the marble with the ball bearing and repeat steps 6-8.

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7. Calculate the average distance and record it in the appropriate table on the next page.

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Test 1

Mass of marble (kg)

Height half way up ramp (m)

Velocity (m ⁄ s)

Distance rolled (m)

1 2 3

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4 5

Average

Test 2

Mass of marble (kg)

Height at the top of the ramp (m)

Velocity (m ⁄ s)

Distance rolled (m)

Mass of ball bearing (kg)

Height half way up ramp (m)

Velocity (m ⁄ s)

Distance rolled (m)

Mass of ball bearing (kg)

Height at the top of the ramp (m)

Velocity (m ⁄ s)

Distance rolled (m)

1 2 3 4 5

Average

Test 3 1 2 3 4 5

Average

Test 4 1 2 3 4 5

Average

(b) Describe the effect of increasing the velocity on the distance rolled:

(c) Describe the effect of increasing the mass on the distance rolled:

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2. (a) Calculate the velocity of the marble and ball bearing as they leave the ramp and add this the table above:


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3. The mass (m) and velocity (m/s) of any moving object can be combined into a single measure called momentum (p), which has the unit kilogram meters per second (kg m/s):

p = mv

Calculate the momentum of the ramp marble/ball bearing for each of the four tests:

i:

ii:

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iii:

iv:

4. Plot the momentum of the marbles against the distance rolled:

5. How does momentum affect the distance rolled?

EXPLORE: Momentum

`` If an object has a lot of momentum (large mass or large velocity or large mass and velocity) then it is very hard to slow it down or deflect it off its course.

`` Because momentum has a velocity component, it is a vector and points in the same direction as the velocity.

(b) A 990 kg car reduces it velocity from 22 m ⁄ s to 13 m ⁄ s. Calculate the change in the car's momentum:

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6. (a) Which the greater momentum: a 25,000 kg truck moving at 5 m ⁄ s, or a 1200 kg car moving at 21 m ⁄ s?

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EXPLAIN: Collisions and conservation of momentum

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Moving objects have momentum. But what happens when two objects moving in opposite directions crash into each other? Where does the momentum go?

`` Some students wanted to investigate this problem. They set up two carts on an air track to minimize friction. The mass of each cart was measured. Cart 1 had a mass of 0.75 kg, cart 2 had a mass of 0.73 kg

`` The students noted that sometimes objects stick together when they collide, and other times they rebound. To

simplify their investigation, they fitted magnets to the carts so that they would stick together when they collided. A radar speed gun was available to measure velocity before and after the collisions.

`` For the first investigation, cart 2 was made stationary in the center of the air track. Cart 1 was given a push in the

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direction of cart 2. The results of four trials that they carried out are shown in table 1 Cart 1

Magnets

Cart 2

Air track

0.73 kg

0.75 kg

Table 1

Velocity cart 1 (m ⁄ s)

Momentum cart 1 (kg m ⁄ s)

Velocity cart 2 (m ⁄ s)

Velocity cart 1&2 after collision (m ⁄ s)

Momentum cart 2 (kg m ⁄ s)

0.52

0.00

0.26

0.64

0.00

0.33

0.32

0.00

0.16

0.13

0.00

0.07

Total momentum of carts (kg m ⁄ s)

`` The students then decided to investigate both carts in motion. They pushed the carts in opposite directions towards each other. They kept the magnets in place so that the carts would stick together after the collision.

`` Because cart 2 was moving in the opposite direction of cart 1, the students recorded this as a negative velocity. The results of four trials that they carried out are shown in table 2. Table 2

Velocity cart 1 (m ⁄ s)

Momentum cart 1 (kg m ⁄ s)

Velocity cart 2 (m ⁄ s)

Velocity cart 1&2 after collision (m ⁄ s)

Momentum cart 2 (kg m ⁄ s)

0.41

–0.11

0.15

0.12

–0.35

–0.11

0.37

–0.36

0.01

0.29

–0.30

0.00

Total momentum of carts (kg m ⁄ s)

(b) Explain the students' results:

(c) Write a mathematical expression that will model the students' results:

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7. (a) Complete tables 1 and 2 (above) by calculating the momentum of each cart:


32

EXPLAIN: More collisions

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`` The students decided to investigate collisions in which the objects rebound. They reversed the orientation of one set of magnets so that the magnets would repel each other as the carts came together. The carts would then "rebound" after the collision.

`` In the first two trials cart 2 was stationary. In trials 3-5, cart 2 was moving. The results of the five trials that they carried out are shown in table 3: Table 3

Velocity cart 2 (m ⁄ s)

Velocity cart 1 after collision (m ⁄ s)

Velocity cart 2 after collision (m ⁄ s)

0.49

0.00

0.01

0.50

0.55

0.00

0.01

0.56

0.21

–0.56

–0.55

0.22

0.45

–0.43

–0.42

0.46

0.40

0.10

0.10

0.40

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Velocity cart 1 (m ⁄ s)

`` The students then decided to vary the mass of cart 1 and then cart 2 and repeat the investigation. The results of four trials that they carried out are shown in table 4: Table 4

Velocity cart 1 (m ⁄ s)

Mass cart 1 (kg)

Velocity cart 2 (m ⁄ s)

Mass cart 2 (kg)

Velocity cart 1 after collision (m ⁄ s)

Velocity cart 2 after collision (m ⁄ s)

0.42

1.5

0.00

0.73

0.15

0.57

0.59

1.5

0.00

0.73

0.20

0.79

0.36

0.75

–0.46

1.5

–0.73

0.09

0.51

0.75

–0.55

1.5

–0.90

0.16

8. Complete table 5 (below) using the results in table 3. Recall that mass of cart 1 = 0.75 kg and mass of cart 2 = 0.73 kg. Table 5. Momentum from table 3 results Momentum cart 1 (kg m ⁄ s)

Momentum cart 2 (kg m ⁄ s)

Momentum cart 1 after collision (kg m ⁄ s)

Momentum cart 2 after collision (kg m ⁄ s)

9. Complete table 6 (below) using the results in table 4: Table 6. Momentum from table 4 results (kg m ⁄ s)

Momentum cart 1 after collision (kg m ⁄ s)

Momentum cart 2 after collision (kg m ⁄ s)

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Momentum cart 2

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Momentum cart 1 (kg m ⁄ s)

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10. (a) Explain the students' results from tables 3-6:

(b) Does the mathematical expression you produced in question 7(c) explain these new sets of results? If not, try to modify your expression:

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EXPLAIN: Collisions beyond the lab

Momentum (p) is always conserved (i.e. total momentum is the same before and after a collision or interaction) as long as there are no forces outside the immediate situation affecting the colliding objects (i.e. causing additional accelerations). The following examples illustrate these ideas. Before colliding

A

After colliding

m1 = 1500 kg

m2 = 1000 kg

m1 = 1500 kg

m2 = 1000 kg

v1 = 30 m/s

v2 = 20 m/s

v3 = 20 m/s

v4 = ?? m/s

Explanation

No forces outside the immediate interaction causing significant accelerations of the colliding objects so… p after = p before

Relatively smooth horizontal surface

B

Relatively smooth horizontal surface

m1 = 1500 kg

m2 = 1000 kg

m1 = 1500 kg

m2 = 1000 kg

v1 = 30 m/s

v2 = 20 m/s

v3 = ?? m/s

v4 = ?? m/s

m1v1 + m2v2 = m1v3 + m2v4 There are at least two forces outside the immediate interaction that will cause significant extra accelerations Momentum (p) will not be conserved!

Rough sloping surface

Rough sloping surface

11. (a) For example A above, calculate V4:

(b) In example B above, what two forces outside the immediate interaction are causing extra accelerations?

Car 2

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Car 1

`` The image above shows a collision of two cars both traveling at 70 kmph (19.4 m ⁄ s). Assume that each car has mass of 1000 kg.

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12. (a) Calculate the momentum of each vehicle before the collision: (b) Using equations, explain why the momentum before and after the collision is the same (momentum is conserved):


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EXPLAIN: Explosions are collisions in reverse

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Why are explosions, like the fireworks right, spherical? Where is the center of the explosion? Assuming all the fragments within the firework are all the same, how does this explain the shape of the firework?

`` Explosions throw objects in all directions, but they still obey

the law of conservation of momentum. Imagine the firework shown right has been fired straight up and has reached the highest point of its flight. Its momentum in that instant is zero.

`` At that exact moment, it explodes. What is the momentum of

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all the fragments now? Conservation of momentum states that they must add up to zero.

`` Consider the simplified diagram below: A= 2 kg, –2 m ⁄ s

AB 4 kg, 0 m ⁄ s

B= 2 kg, 2 m ⁄ s

`` The momentum of fragment A is exactly opposite the momentum of fragment B.

35 kg

`` The drawing right shows a man (mass 70 kg) and a child

70 kg

Fchild

Fman

(mass 35 kg) standing together on smooth ice (friction is negligible). The two push each other apart and the man moves away with a speed 0.3 m/s relative to the ice.

13. (a) Calculate the velocity of the child relative to the ice:

70 kg

35 kg

(b) Determine how far apart the man and the child are after 5 seconds. Show your working:

Drawing by F.Hicks

vman

vchild

`` Now consider the cannon and cannonball below: Powder charge

Cannonball

Explosion

Cannonball

`` The explosion of the powder charge pushes the cannon and the cannonball apart in opposite directions. The mass of the cannon is much larger than the cannonball. As a result the cannonball flies out of the barrel at high speed while the cannon itself rocks back on its wheels less than a meter or so at a much lower speed.

Calculate the velocity of the cannon after it is fired:

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14. Considering the cannon above, the cannon has a mass of 900 kg and is at rest before firing. The cannonball weighs 5 kg. When fired, the cannonball exits the barrel at 230 m ⁄ s.

15. An object at rest explodes into two equal parts, A and B. Part A flies off at 20 m ⁄ s. What is the velocity of part B?

CL

16. A 12 kg object at rest has two parts, C and D. C has a mass of 4 kg and moves off at 6 m ⁄ s. What is the velocity of D?

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ELABORATE: Impulse

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Collisions can be instantaneous, or they can occur slowly. Imagine falling out of a plane at an altitude of 5500 meters. You would expect that when you hit the ground, the force of the impact would be fatal. True? Wrong.

`` In 1944 Royal Airforce tail gunner Nicholas Alkemade jumped

from a flaming Lancaster Bomber at 5500 meters without a parachute after it was destroyed over Germany. He survived with only a few bruises and a sprained ankle because his fall was cushioned by thick tree branches and nearly 0.5 m of snow.

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`` Because the force of the impact was spread out over a long

period, Alkemade was able to survive the fall. Vesna Vulovic, an air hostess in Yugosalvia, holds the record for surviving the highest fall, from a DC-9 that blew up at 10,160 m in 1972.

`` • Recall F=ma. We know that a = Dv ⁄ Dt so we can substitute a in the equation to give F = D(mv) ⁄ Dt.

• Multiplying both sides by Dt gives FDt = Dmv. • Thus the force multiplied by the change in time (or impulse) equals the change in momentum of the object. • It has the unit of Ns (newton seconds). Impulse = FDt = Dmv

17. Consider an object with a mass of 100 kg moving at 10 m ⁄ s. Its momentum is therefore 1000 kg m ⁄ s. How can this object be stopped? It can be stopped quickly by applying a large force or slowly by applying a small force.

(a) The object mentioned above has a momentum of 1000 kg m ⁄ s. A force of 200N is applied to the object. How quickly will the object stop?

(b) The object has a force of 10 N applied to it. How quickly does the object stop now?

18. An 3 kg object traveling at with a velocity of 20 m ⁄ s experiences a force of 15 N for 5 seconds in the same direction of travel. Calculate the object's new velocity:

19. A car with an occupant weighing 80 kg is moving at 27 m ⁄ s (about 100 kmph). The car hits a tree head on and comes to a complete stop in 0.3 seconds. (a) The occupant is wearing seat belt and thus stops at the same rate as the car. Calculate the force experienced by the occupant:

(b) In the case of an airbag inflating, the impact time is increased by 0.1 seconds. Calculate the force experienced by the occupant in this case:

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20. In terms of impulse and momentum, explain why gymnasts prefer to fall on soft thick pads than harder thinner pads:

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21. A tennis racket hits a stationary ball (mass 60 g) at 62.5 m ⁄ s. The impact time is 0.001 seconds. Calculate the force exerted on the ball:


7

Engineering and Forces

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36

ENGAGE: Crash!

Kevauto CC4.0

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1. Consider the two photographs below. The car on the left was built in about 1960, the car on the right was built in 2018. Imagine the cars were both traveling at 80 kmph and were involved in a head on crash into a power pole. In which of these vehicles would the occupants experience the greater impact force and why?

EXPLORE: Landing on Mars

`` Of all the space agencies that have tried to land probes and rovers on Mars, NASA is by far the most successful.

NASA has devised two main ways of landing its probes and rovers on to the surface safely: using parachutes and retro-rockets, or parachutes and air bags.

`` The first of NASA's Mars landers to successfully touch

down was Viking 1 in 1976. The lander used parachutes to slow its descent from 250 m ⁄ s to 60 m ⁄ s. It then used retro-rockets to slow its descent below 2.4 m ⁄ s before touch down. Shock absorbers in the legs reduced the final force on landing to a slight jolt.

`` The Mars Pathfinder lander, which touched down in 1997, used a slightly different landing technique. After entering the atmosphere, the lander also deployed a parachute to slow its descent. Air bags around the lander's frame were inflated. At just 98 meters above the ground, retro-rockets were fired to bring the lander to a sudden halt. The lander was then cut loose from the parachute and fell to the ground, using the inflated air bags to cushion its landing. When it hit the ground, it bounced up to 15 m high and experienced a maximum force of 18 G.

Mars Pathfinder lander

`` Both the Spirit and Opportunity rovers, which landed in

2004, used similar landing devices to the Mars Pathfinder.

PS2.A

ETS1.B ETS1.C

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SF

NASA

Curiosity rover and sky crane

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particularly advanced retro-rocket package. Because the rover was so heavy (899 kg), it was not feasible to use parachutes and air bags to land. NASA therefore developed a sky crane (right) which lowered the rover to the ground. The huge 16 m diameter parachute, deployed after entry into the atmosphere, produced up to 289 kN of drag. At 1.8 km in altitude, the powered descent stage was released. Using retro-rockets, this hovered above the surface and lowered the rover 7.6 m to the ground before detaching and flying away far enough not to interfere with the rover. It later crashed into the Martian desert.

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`` The Curiosity rover, which landed in 2012, used a

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2. (a) What are the two main methods used by NASA to land its rovers or landers on Mars?

(b) Would these methods work on the Moon or Mercury?

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3. (a) Explain why the Curiosity rover used a sky crane to lower it to the surface:

(b) The acceleration due to gravity of Mars is 3.71 m ⁄ s2. What is the weight of the Curiosity rover on Mars?

(c) What equivalent mass on Earth would produce this weight?

4. Why was reducing the force experienced during landing so important for these rovers?

EXPLAIN: Crumple zones

`` Is this thinking logical when it comes to a crash?

From your studies on force, momentum, and impulse, would you rather be in a car that crumpled when it had a crash or was rigid and kept its shape?

`` Cars today have sophisticated safety systems that in many cases allow the car to avoid a collision. However these do not prevent all crashes and in the case of an actual crash the frame of the car is designed to crumple up.

`` The crumpling effect increases the time the force of

NHTSA: National Highway Traffic Safety Administration

"Cars today, they're just not built tough. A small crash and they're just wrecked". Have you heard this before? Or how many times have you heard someone say "I like being in a SUV or four wheel drive, they're solid, tough, and can take a crash."

the crash is applied and so reduces the impact force felt by the occupants.

5. Why do cars have crumple zones?

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6. What other safety devices do modern cars regularly have installed to protect the occupants in the event of a crash?

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7. Motorbikes have little capacity for crumple zones (although this is performed to a degree by the front wheel and steering system). Bicycles have virtually no capacity for a crumple zone. How do riders protect themselves in a crash?


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8. The graphs below show acceleration data from crash tests performed on a modern 2018 vehicle and a older vehicle from 1980. Crash test 1980

10

0

Acceleration (g)

0

-40 -80

-40 -80

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Acceleration (g)

Crash test 2018

10

-120 -160

0

25

50

75

100

-120 -160

125

150

175

200

0

50

25

75

Time (ms)

100

125

150

175

200

Time (ms)

(a) In which vehicle did the occupants experience the greatest forces?

(b) Both cars were traveling at 56.3 kmph (15.6 m ⁄ s). From the graphs, explain why the occupants experienced different forces:

EXPLAIN: Crash helmets

Helmets come in all shapes and sizes and serve many purposes. In virtually all cases, protecting the head has at least some importance in the helmet design.

`` Crash helmets are specifically designed to reduce the force of impact during a

crash. The design of the helmet is constrained by the conditions under which it will be used.

`` Motorcycle helmets (right) are normally designed to protect the entire skull and

face. For a pedal cyclist this design would be very heavy and would quickly become much too hot. The much lower speeds involved allow cycle helmets to be designed with air gaps and protect only the skull.

`` The graphs below show the effect of a simulated impact with and without a helmet.

With helmet

1500

1500

1250

1250

Measured force (N)

1000

750

500

Average force ~ 618 N

250 0 0.000

1000

750

Average force ~ 544 N

500

250 0.003

0.006

0.009 0.012 Time (s)

0.015

0.018

9. (a) What is the peak force experienced without a helmet?

0 0.000

0.003

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Measured force (N)

Without helmet

0.006

0.009 0.012 Time (s)

(b) What is the peak force experienced with a helmet?

(c) Why would both the peak and average force experienced be lower when wearing a helmet?

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0.015

0.018

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ELABORATE: Designing to meet specifications INVESTIGATION 1.7: Building a lander

``

See appendix for equipment list.

1. You will now have the opportunity to put your knowledge of forces and momentum to the test. The objective of this investigation is to build a device that will protect a lander from descent of at least five meters.

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2. The conditions: You will build a landing device that will protect a raw egg from a fall of at least 5 m. Your are free to use the equipment (below) in any way but there may be no platform for the lander to fall onto (landers don't have convenient foam landing pads to fall onto when they reach their destination). 3. The equipment: 1 egg, 60 cm of tape, 5 rubber bands, 1 small garbage or plastic bag, 10 paper clips, 1 m string, 20 plastic or paper straws, 1 plastic egg or similar sized object for testing. Your teacher may modify this equipment as they wish. 4. Building time will be determined by your teacher.

5. Before you begin, discuss with your group how you will construct the lander and in what ways you could cushion the egg at impact or slow its descent to reduce the shock of landing.

EVALUATE: Lander design

10. Now that you have built and tested your egg lander you must evaluate its structure and performance. (a) Describe the structure of your lander:

(b) On a scale of 1-5, how did your egg survive the fall? (1= completely scrambled, 5 = safe and sound):

(c) If your egg cracked, what could have been done to keep it from cracking if you repeated the test?

(d) Recall the landing devices designed used by other groups in your class. Which of these where the most effective? Can you explain why?

(e) Given enough material, it would be easily possible to design a lander than would protect the egg from a much higher fall than 5 m. The same applies to planetary landers. However, there are numerous constraints on the development of these devices, one of which is cost. Discuss with your group what other constraints there might be on the design on a lander for Mars:

CL

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8

Forces of the Earth

CL N AS OT SR F OO OR M US E ENGAGE: Faults and forces

Newton's laws apply to the Earth itself just as much as they apply to any other object. We know the Earth must produce enormous forces within it from evidence such as earthquakes, fault lines, and plate tectonics.

The microfault shown above has caused the fracture of this stone.

A normal fault has occurred in this cliff. The left side has slid up relative to the right.

NASA

Qfl247 CC3.0

Luka Adikashvili CC 3.0

PR E O V N IE LY W

`` Consider the images below:

A strike-slip fault has displaced this mountain range by nearly 3 km.

1. Compare the relative forces that caused each of the faults above:

EXPLAIN: Forces and mountains

Mountains form when parts of the Earth's crust are forced together. Over long periods of time, the rock bends and folds, or sometimes breaks causing faults as in the photos above.

`` The image right shows the Himalaya mountain ranges

(white through the center of the image). To the left is India (blue), to the right is the Tibetan plateau (brown).

India

`` The Indian sub-continent is driving into the continent of

Eurasia. The collision of these two massive land masses has caused the formation of the highest mountains on Earth, reaching over 8000 m above sea level.

Tibetan plateau

`` When the supercontinent of Gondwana broke up around 180 million years ago, the sub-continent of India raced across the ocean (in geological terms it really did race, moving up to 15 cm a year) towards Eurasia.

`` About 50 million years ago, India crashed into Eurasia.

The diagrams on the right show how India pushed under Eurasia, causing the Eurasian plate to buckle and producing the Himalayas.

NASA

40

Eurasian plate

Indian plate

2. The continents (carried on tectonic plates) move at relatively constant speeds and directions. Clearly huge forces are involved. Can you explain why the continents are not accelerating across the face of the globe?

50 million years ago Eurasian plate

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Indian plate

Himalayas

Tibetan plateau

PS2.A

CE

SPQ

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Present day

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3. Study the diagrams of various Earth systems right. The forces that move the tectonic plates and the attached continents about the globe are counteracted by friction. Use the images right to describe the places where friction associated with tectonic movement would be occurring.

Continental crust

Oceanic crust

Subduction zone

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Crust Mantle Outer core Inner core

Layers of the Earth

Boundary

4. Study the image below showing a cross section through a box of layered dough being compressed by a wooden board to simulate mountain building.

Plate boundaries

Board

Movement of board

Layers of dough

A

(a) Draw and label arrows on the diagram to represent the horizontal forces acting on the point labeled A in the diagram:

(b) Draw an arrow from point A in the direction point A has been moving, assuming the layers started out flat and filled the box:

(c) Explain your answer to (b):

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5. Working in small groups, use a virtual globe, map, and geographical information program such as Google Earth to investigate one of the following land and sea-floor features: i) Trenches, e.g. Mariana, Aleutian, Puerto Rico, Japan, Tonga ii) Oceanic ridges, e.g. Mid-Atlantic, East Pacific, Nazca, Mid-Indian iii) Seamounts, e.g. Loihi, Davidson, Tamu Massif iv) Mountain ranges, e.g. Himalaya, Sierra Nevada, Rocky Mountains, Andes v) Valleys, e.g. California Central Valley, Ethiopian Rift Valley, Yosemite Valley vi) Plateaus, e.g. Table Mountain, KukenĂĄn-tepui, Mount Roraima

(a) Name the feature has your group chosen:

USGS

The Sierra Nevada, CA: mountain building along a convergent plate boundary.

G310Luke

Ang MoKio cc 2.5

Cleveland Volcano, Aleutian Islands Alaska is part of the Pacific ring of fire.

Debris avalanche WA. Landslides suddenly move large volumes of material.

The San Andreas fault in California: a transform plate boundary.

Julius Reque CC3.0

ISS

Jeffrey Pang CC2.0

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(b) Describe the various forces that have shaped your geomorphic feature. These may be: i) Constructive forces such as volcanism and tectonic movements (top panel of images below) ii) Destructive mechanisms, such as weathering, erosion, and landslides (bottom panel of images below)

The Yosemite Valley was carved out by glaciers after uplift of the Sierra Nevada.

The Grand Canyon (CO) was formed by the Colorado River while the plateau was uplifted.

(c) Present your findings to your class, using your understanding of forces and motion from this chapter to explain the formation of your chosen feature.

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6. Give a brief explanation of how Newton's three laws of motion apply to the movement of tectonic plates and continents:

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Start Your Engines Revisited

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9

43

At the start of this chapter you were asked questions about the features of a domestic car and a race car and how they might affect various aspects of performance.

`` From what you have learned in this chapter you should now be able to reexamine those questions and your original answers in terms of force and motion.

1. It was mentioned in the first activity that a formula 1 car at top speed would be able to drive upside down. Tests with scale models in wind tunnels have confirmed this. Remember that the wings on the race car create down force.

(a) If the Formula 1 car has a mass of 760 kg what is the minimum force needed to hold the car upside down?

(b) The full downforce produced by the wings is 3.5 x the force of gravity (3.5 x g). What is the effective weight of the car experiencing this downforce?

(c) Explain why this amount of downforce helps the car corner at much higher speeds than a domestic car:

2. Recall the diagrams below. The angle of a race car's wheel is often angled outwards (negative camber) to help cornering. Now that you have studied forces involved in friction you can review your answer to the question of why the domestic car below is much more likely to slide off the track than the race car.

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Turning direction


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10 Summative Assessment

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1. (a) Draw a displacement-time graph for the following: A person walks at a steady speed 10 m along a straight footpath in 5 seconds. He then stops for 3 seconds before walking at a steady speed another 5 m in 3 seconds. He then turns around and jogs at a steady speed 18 m in the opposite direction in 4 seconds.

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SSM

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(b) Draw a velocity-time graph for the person's walk in 1. (a):

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2. The graph below shows the velocity-time graph of the space shuttle Atlantis as it lifts off from the launch pad and reaches space. Space shuttle velocity

Fuel tank

8

Fuel tank separation

SRB

6

5

4

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Velocity (m/s x 1000)

7

45

SRB separation

3

2

1

0

0

200

100

300

400

500

600

Time (seconds)

(a) Calculate the average acceleration of the shuttle for the 510 second flight:

(b) The space shuttle (including rockets and tank) had a total mass of 2300 metric tonnes. The engines on the space shuttle (including the external solid rocket boosters (SRBs)) combined to produce 30 million newtons of thrust. Calculate the acceleration of the space shuttle off the launch pad, assuming it is at full thrust:

(c) What does the curved line of the velocity-time graph mean in terms of the motion of the shuttle. How is this possible given that the thrust from the engine is constant between 120 and 510 seconds? See activity 58

3. (a) A block with a mass of 2 kg is at rest on a frictionless surface. Read the descriptions above the diagrams below then complete the diagrams by adding in arrows and labels to show the unbalanced forces involved: (b) Complete the table under the diagrams:

Acceleration

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The block is no longer pushed. It is left to move for 3 seconds.

Velocity

The block is brought to a stop by applying a force of 5 N

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The block is pushed from its left with a force of 10 N for 1 second.

Acceleration

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46

Direction of travel

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4. For long distance space travel, the following method is sometimes proposed: A spaceship fires its engines at full thrust at its point of origin. The spaceship continues traveling with engines on full thrust for half of its journey. It then switches off its engines, turns around (180°) and restarts its engine at full thrust for the second half of the journey facing back the way it came. Explain why this method would produce the shortest travel time and would bring the ship to a rest at the end of the journey.

First half of journey

Second half of journey

5. A ball is placed 1 km from surface of the Earth. The mass of the ball is 1 kg. The mass of the Earth is 6.0 x 1024 kg. The force between them is about 9.8 N. Use Newton's second and third laws to explain why both the ball and the Earth will accelerate towards each other, yet it is only the ball that appears to move:

6. Two skydivers jump out of a plane. They both adopt the same body orientation while falling (horizontally in a star position). Skydiver A has a mass of 75 kg. Skydiver B has a mass of 85 kg.

(a) What is the magnitude of the force on skydiver A?

(b) What is the magnitude of the force on skydiver B?

(c) Both skydivers achieve terminal velocity (their acceleration is zero). Explain why Skydiver A's terminal velocity is less than Skydiver B's terminal velocity. Terminal velocity is the point at which the force of air resistance equals the weight:

(d) The skydivers open their parachutes. Explain why their velocity decreases until they reach a constant velocity of about 25 kmph:

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7. An astronaut floating in space holds a ball. The astronaut-ball system has a velocity of 0 m ⁄ s. The 70 kg astronaut pushes the 1.3 kg ball directly away from her so that the ball attains a velocity of 1.5 m ⁄ s. Calculate the velocity of the astronaut after she releases the ball:

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47

(a) Calculate the velocity of the 'unloaded' astronaut:

(b) Determine how far apart the astronauts are after 5 s. Show your working:

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Drawing F.Hicks

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8. Two astronauts (each with mass 70 kg) push off each other in space. One carries 46.7 kg of equipment and moves away with a speed 0.3 m/s.

9. A truck with a mass of 15,000 kg moving at 25 m ⁄ s crashes into the back of a small 1100 kg car moving at 15 m ⁄ s. They stick together after the collision.

(a) Calculate the momentum of the system before the collision and after the collision:

(b) Calculate the velocity of the truck-car system after the collision:

10. A golf club swings and hits a golf ball from a tee. The golf club makes contact with the golf ball for 0.5 milliseconds (5.00 x 10-4 seconds). The mass of the golf ball is 0.045 kilograms. The velocity of the ball off the tee is 78 m ⁄ s.

(a) What is the impulse experienced by the golf ball?

(b) What is the force applied to the golf ball?

(c) Use two different methods to show that the acceleration of the golf ball off the tee is 156,000 m/s2.

(d) If the club has a mass of 0.3 kg. What is the change in the club's velocity as it contacts the golf ball?

11. A student builds a cart powered by a fan. When the fan is turned on, the sail will catch the air moved by the fan.

Explain why the cart will not move when the fan is turned on:

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Fan

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Sail


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Forces at a Distance

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Instructional Segment 2

Activity number

Anchoring Phenomenon Let's go climbing! There is a limit to how tall a mountain can be. What determines it?

11 18

How can different objects interact when they are not touching? 12

1

Recall your understanding of weight from the previous chapter. Predict what would happen to your weight if your mass was doubled, or the Earth's mass was doubled. You should now understand gravity as an attractive force between objects with mass. Why is gravity always an attractive force? Investigate the gravitational attraction between objects by replicating Cavendish's experiment to measure the force of gravity between masses. Interpret your results and predict the outcome if the masses in the experiment were changed.

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2

Use Newton's law of gravitation to calculate the effect of changing variables such as mass or distance between celestial objects and to explain why your weight is effectively the same no matter where you are on Earth. What would your weight be on a planet, e.g. Jupiter, which has a much larger mass than Earth? Explain the significance of the inverse square law described in Newton's law of gravitation to the weight force of objects of the same mass at different locations, e.g. on Earth and on the International Space Station.

12 19

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3

Identify examples of electrostatic phenomena. Investigate electrostatics using everyday objects and explain your observations. Electrostatic forces occur when charged objects interact with objects around them and they obey the inverse square law in the same way as gravity. However, unlike gravity, electrostatic forces can attract or repel. Demonstrate the inverse square law using a simple investigation. Next apply a mathematical model to demonstrate the inverse square law for gravity (Newton's law of Gravitation) and electrostatic forces (Coloumb's law) . What happens to the magnitude of the force when we change the mass of one object or the distance between two objects in a system?

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4

What makes an object magnetic and what sorts of objects are attracted to magnets? Investigate magnetic fields using bar magnets and iron filings or powder. How do you explain the patterns you see? Magnetic fields are like electric fields and gravitational fields in that they enable forces to be exerted from a distance, even when there are other materials between the source of the field and the object acted on. Magnetism and electricity are linked in the electromagnetic theory.

NASA/JPL

NASA

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16

How do interactions between matter at the microscopic scale affect the macroscopic properties of matter that we see?

c

5

Use your understanding of atomic structure and electrostatic forces to explain the properties of substances in which the intramolecular bonds of the molecules are ionic, covalent, or metallic. Investigate the interaction of a polar and a non-polar substance with a charged object. How do intermolecular forces help us to explain the properties of substances and their interactions with other substances?

15 17

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6

Investigate the properties of a range of different everyday materials and group them according to different criteria. Are some materials always grouped together? Obtain information about the molecular level interactions of various materials (conductors, semiconductors, and insulators). How does the molecular structure relate to the material's properties at the macroscopic level and therefore its various industrial and everyday applications.

17 19

7

Astronomers use parallax to measure the distance to stars and planets. Investigate the use of parallax to measure the distance to far away objects using simple equipment and your classmates as 'celestial bodies'.

13

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What is an orbit and how is it determined? Investigate orbital shapes using a physical model with varying focal points. Recognize patterns in the distance of objects from the Sun and their orbital period (Kepler's ratio). Use this pattern to predict orbital parameters using Kepler's laws. Recognize that cyclical changes in the Earth's orbit has had significant impacts on the Earth's systems throughout its history.

13 19

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9

Newton was able to derive all of Kepler's laws from his law of gravitation. Use these equations to calculate the mass of celestial bodies based on the orbital period and distance from an orbiting body.

13 19

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Develop and use a computational model to investigate orbital relationships in simple two body systems. How does altering the parameters of the model affect the path of a planet or satellite?

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Mirceas Madau public domain

How do satellites stay in orbit?

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11 Let's Go Climbing

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ANCHORING PHENOMENON: There is a limit to how tall a mountain can be.

Mount Everest

`` Mountains are immense geological structures that are formed in a variety of ways. On Earth, mountains are primarily formed through volcanic activity or collisions between tectonic plates.

`` Mount Everest (above) is in the Himalayas on the border between

Nepal and China. It rises to an elevation of 8.8 km above sea level making it the highest mountain on Earth. However, since Everest's base is already over 4 km above sea level, the mountain is only 4.6 km tall from base to peak. Other mountains can lay claim to being the tallest mountain on Earth.

`` Mauna Kea of Hawaii is recognized as the tallest mountain on Earth.

It measures 10.2 km from base to peak. The majority of the mountain is under water with only 4.2 km rising above sea level.

`` Of the mountains found entirely on land, Denali in Alaska is

`` The tallest known mountain in the solar system is Olympus Mons on

Olympus Mons from orbit

Mars (right). It is a massive shield volcano that measures 22 km tall.

NASA

recognized as the tallest mountain, rising to a height of 5.9 km from its base to its peak.

1. What are some factors which may limit the height of a mountain?

2. Suggest why Olympus Mons is so much taller than Mauna Kea:

`` Up to a certain height tall buildings tend to be built as tall rectangular boxes. Beyond that height they begin to

become more pyramidal in shape. Think of building a sand castle. How tall can it be made with vertical sides (e.g. made using a bucket as a mold) compared to building it with sloped sides (like a pyramid)?

`` The tallest all wood building is Mjøstårnet in Norway, at 85 m tall. The tallest load bearing brick building is the

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Monadnock Building in Chicago, USA, at 60 m tall. The world's tallest building is the Burj Khalifa in Dubai, standing 830 m tall. It is made of a combination of steel and concrete.

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3. What limits the height of a building? Why do you think the tallest buildings are made using concrete and steel?


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12 Exploring Gravity

ENGAGE: What is gravity?

`` Gravity is a property of mass which acts as an attractive force between objects with mass. The greater the mass of the object, the greater the gravity it possesses.

`` We used the word weight to describe gravitational force acting on an object. Weight (in N) is based on the mass of the object and multiplied by the strength of gravity (on Earth, this is 9.8 N/kg).

1. Using the equation W = mg where W is your weight, m is your mass and g is the strength of gravity: (a) Describe what would happen to your weight if your mass doubled:

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(b) Now, instead, what would happen to your weight if the same sized Earth doubled its mass (which doubles its gravity):

(c) What do you notice about your weight when you compare the values in 1(a) and (b)?

(d) What then are the main factors that determine your weight on earth and how are they related to your mass?

`` Recall the laws of motion from chapter 1. When you fall

towards the Earth the Earth also falls a little towards you.

2. (a) If you had the same mass as the Earth would you now fall towards the Earth or would the Earth fall towards you? Explain your answer:

(b) What if you now had double the mass of the Earth? How would the falling situation now change?

3. Why do you think we do not feel the attractive force of gravity between ourselves and other objects on Earth (our classmates, our desks, our writing utensils, etc)?

EXPLORE: Gravitational attraction between objects

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`` There is a symmetrical gravitational force of attraction between all pairs of objects that have mass. Consider object

A in the gravitational field of object B: the strength of the field where A is depends on B's mass. The force of gravity on A depends on its own mass and the strength of B's gravity at that position. Thus the size of the gravitational force on A depends on the mass of both objects. Logically, this situation can be viewed totally in reverse. Hence A and B exert exactly the same amount of gravitational force on each other but in opposite directions.

`` Everyday objects (pens, cups, tables, people, cars etc) each have gravity too, but their masses are minuscule when

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compared with moons, planets and stars. The gravitational force they exert on each other is so extremely small we do not notice it.

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51 `` In 1798 Henry Cavendish demonstrated it is possible to observe the gravitational attraction between objects. A

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modern representation of his experiment is shown below:

Reflecting the laser beam "amplifies" the movement by doubling the angular deviation.

Wire thread

Mirror Laser light

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Small masses hang from a thread so they can pivot.

Light source / laser

Large masses fixed in place.

`` Originally Cavendish was able to measure the force of gravity between masses by precisely measuring the twisting force on the wire thread used to suspend the smaller masses. The twisting was produced by the movement of the smaller masses towards the larger fixed masses.

`` Gravity is the weakest of the universe's four fundamental forces. Its effects are only noticeable when there is a huge amount of mass in one place. Even so, the force of gravity can be measured using the simple experiment below.

INVESTIGATION 2.1: Cavendish's experiment

See appendix for equipment list.

1. Construct a torsion bar by fixing two 1 m rulers together using tape or rubber bands (or just use one 2 m long piece of (thin) wood). 2. Loop nylon fishing line around the center of the torsion bar to produce a torsion balance. Don't worry if the bar doesn't balance perfectly.

3. Hang the torsion balance from a ceiling beam or hook using the fishing line so that the bar hangs a few centimeters over the ground or a table and swings freely.

Large masses (5 - 10 kg)

Fishing line

4. Hang 1 kg masses on each end of the torsion bar. Adjust their placement until the torsion bar is horizontal (carefully measure the height at each end). Make sure the bar still swings freely. Allow the balance to come to a rest before going on to the next step.

Torsion balance

Small masses (1 kg)

Plan view of investigation

5. Place large masses several centimeters away from each end of the torsion bar in clockwise positions to the small mass (as in the diagram above). 6. Set a video recorder (e.g. your device's camera) so it can view the experiment, close all windows and doors, and cover any vents and openings into the room to prevent air flow.

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7. Predict how the balance will behave:

8. Everyone should now leave the room (very carefully and quietly!) for a few minutes to allow the torsion balance to settle. 9. After 10 minutes reenter the room and turn off the video recorder.

10. Watch the video in 5-10x speed and observe what happens to the torsion balance.

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11. Move the large masses away from the torsion bar and repeat the investigation from step 5. This time place the large masses in counterclockwise positions.


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4. (a) After viewing the recording, write down what you observed:

(b) Why do you think this happened?

(c) Why wouldn't you place the larger masses on the same side of the torsion bar?

(d) What is the purpose of repeating the experiment with the large masses in the counter clockwise position?

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5. (a) Why does the torsion balance need to swing freely? What effects does this eliminate?

(b) What do you think would happen if the large masses were halved in mass?

EXPLORE: Newton and gravity

`` In 1687 Issac Newton published his law of gravitation, it included the equation:

F=G

M1M2 r2

M1

F2

F1

M2

`` The equation allows us to calculate the force of gravity acting

between two objects, where M1 and M2 are the masses of the two objects (in kg), r is the distance between their centers of mass (in meters), and G is the gravitational constant 6.673 x 10–11 m3/kg/s2 (Nm2 /kg2)

`` Even though Newton came up with the equation, the

gravitational constant was unknown at the time. Cavendish was the first to calculate the gravitational constant from his experiments with his torsion balance 71 years after Newton's death.

r

Force 1 and force 2 are equal. M is the mass of the objects involved and r is the distance between their centers. The force of gravity between the objects is inversely proportional to the square of their distance (i.e. doubling distance reduces the force to a quarter, halving distance quadruples the force etc.).

6. Using Newton's equation for the law of gravitation, what would be the effect on the force between the Earth and the Moon of changing the following: (a) Doubling the distance between the Earth and the Moon: F would (increase / decrease / remain the same) (circle one).

(b) Doubling the mass of the Moon: F would (increase / decrease / remain the same) (circle one).

(c) Halving the mass of the Earth: F would (increase / decrease / remain the same) (circle one).

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7. Imagine the masses in the diagram above are asteroids orbiting each other in space. The mass of asteroid M1 is ten million kilograms. The mass of M2 is 4 million kilograms. Their centers are 3600 m apart. Calculate the force F that is acting between them:

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EXPLAIN: Distance and its effect on gravity

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`` Remember that gravitational force is an interaction between two objects. The same amount of force is acting on them both. Newton’s law of gravitation describes the force between any two objects (the Sun and the Earth, the Earth and the Moon, you and the Earth, etc).

`` Recall that the force changes when the distance between two objects (r) changes. `` The Earth has a radius of about 6371 km. The difference between the top of Mount Everest (the highest point on Earth) and the Mariana Trench (the lowest point on Earth) is about 20 km.

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8. (a) We can express the distance from the center of the Earth to the top of Mt Everest as 6.381 x 106 m and from center of the Earth to the Mariana Trench as 6.361 x 106 m from the center of the Earth. Use Newton's equation on the opposite page to calculate the force acting between a person with a mass of 50 kg and the Earth with a mass of 5.972 × 1024 kg at each of the two locations:

(b) What can be said about how these locations affect the force of gravity acting on a person?

ELABORATE: Deriving Earth's gravity

`` The force of gravity is always attractive and is considered to come from the center of each object.

`` Recall the equation for weight is W = mg (which is a specific case of F = ma). Neither of these equation look

anything like Newton's equation for force. That is because the equation is simplified for objects on or near Earth’s surface.

`` Depending on where you are on Earth (the top of Mount Everest, or the bottom of the Mariana Trench), you are

different distances from the center of the Earth. This means that there is a difference in gravitational force between different locations, but that difference is so small it is insignificant and so your weight is effectively the same no matter where on Earth you are.

`` When we look at Newton’s equation we see that in relation to Earth three of the variables are constant: • The universal gravitational constant (G): G = 6.673 x 10-11 Nm2/kg2 • The mass of the Earth: (Me): Me = 5.972 × 1024 kg

• The distance to the center of the Earth, i.e. the radius of the Earth (re): re = 6.371 × 106 m

`` If we rewrite Newton's equation so that M1 (mass of an object on Earth) and M2 (mass of the Earth (Me)) are separate we get:

F=mx G x

Me re

= m x 6.673 x 10-11 m3/kg/s2 x

5.972 × 1024 kg

(6.371 × 106 m)2

= m x 9.8 m/s2

`` Thus we can now see that g in W = mg (or a in F = ma) incorporates one mass (Me), G and r, leaving us with

simply the second much smaller mass (m) to add to the equation. Multiplying mass by g (9.81) gives us our weight.

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NASA/JPL

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9. W = mg. For a person with a mass of 70 kg they have a weight of 70 x 9.8 = 686 N on Earth. Jupiter has a mass of 1.898 × 1027 kg. Its radius is 69.911 x 106 m. Use the information above to work out g on Jupiter and therefore the weight of a 70 kg person if they were able to stand on the "surface" of Jupiter:


54 `` The further away an object is from

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Earth (or another large celestial body), the less the influence of gravity. This relationship is based on the square of the distance between the objects’ center of masses and is called the inverse square law.

`` The inverse square law models

r

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the behavior of many forces that act over a distance. Because the distance is squared, the strength of the field of force decreases rapidly.

Light traveling from a star moves in straight lines. The further away from the star we get, the more spread out the lines of light become. If each line creates a point of light, the intensity of light falling on an object becomes less the further away from the star the object is. The same thing happens with gravity, electrostatic forces, sound and particle radiation.

2r

3r

`` This relationship is described in Newton’s law of gravitation and implies that a person on the surface of the Earth

will have a different weight from a person in the International Space Station (ISS) because the person in the ISS is further away from the center of the Earth (greater r) than the person on the surface.

`` For example, how much would a 60 kg person weigh on the ISS? We have values for the gravitational constant (G), the mass of the Earth (Me), the person (M2), and the radius of the Earth, we simply need the radius of the space stations orbit. We can find this by adding the average altitude of the space station (4.08 x 105 m) to the radius of the Earth (6.371 x 106 m).

`` Putting all these variables into Newton's equation we can solve for the weight of a 60 kg individual on the ISS.

W = 6.673 x 10-11 x

(5.972 x 1024 x 60) 6.779 x 106

= 520 N

`` This is about 70 N less than we would expect for someone of that mass standing on the surface on the Earth. Remember their mass hasn't changed, but the force they experience has.

10. Calculate the weight for an individual at the Moon’s distance from the Earth (3.84 x 108 m):

11. Use the Newton's equation to calculate the force of attraction between the Earth and the Moon (Me = 5.972 x 1024, Mmoon = 7.35 x 1022, r = 3.84 x 108 m):

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12. Rearrange Newton's equation to solve for the mass of a satellite 600 km above the Earth’s surface experiencing an attractive force of 10,000 N:

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13. If you have ever seen a video of astronauts on the ISS, you would notice how they are "floating" around inside the station and appear to be weightless. But according to Newton's law they definitely have weight. How do you explain this?

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13 Planetary Motion

ENGAGE: The cannon conundrum

`` Imagine a cannon on top of a tall hill. The cannon is aimed so that the barrel is horizontal. All around it is a flat level plain that stretches forever, with no curvature. The force of gravity is equal to that on Earth. There is no air.

`` A second cannon also sits on top of a tall hill. The barrel of the second canon is parallel with the barrel of the first canon. However, the "flat plain" this time is the curved surface of a planet. The force of gravity is again equal to Earth's gravity.

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`` The diagrams below show each of the situations described above:

Cannon 1

Cannon 2

1. Cannon 1 fires three cannon balls, each with increasing force, as illustrated in the top diagram. Cannon 2 also fires three cannon balls, each with the same force as by cannon 1.

On the diagram above draw how you might expect the cannon balls from cannon 2 to fall (as in the top diagram). Discuss your drawings in groups and explain your diagram below:

EXPLORE: What is an orbit?

`` The Sun is the overwhelming source of gravity in our

solar system. Its gravity reaches far into space and all the objects in the solar system orbit around it.

2. The planet moves away from the Sun because of its relative sideways movement.

`` An orbit is the path an object follows around

another. In space, orbits are what result when a moving object is trapped in the gravity of a much larger body.

3. This continual motion produces an elliptical orbit.

`` The planets are all being pulled by the Sun's gravity,

`` It is important to remember the gravitational forces

between the Sun and the planet are equal but because the Sun is so much larger, it barely moves, orbiting in its own small ellipse around their common center of mass.

1. A planet is always accelerating towards the center of the Sun.

orbiting objects, the more pronounced the orbit of the larger body becomes. The center of the Earth-Moon system for example is 4670 km from the center of the Earth (i.e. within the radius of the Earth). SC

SSM

SPQ

P

ESS1.B

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`` The closer the match between the masses of the

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effectively falling towards the Sun. However, they are also moving sideways relative to the Sun. The effect of this is they trace elliptical orbits through space.


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2. The Earth exerts the same gravitational pull on the Sun as the Sun does on the Earth. Explain why the Earth orbits the Sun in a wide orbit, while the Sun only wobbles on its axis:

3. In order for an object to follow an orbit it must be moving at just the right speed for that orbit: (a) What would happen to the orbit of a planet if its speed were to increase slightly?

(b) What would happen to the orbit of a planet if its speed were to decrease slightly?

(c) What would happen to the orbit of a planet if it completely stopped?

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4. On Earth, objects in motion slow down and eventually stop unless a force is added to keep them moving:

(a) On Earth, what happens to an object after you push it?

(b) Why do planets not slow down while orbiting the Sun?

EXPLORE: Measuring the distance to planets (parallax)

`` Obtaining a reasonably accurate distance measurement to at least one planet became important for astronomers since this would provide a "yardstick" to compute the distance to other planets. But how do we do this?

`` Astronomers use an effect called parallax to measure the distances to faraway objects such as stars and planets. `` Parallax is the apparent displacement of an object due to a change in the observer's point of view.

`` Hold your thumb in front of you and look at it with your left eye closed. Then look at it with your right eye closed. Your thumb hasn't moved but it will appear to move against the background.

`` This effect can be used to measure distance to far away objects.

`` As the Earth orbits the Sun, a distant planet or nearby star will appear to move against the more distant

background stars, in the same way your thumb appeared to move against the background when you viewed it with one eye and then the other.

`` Astronomers can measure a planet's or star's position once, and then again at a later date (6 months for stars) or at widely spaced positions on Earth (e.g opposite sides of the planet) and calculate the apparent change in position.

The distance to a star can be calculated using the equation d = 1/p where d is the distance in parsecs (1 parsec = 3.6 light years) and p is the parallax angle.

Distant "fixed" background of stars.

Apparent position of star in January

Observation in July

Parallax angle

Observation in January

Measuring the distance to the stars is possible only to about 1000 parsecs. However the distances to stars measured by parsecs act as a calibration for other less direct ways of measuring distance to stars further away.

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Orbit of Earth

Apparent position of star in July

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Actual position of star

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INVESTIGATION 2.2: Parallax

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See appendix for equipment list.

1. Creating a parallax angle measuring tool (diagram right):

To reference point

a. Place a protractor on a corkboard or thick cardboard and tape it in place. b. Push a pin completely through one end of the straw. c. Place the straw on the protractor and push the pin through the hole in the protractor into the board. The straw should be able to pivot on the pin.

To target

Straw Target angle a

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2. In groups of 4 head out to the school’s field. Face in a direction where there is a visible background with variation to observe (the school building itself, goalposts, etc).

A large pin fixes the straw and protractor to the card

3. One student from each group should stand somewhere distant between the background and the rest of the group of students. This student represents the distant planet you are trying to find the distance to.

Reference point

4. The student in the group doing the measuring should pick a distant reference point somewhere behind the student in the field. 5. Lay down a measuring tape to act as your group's baseline. It should be roughly perpendicular to the direction of your target object and the reference point. Record the length of your baseline (e.g. 2 m) in the table below.

a

a

b

6. At the start of the baseline turn the straw of the parallax measuring tool to 90°and sight down the straw so that the distant reference point is lined up.

Target student

7. Still at the start of your baseline and keeping the parallax measuring tool still, turn the straw so that it is lined up with the target student. Record the target angle shown by the straw on the parallax measuring tool (reading degrees L→R on the protractor) .

a

a–b=a

8. Move to the other end of the baseline. Keeping the parallax measuring tool parallel with the baseline, turn the straw, and sight the target student. Record the angle as shown by the straw. 9. Repeat the process for each student in the group (each student should be a different distant planet).

10. Find the parallax angle for each student planet by subtracting the larger target angle from the smaller.

Target angle a

Target angle b

11. You now need to use a little trigonometry to calculate the distance to the planets in your group. The distance to your object (D) is related to the parallax angle (α) and the baseline length (B) by the trigonometric relationship (tangent): 0.5B Measuring student D= tan(0.5α) Target angle a

Target angle b

Parallax angle (a) (subtract the larger target angle from the smaller)

Baseline (B) length (m)

Baseline

Distance (D) to target (m) D = 0.5B ÷ tan(0.5α).

Student 2 Student 3 Student 4

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Student 1

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An alternative set up for this investigation, which is a little more involved but provides a somewhat more accurate simulation, is provided on BIOZONE's Resource Hub.


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5. In 1672 Giovanni Cassini measured the parallax of Mars to work out how far away it was. At this time Mars was at its closest approach to Earth in its orbit (in opposition), which would give the best conditions for calculating its distance. He sent his colleague to Cayenne, in French Guiana, to simultaneously take a measurement of Mars while he stayed in Paris, France. This gave him a baseline of about 6650 km. The two men measured a difference in Mars' position of about 0.0071 degrees. Use this information to calculate the distance to Mars from Earth when Mars is at its closest approach:

EXPLORE: How do planets travel?

`` We have seen earlier that further away from a gravitational source an object is the less force that object

experiences from the gravitational source. This affects how an object orbiting the gravitational source moves.

`` In addition, there are other planets, moons, and rocky bodies, which affect how an object orbits. In a perfect

situation a planet might orbit a star in a circular orbit, but due to all these gravitational interactions a circular orbit is most unlikely. The planet Venus has the most circular orbit in the solar system, being off by less than 1%.

`` A circle is in fact a special occurrence of a shape called an ellipse. Whereas the points of a circle "orbit" around a

central focus, the points of an ellipse "orbit" around two foci. A circle is an ellipse with both foci in the same place.

INVESTIGATION 2.3: Orbits

See appendix for equipment list.

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1. In the box below, draw a series of ellipses using each bracketed pair of dots as focal points (foci). You will need a piece of string 15 cm long, two thumbtacks, and a pencil. Tie the string into a loop. Press the thumb tacks into the dots as focal points (put corkboard or thick card behind the page to protect your book). Loop the string around the thumbtacks and your pencil. Keep the loop tight by gently pushing outwards with your pencil as you draw the curve.

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EXPLORE: Orbits

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`` Our solar system consists of the Sun, eight planets, numerous dwarf planets, and almost uncountable numbers of comets and asteroids. Many of these objects orbit the Sun in elliptical orbits that are roughly circular, with the Sun near the center of the circle. However many do not. The most well known of these are comets, but many of the dwarf planets, (especially those in the outer solar system) also orbit with highly elongated orbits.

`` How an object orbits depends on many things. These include how it formed, where it formed, the gravitational force from nearby objects, and its velocity during an encounter with any other object.

Orbits and escape velocity

Circle: v = vC. The velocity of the planet gives it sufficient momentum, perpendicular to the radius, to counteract the inwards pull of the star's gravity.

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The velocity required for a circular orbit can be calculated using the equation: vC =

GM r

Escape velocity is the velocity required to escape the gravitational pull of an object at a particular distance from it. It can be calculated using the formula: vE =

Ellipse 1: v < vC. The planet will orbit in a small ellipse as the velocity is not fast enough to prevent the gravity of the star pulling it back before a circular orbit forms.

2GM

Star

r

The diagram right shows the orbit of a planet around a star of mass M based on the planet's actual velocity (v) compared to its escape velocity (vE) and the velocity needed for the planet to orbit in a perfect circle (vC). All orbits start at point P.

Ellipse 2: vC < v < vE. The planet will orbit in a large ellipse as it is traveling faster than the velocity required for a circle, but not fast enough to escape the pull of the star.

Scott McDougall

Parabola: v = vE. The planet will coast away from the star at an ever decreasing relative velocity but will never actually return.

Hyperbola: v > vE. The planet will escape the pull of the star.

NASA

Sedna is one of the most distant dwarf planets. It has a dramatically elongated orbit compared to the planets of the solar system. At its closest approach to the Sun, Sedna closes to 72 AU, but then swings back out to 936 AU from the Sun. Its orbit takes over 11,400 years to complete.

In 2017 the interstellar object "Oumuamua" entered the solar system. Its trajectory brought it close to the orbit of Mars. Oumuamua was traveling at such a high speed that although the Sun's gravity bent its path it was not captured, and it has since travelled back out past the outer planets on its way out of the solar system.

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NASA

NASA Ricardo Nunes

Comets have a highly elliptical orbit

Venus has the most circular orbit in the solar system, being less than 1% off a perfect circle. At its closest approach to the Sun Venus is 0.716 AU away from the Sun, while at its furthest away it is 0.726 AU from the Sun. One AU (astronomical unit) is the average distance from the Sun to the Earth, about 150 million km.

6. (a) Of the five orbits shown in the diagram top right, which most likely matches the orbit of Oumuamua?

(b) What would happen to the shape of Venus's orbit if it gained velocity as it moved along its orbit?

(c) How would the size of the escape velocity be affected if a planet orbits closer to a star?

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EXPLAIN: Kepler's laws

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`` In 1609 Johannes Kepler using the observations of Tycho Brahe formulated three laws of planetary motion (below):

1

Each planet moves in an elliptical orbit with the Sun at one focus. An ellipse is a curve around two focal points (f1 and f2). It has a semimajor and a semiminor axis. The further apart the foci are the more elongated the ellipse is.

b = semiminor axis

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a = semimajor axis

Geometric center

f1

R1

f2

Major axis

R2

Minor axis

Semimajor axis: a = ½(R1 + R2)

The deviation of an ellipse from being circular is called its eccentricity which is given a value between 0 and 1. The closer the value to 0 the closer the ellipse is to a perfect circle. The eccentricity of Earth's orbit is 0.0167 (nearly circular), whereas comets may have eccentricities of 0.9.

2

e = R2 – R1

Eccentricity:

R2 + R1

A line between the Sun and a planet sweeps over equal areas during equal time periods. The further a planet is from the Sun the slower it orbits. As it comes closer, the speed at which the planet orbits increases. However, over a set time a line drawn from the Sun to the planet will still sweep over an area of space equal to when it was moving slowly.

Area 1

Area 1 = Area 2

Area 2

The square of any planet's orbital period (T) is proportional to the cube of its semi-major axis (a) therefore: T2 = constant x a3

T12

If a is measured in AU, and T is measured in Earth Years, then this combination of units makes the value of the constant = 1. The result is the simple equation T2 = a3

a13 = T12 a1 T1

=

T22

a23

* 1 AU = the distance from the Earth to the Sun = 150 million km.

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A further consequence of T2 being proportional to a3 is that the ratio is the same for all planets (see the dark blue box).

a13

a2

T2

a23 = T22

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3

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7. For each elliptical orbit shown below, rule in the major and minor axes then (i) measure a, R1 and R2 (ii) calculate T and e (NOTE scale: 1 cm = 10 AU. x marks the position of the star, o is the orbiting object. (a) (b) o

(c)

o

o

x

R1

x

a

T (Earth Years)

e

a3

T2

T (Earth Years)

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R2

x

(a) (b) (c)

8. Complete the table below using a3 = T2: Planet

a (AU)

Earth

1.00

Venus

0.72

1.00

Jupiter Saturn

140.85

867.43

9. Why does a line between a planet and the Sun sweep out equal areas during equal time periods no matter the planet's distance from the Sun during its orbit:

10. Calculate the following:

(a) Mercury's distance to the Sun is 0.39 AU. Calculate its orbital period in years:

(b) Neptune takes 164.79 years to orbit the Sun. What is its distance from the Sun in AUs?

(c) How far is your answer to (b) in km?

(d) Calculate the orbital period of a new planet found to be orbiting 62 AU from the Sun:

11. (a) Use T12/a13 = T22/a23 to solve the following: Jupiter's moon Ganymede, takes 7.15 Earth days to orbit Jupiter. Ganymede is measured to be 1,070,000 km from Jupiter's center. A second moon of Jupiter, Callisto, takes 16.69 Earth days to orbit Jupiter. How far away is Callisto from the center of Jupiter?

(b) Jupiter's moon Io takes just 1.77 days to orbit the planet. How far away from Jupiter is Io?

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12. Recall question 5 in this activity regarding the distance to Mars from Earth. It was known at the time from observations that Mars took about 1.9 Earth years to orbit the Sun. Use a3 = T2 to explain how to use the distance from Earth to Mars to calculate the distance of Earth to the Sun and Mars to the Sun:


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ELABORATE: Applying Newton's laws to Kepler's laws Isaac Newton realized that the orbital period of a planet was related to the mass of the star and the mass of the planet. He was able to derive all of Kepler's laws from his law of universal gravitation, producing simple formulae that could be used to calculate the mass of any orbiting body based on the orbital period and the distance of the body orbiting it.

Example 2: Planet X orbits star 1 and planet Z orbits star 2. Both planets take Earth 2 years to orbit their respective stars. However, planet X is 2 AU from its star, while planet Z is 1 AU from its star. What is mass of each star and many times bigger is one star than the other?

``Newton rewrote Kepler's third law as:

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EQUATION 1

4π2 a3

M1 + M2 =

M = mass in kilograms a = distance in meters T = orbital period in seconds

G T2

Star 2

Star 1

Planet Z

`` In many orbiting systems, M1 and M2 are very different

(one is usually very big and the other is very small, e.g. a star and a planet) so M1 + M2 are often rewritten simply as M (the mass of the larger object).

`` 4π2 and G are constant numbers. They give us a precise answer by modifying a3/T2. If we remove them from the equation we find that M is equal to a3/T2. EQUATION 2

a3

M =

M = mass in solar masses a = distance in AU T = orbital period in Earth Years

T2

`` This looks similar to Kepler's law. If we use astronomical

units (AU) for a and Earth years for T (as we have earlier), then using Newton's realization that T is related to the mass of the star, M must be in solar masses, where 1 solar mass is equal to the mass of the Sun (1.99 x 1030 kg).

`` Using these equations, we can calculate the mass of any

central body based on the orbital period and distance of the orbiting body.

Example 1: A star has a mass of 7.96 x 1030 kg and has a planet orbiting 7.50 x 1011 m from it. What is the period of the planet's orbit in years?

Planet X

If we are to use equation 1 we need to convert the units above into kilograms, meters, and seconds. There are 1.5 x 1011 meters in 1 AU and 31,536,000 seconds in a year. M star 1 = 4π2a3 / G T2,

= (4 x 3.1422) x (2 x 1.5 x 1011)3 6.673 x 10–11 x (2 x 365 x 24 x 60 x 60)2 = 39.478 x 2.7 x 1034 6.673 x 10–11 x 3.978 x 1015

= 1.066 x 1036 265,457

= 4.016 x 1030 kg

M star 2 = 4π2a3 / G T2,

= (4 x 3.1422) x (1.5 x 1011)3 6.673 x 10-11 x (2 x 365 x 24 x 60 x 60)2 = 39.478 x 3.375 x 1033 6.673 x 10–11 x 3.978 x 1015

= 1.332 x 1035 265,457

= 5.019 x 1029 kg

4.016 x 1030 kg / 5.019 x 1029 kg = 8.00.

Star 1 is 8 times more massive than star 2.

T2

M star

a3

We can use equation 2 to provide a similar answer:

Planet X

M star 1 = a3/T2 = 23/22 = 2 solar masses

M star 2 = a2/T2 = 13/22 = 0.25 solar masses

Using equation 1: = 4x

3.1422

2 / 0.25 = 8

T2 = 4π2a3 / MG

x (7.50 x

1011)3

/ 7.96 x

1030

x 6.673 x

10–11

T2 = 1.6659 x 1037 / 5.3117 x 1020 = 3.1578 x 1016 T = 176,387,215.7 s = 5.6 years

=

a3/Mstar

Mstar = 7.96 x

So: 4.016 x 1030 kg / 1.99 x 1030 kg = 2.02 1030

/ 1.99 x

1030

a = 7.5 x 1011 / 1.5 x 1011 = 5 T2 = 53/4 = 125/4 = 31.25.

And checking to be sure the second equation is an accurate representation of the first: One solar mass ~ 1.99 x 1030 kg

And equation 2: T2

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T2

T = 5.6 years.

= 4 solar masses

5.019 x 1029 kg / 1.99 x 1030 kg = 0.25 2.02 / 0.25 ~8

CL

Mstar = 4π2a3 / GT2

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13. (a) Observations of a star 30 light years away showed it was being orbited by a planet once every 1.5 Earth years. It was also calculated that the planet was 1.75 AU from the star. What is the mass of the star in solar masses?

(b) Observations of a second star showed that its planet orbited it in 0.5 years and was 0.9 AU distant. Calculate the difference in solar masses between the two stars and state which star is larger:

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14. Mars' moon Phobos orbits Mars with an average distance of about 9380 km from the center of the planet and has an orbital period of about 7 hr 39 min. Use this information to estimate the mass of Mars in kg:

15. Calculate the distance (in AU) of a planet from its star's center for a planet with an orbit of 145 years and a star 2.5 times the mass of the Sun:

16. (a) The largest star so far observed is estimated to be 315 times as massive as the Sun. Assuming it was possible for a planet to orbit this star at the same distance as the Earth is from the Sun, calculate the planet's orbital period in days:

(b) At what distance (in AU) from the star's center would the planet need to be in order to orbit it in one Earth year?

17. The Sun is about 30,000 light years from the center of the Milky Way. It takes about 250 million years to orbit the galaxy. Use this information to estimate the mass of the Milky Way galaxy in solar masses and in kg (1 light year = 63,241 AU):

18. Jupiter's moon Ganymede takes 7.15 Earth days to orbit Jupiter. Ganymede is measured to be 1,070,000 km from Jupiter's center. Use this information to calculate the mass of Jupiter:

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19. Trappist-1 is a small star about 40 light years from Earth. It is orbited by seven planets. The orbits of these planets have been calculated from data collected by Earth-orbiting observatories. The planet labeled Trappist-1g takes 12.35 days to orbit the star and is about 6.75 million km from the star. How big is Trappist-1 compared to our Sun?


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ELABORATE: Satellites

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`` There are hundreds of satellites orbiting the Earth. The majority are used in communications but others are used in monitoring weather or surveying the Earth's surface. Satellites orbit the Earth at different altitudes and at different inclinations, some orbit around the Earth's equator, others have a polar orbit.

Orbiting the Earth

Low Earth orbit (LEO) is around 200-3000 km above the surface. The International Space Station and the Hubble Space Telescope are both in LEO.

Medium Earth orbit (MEO) is at an altitude of about 3000 km to 30,000 km. It is used for communications and GPS satellites.

Geostationary satellite

Hubble Space Telescope

NASA

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Geostationary orbit (GEO) is at an altitude of about 36,000 km. At this distance the satellite takes the same time to orbit the Earth as the Earth takes to complete one rotation, keeping the satellite above the same point on the Earth.

NOAA

There are three basic orbital heights in which satellites are placed:

Communication satellite

`` In the same way as a planet orbiting closer to a star, the closer a

satellite is to the Earth, the faster it has to move in order to stay in orbit. Satellites orbiting too close to the Earth encounter drag from the Earth's atmosphere and slow down, falling to a lower orbit. Occasionally these need to be maneuvered to maintain their altitude. We can use Kepler's third law and v= d/t = circumference/T to estimate the speed and orbital period of a satellite.

`` The International Space Station (ISS) orbits at about 400 km above the Earth. How long does it take to complete one orbit and at what speed is it moving?

determine the distance of the ISS from the center of the Earth: 6.371 x 106 m + 4 x 105 m = 6.771 x 106 m. The mass of the Earth is 5.972 x 1024 kg. Applying Kepler's third law we find that T2 = 30,752,275 and T = 5545 s = 92 minutes, or about 1.5 hours.

`` The ISS orbit is almost circular, so calculating the circumference of a circle the size of its orbit using c = 2pr = 42,543,448 m. Dividing distance by time = 42,543,448 m / 5545 seconds = 7672 m/s.

International Space Station (ISS)

NASA

`` First we must add the Earth's radius to the altitude of the ISS to

We can also use the equation v = â&#x2C6;&#x161;(GM/r) to calculate orbital speed: Where v is the velocity (orbital speed) in m/s, G is the gravitational constant, M is the mass of the Earth (kg), and r is the radius of the orbit (m).

20. (a) The Hubble Space Telescope orbits 559 kilometers above the surface of the Earth. Calculate the time (in hours) it takes to orbit the Earth:

(b) Calculate the HST's orbital speed:

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(b) Calculate the orbital velocity of this satellite:

CL

21. (a) The Moon orbits Earth at a distance of 0.00257 AU and takes 0.074 years to complete one orbit (27 days). Use this information and Kepler's third law to calculate the orbital radius of a geosynchronous Earth satellite:

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ELABORATE: Maintaining the ISS orbit

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`` The orbit of the International Space Station (ISS)

Altitude of ISS

varies over time, sometimes dropping to an altitude of 330 km or rising to an altitude of 410 km (right). It orbits at an angle of 51.6° compared to the Earth's equator.

440 420

`` At times, the ISS is deliberately raised and

380 360

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`` After the retirement of the space shuttles in 2011,

400 Altitude (km)

lowered in its orbit. This would occur especially for scheduled launches of the space shuttles so that the orbiter wouldn't have to fly quite so far. the nominal orbit of the ISS was raised. Modern supply rockets are much lighter than the shuttle, so the extra distance is not as critical.

`` Because the ISS is in LEO, its orbit is affected

by friction with the remnants of the upper atmosphere. This reduces its velocity and causes its altitude to reduce over time. The ISS requires about 7.5 tonnes of fuel per year to maintain orbit.

340 320

300 1998

2002

2006

2010

2014

2018

Year

22. Why would NASA engineers want to reduce the flight distance of the space shuttle?

EVALUATE: Modeling an orbit

`` How do we calculate the position of a satellite or planet? Computer scientists and astronomers use computer

programs to calculate future positions of satellites. These can be very complicated, involving the interaction of many planets and other celestial bodies.

`` The investigation below steps you through the creation of a simple program to model any satellite's orbit. Start by opening a spreadsheet (in a program such as Microsoft Excel). Although it may look complicated, it is straightforward if you follow the steps carefully. If time is short, the spreadsheet is also available on the BIOZONE Resource Hub.

INVESTIGATION 2.4: Computational models of orbits

See appendix for equipment list.

1. To start, set your spreadsheet so that you can see the formula. This is not essential but may make things easier to start.

2. In cell A1, type the heading GM. This stands for the gravitational constant (G) x the mass of the Earth (M). G is constant but M can be varied (as you will test later). The mass of the Earth (5.972 x 1024 kg). In cell B1, add the formula: =(5.972E24*F1)*6.674E-11 3. In cell A2, type the heading dt. This is the length of time (the time step) between each calculation of position of the satellite. The time step needs to show enough points to complete one orbit. The number changes depending on the period of the orbit. In cell B2, type =F3/47 4. In cell A3, type the heading vi (initial velocity). This will be entered manually. A separate formula set will calculate it for you later. In cell B3, enter the number 7672 (the velocity of the ISS in m/s). 5. In cell E1, type the heading Earth units. In cell F1, type the number 1. This allows us to vary the mass of the planet later on.

6. In cell E2, type the heading Altitude (m). In cell F2, type the number 400000 (the altitude of the ISS in meters). This will allow us to control the height of the satellite later on.

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7. In cell E3, type heading Time (s). This is the period of the orbit. It will be calculated automatically by the spreadsheet. In cell F3, type the formula =SQRT(((4*PI()^2)*A6^3)/B1). This uses a rearrangement of Kepler's law to calculate the period in seconds. 9. Your first four rows of the spread sheet should look like this:

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8. In cell G3 type the formula =F3/60/60. This converts seconds into hours.


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10. Now we must enter the formula to calculate and plot the position of the satellite over time. This requires formulae that calculate the change in acceleration and velocity of the satellite as is orbits the Earth. In cell A5, enter the heading x. In cell B5, enter the heading y. These will be the x and y coordinates for the graph you will plot. In cell A6 (under x) enter the formula =6371000+(F2). This adds the altitude of the satellite to the radius of the Earth. It gives the initial position of the satellite on the x axis. In cell B6, type the number 0. This is the initial position on the y axis.

11. In the following cells, type the following headings: In C5, type r (radius of orbit). In D5, type a (acceleration). In E5, type ax (acceleration in x direction). In F5, type ay (acceleration in y direction). In G5, type vx (velocity in x direction). In H5, type vy (velocity in the y direction).

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12. You are now set fill in the formulae that will calculate the x and y positions of the satellite over time. Your spreadsheet should look like this:

13. From the x and y coordinates you can calculate the radius of the orbit. Since x and y are always at right angles to each other, the radius r can be calculated using Pythagoras where r = √(x2 + y2). In cell C6, add the formula =SQRT(A6^2+B6^2). Highlight cell C6 and fill down to row 52.

14. You can now calculate acceleration (cell D5) using r. Recall a = GM/r2. You have calculated GM earlier in cell B1. In cell D6, add the formula =($B$1/C6^2). The $ tells Excel that the cell is a reference that must not change. Highlight cell D6 and fill down to row 52. 15. You must now calculate the x and y components of acceleration. It is best to visualize these as a triangle as below: (a) ion t a ler ce r Ac

x

ax

1. From the diagram we see that ax/a = –x/r and ay/a = –y/r. By rearranging these equations we can calculate ax and ay:

y

ay

2. ax = a x (–x/r)

3. ay = a x (–y/r)

4. Note that acceleration is opposite to the directions of x and y (thus –x and –y).

16. You can now add these formulae to the cells for ax and ay. In cell E6 add the formula =-D6*(A6/C6). In cell F6, add the formula =-D6*(B6/C6). Highlight cells E6 and F6 and fill down to row 52. 17. Now you need the initial velocity of the satellite. In cell G6 (velocity in x direction) enter the number 0 (no movement). In cell H6 (velocity in y direction) enter the formula =B3 (our initial velocity entered earlier).

18. This completes the first row of the calculations for the position of the satellite.

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19. The second row calculates the changes that occur as the planet moves from its initial position to its next position. Now that you have calculated acceleration, you can calculate that change in velocity from the initial condition. Recall that a = v/t, so v=at. You know a for both x and y coordinates, t is the time between each calculation (the time step). In cell G7, add the formula =G6+E6*$B$2. This adds the change in velocity to the initial velocity to provide the new velocity at the satellite's next x position. In cell H7, add the formula =H6+F6*$B$2. This does the same for the next y position. Highlight cells G7 and H7 and fill down to row 52

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20. You can now calculate the next x and y positions of the satellite and complete the part of the spreadsheet that plots the orbit. Recall that v = d/t and d = vt. Again you know vx and vy and t is the time step. In cell A7, add the formula =A6+G7*$B$2. In cell B7, type =B6+H7*$B$2. These formulae calculate the change in position in the x and y direction (the distance d) and add them to the initial x and y position. Highlight cells A7 and B7 and fill down to row 52.

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Formulae

Results

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21. You can now switch the spreadsheet back to showing the numbers rather than formulae. The first few rows of your spreadsheet should look like the screen shots below. If they don't, recheck your entries.

22. Now you can plot the x and y positions on a scatter plot. Select all the x and y data points. Click Insert > chart and select a scatter graph without lines. If you have done everything correctly your plot should produce an ellipse (right).

23. There are now a few last formulae to enter into the spreadsheet to improve its function. To start, you will make a calculator that calculates a (the semi major axis) if T (the period) is entered. To make this simple, we will enter p as hours (e.g 1.5 h) and calculate seconds. In cell J2, type the heading p(hr). Below that, in cell J3, type the heading p(s).

24. In cell K1, type the heading Input p Below that, in cell K2, type 1.5 In cell K3, type the formula =K2*60*60.

25. Now in cell K6 type the heading a. Below that, in cell K7, type the formula =IF(K3=0,0,(((B1*(K3^2))/(4*PI()^2))^(1/3)-6371000)). Be careful with entering this. It uses Kepler's third law to calculate a and removes the radius of the Earth to provide the altitude in meters. The IF statement stops a negative altitude being shown. In cell K8, type the formula =K7/1000. This turns meters into kilometers for easy reference. 26. In cell L7, type m (meters). In cell L8, type km (kilometers).

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28. Finally we can add a formula that will look through the data to find if the satellite crashes into the Earth. Remember, the Earth is very large and the satellite may orbit just a few hundred kilometers away. If it gets too close it will crash into the ground rather than stay in orbit. In cell K13 Type the formula =COUNTIF(C6:C52,"<6371000"). This looks at the range of r to see if it is less than the radius of the Earth. If it is a number is returned for each time. This means the satellite has crashed.

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27. You also need to calculate the orbital velocity so that this can be entered into B3. You will use the formula or circular velocity: v = â&#x2C6;&#x161;GM/r.. In cell J11 type the heading vi. In cell K11 type the formula =SQRT(B1/A6).


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29. Lastly (just for fun) in cell K14, type the formula =IF(K13>=1,"CRASHED",""). If a number is returned in K13 then this formula will make the word "crashed" appear. 30. It is worth coloring these cells so that this block of formula stand out.

31. The spreadsheet should now be ready for testing. In cell K2 input the number 24. Cell K3 should show the number 86400, the number of seconds in 24 hours. Cell K7 should show the number 35869537.05 and K8 should show 35869.53705.

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32. Now in cell F2 (altitude) enter the altitude in meters from K7. The cell K11 should show the number 3071.818539 and the plot should show the satellite flying off into space.

33. Enter the number from K11 into cell B3, the initial velocity. The plot should return to a circle but with larger numbers than earlier. This shows the orbit of a geosynchronous satellite. 34. One last test. Reduce the velocity in B3 to 500. The plot should dive steeply to the left and CRASHED should appear in cell K14. If this happens you are now ready to test the orbits of satellites. If not, go back and check your programming. SAVE YOUR SPREADSHEET

Whoops! That was costly.

23. Set the altitude of the satellite to 500,000 meters. Check the velocity in cell K11. Enter this into cell B3.

(a) For a satellite at this altitude, how many hours does it take to orbit the Earth?

(b) What happens if the velocity is reduced to 5000 m/s?

(c) What happens if the velocity is increased to 9000 m/s?

(d) Return the satellite to its initial velocity. Now reduce the altitude to 400,000 m. Describe the result:

24. An astronomy team wants their satellite to orbit the Earth once every twelve hours. (a) At what altitude would the satellite need to be?

(b) What would its velocity be for a circular orbit?

(c) The rocket putting the satellite into orbit does not quite reach the velocity required because of a miscalculation and inserts the satellite into orbit at 3500 m/s. What is the result?

(d) The astronomy team uses some of the satellite's onboard thrusters to boost its speed, but a fuel pump fails to shut down correctly and the satellite's velocity is boosted to 6000 m/s. What happens to the satellite?

(e) What is the satellite's final plotted distance from Earth (the radius)?

(f) The team try to rescue the satellite. Use the radius (r) to work out the velocity the satellite needs in order to return it to a circular orbit:

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25. (a) Set the altitude to 36,000,000 m. What velocity does the satellite need to have to maintain a relatively circular orbit?

(b) Imagine the Earth had twice the gravity it does now. You can do this in the spreadsheet by setting the Earth units to 2. Recalculate the velocity the satellite needs to be moving at to maintain circular orbit:

(c) At what altitude does the satellite need to be to have a geosynchronous orbit?

26. The spreadsheet can be modified to plot the orbit of the Earth and other planets around the Sun. (a) The Earth units need to be set to 333,333 (the number of times more massive the Sun is that the Earth). Note: There is also another way of producing the mass of the Sun, can you work out what it is?

(b) Altitude simply needs to be scaled up (i.e. the distance from the Sun to the Earth is 150 billion meters).

(c) The time step needs be modified to =F3/365.

(d) You need to modify the number of points plotted on the graph to 365 points.

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(e) What modifications can be made to make the spreadsheet more accurate or able to display a greater range of data? Can you get the plot to show just one point at a time? Or plot two or satellites or planets at the same time? Try making some modifications and see what happens. 27. The online simulation PhET Gravity and Orbits (see the BIOZONE Resource Hub for the link) is a simple program that models the orbits of the Earth-Moon-Sun system and can vary the size of the star and planet.

(a) Open the program and choose the Model option. You can view the vectors for velocity and gravity by clicking on the check boxes. You can adjust the length of the arrows by clicking and dragging them with the mouse. Select the Earth-Sun system if it is not already selected. View the velocity and gravity vectors. Click play. While the simulation is going, increase the mass of the Earth to 2.0. What happens?

(b) Now set the Earth's mass to 0.5. What happens?

(c) Reset the Earth's mass to 1. Set the Sun's mass to 2.0. What happens now?

(d) Explain the result of (a) and (b), and (c):

(e) Set the system to show the Earth-Moon-Sun system. Click the path check box, then click play. Observe how the Moon orbits the Earth and the paths they take. There is something not quite right with this simulation. Can you describe what it is?

(f) Click on the velocity check box to see the vectors for velocity. Explore the effect of increasing the Moon's velocity and position. Try changing the parameters of the orbit and speed. Can you set up another stable system? Run the system for many years to see what happens in the long term.

(g) You can also set the simulation to show a satellite orbiting the Earth. Try comparing the parameters for this simulation to that of the spreadsheet. What are the similarities and differences? Can you get the satellite into a geosynchronous orbit (taking 1440 minutes)?

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14 Electrostatic Force

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70

ENGAGE: Zap!

`` Ever got out of a car, gone to close the door and received an

electric shock? What about taking off a polar fleece sweater or jacket? Try it in a darkened room and you will see sparks flash as the jersey rubs against the material of your shirt. What about lightning? What causes that? Study the photo of the little girl's hair (right) What's causing that to happen?

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1. What do you think is causing these phenomena? Where does the electricity come from? Discuss your ideas with others in your class and write down a summary of these ideas:

EXPLORE: Balloon electrostatics

`` Balloons are well known for producing some interesting electrostatic effects:

INVESTIGATION 2.5: Balloon electrostatics

See appendix for equipment list.

1. In a still, warm room, fully inflate a balloon and hang it from the ceiling or an insulated support with nylon thread or fishing line.

2. Rub the balloon with a piece of wool/synthetic material or a sweater so that it becomes charged. 3. Predict what will happen if you bring the material or sweater used to rub the balloon near the balloon.

4. Carry out step 3 and record your observations:

5. Fully inflate a second balloon and hang it from the ceiling with more nylon fishing line near the first balloon. 6. Rub both balloons with the same material (wool/synthetic fabric or a sweater). This should give the balloons a charge of the same sign and a similar amount.

8. Carry out step 7 and record your observations:

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7. Predict what will happen to these similarly charged balloons as they hang near each other.

PS2.B

P

SPQ

SSM

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9. Leave the balloons hanging near each other for a few minutes. Record any changes that take place:

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INVESTIGATION 2.6: Threading the needle

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See appendix for equipment list.

1. Try threading a standard sewing needle with thin plastic thread (such as from a thread of plastic string). Keep trying! 2. Now thread the needle with normal cotton thread of the same thickness. Was it easier?

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2. (a) What happened when you tried to thread the needle with plastic thread?

(b) What happened when you tried to thread the needle with cotton thread?

(c) Suggest why there was a difference in how the threads behaved while being threaded:

`` Electrostatics are part of a wider group of non-contact forces called electromagnetism. They push or pull on objects without touching them. Electrostatic forces occur when charged objects interact with objects around them.

`` Charge exists as two kinds (positive and negative) and is the basic ingredient of all electricity. Electricity divides into two general areas: (i) static electricity (or electrostatics) is about stationary accumulations of charge (ii) current electricity, which involves a continuing flow of charged particles (usually negative electrons).

`` Charge is present in all the materials around us, but we are usually unaware of it because most of the positive and

negative charge is balanced and evenly spread. The balance can be "disturbed", e.g. by rubbing materials together. This usually results in electrons being transferred from one material to another. The material gaining the electrons is then said to be negatively charged while the material losing the electrons is said to be positively charged.

`` Objects with like charges repel each other while objects with opposite charges attract each other. 3. For each situation below, state whether the balloons will repel or attract each other:

+

+

+

+

+

+

+ + + +

– + + –+ – – – + – + – +

(b)

+

(c)

+

+ + + + + + + +

– – – – – – – – – – –

+

+

+ +

+

+

+

+

+

+ +

+ + + +

(d)

+ + + +

+

–– – – – – – – – –

–– – – – – – – – –

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(a)

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4. A student rubs a balloon with silk to create a charge on the balloon's surface, then brings the balloon near some small pieces of tissue paper. Predict what will happen to the tissue paper and explain your prediction. Try it and find out:


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EXPLORE: Coulomb's force and the inverse square law

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`` In 1785, French physicist Charles-Augustin de Coulomb published an equation to explain the force between

electric charges (known as Coulomb's law). It stated the magnitude of the electrostatic force between two charges is proportional to the product of the charge magnitudes (their size) and inversely proportional to the square of the distance between them. Coulomb's constant: 8.99 x 109 Nm2/C2*

Force between charges

q1q2 r2

Charge on particle 2

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F=k

*Newton meters squared per coulomb squared.

Charge on particle 1

Distance between charges squared

`` Unlike gravity, which is always attractive, electrostatic force forces are either attractive (if the charges are opposite) or repulsive (if the charges are the same).

`` Note the similarity between the Coulomb’s law and Newton’s law of gravitation:

F=G

M1M2 r2

`` Recall that the effects of gravity decrease over distance, where the strength of gravity is inversely proportional to

the square of the distance between the objects. We can now see that same relationship for electromagnetic forces in Coulomb’s equation.

INVESTIGATION 2.7: Observing the inverse square law

See appendix for equipment list.

1. With a black marker pen, make a dot about 2 cm in diameter on a deflated balloon. Make the dot as round and as uniform as possible.

2. Measure the diameter of dot and calculate its area. Use the formula for the area of a circle: A = πr2 (remember to divide the measured diameter by 2 to get the radius before you make your calculations). 3. Record the area of the dot in the table below. Record the intensity of the dot's color using a scale 0-10 (0 being transparent and 10 being the original opacity of the dot).

4. Partially inflate the balloon, measure the dot again, and calculate its area. Record its intensity (0-10).

5. Continue inflating the balloon one or two breaths at a time, measuring the dot and calculating its area each time. Record the intensity of the black of the dot each time using your 0-10 scale. Dot area (mm2)

Color intensity

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Dot radius (mm)

5. (a) What is the effect on the intensity of the dot's color as the dot's area increases?

(b) Predict what you would observe about the dot as you continue to inflate the balloon (assume there is no upper limit to how large the balloon can get):

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EXPLAIN: More on the inverse square law

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`` When using equations involving the inverse square law, it is important to understand what effect changes to any variable in the equation have on the final force.

`` Let us return to Newton's law of gravitation and see how the inverse square law applies to it before further studying Coulomb's law.

6. (a) Use Newton's law of gravitation to calculate the force in newtons (N) acting between two masses at a distance (r) of 2 m. M1 = 10 kg, and M2 = 10 kg. Recall that G = 6.673 x 10–11 Nm2 /kg2.

(b) Now double the mass of M2 (20 kg). Recalculate the force acting between the two objects:

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(c) What happened to the magnitude (size) of the force between the two objects when the mass of M2 was doubled?

`` We can show what happens to the magnitude of the force when one mass is doubled without actually doing a numerical calculation. Instead we can use algebra to prove the result:

`` First, we add a subscript to the force (F), to designate a specific value: F1 = G `` Double the mass for the 2nd object: F2 = G `` Rearranging the equation, we get: F2 = 2G `` Substituting F1 for G

M1 M2 r2

M1 2M2

r2 M1 M2

since F1 = G

r2 M1 M2 r2

M1 M2 r2

(note: the subscript 2 on the force indicates a different value than from the first equation).

we get: F2 = 2F1.

`` The resulting force from doubling the mass of one object doubles the force acting between the objects.

7. (a) Using the result from 6. (a) above we can also compare how changing the distance (r) between them affects the force. Again M1 and M2 are 10 kg but r will now be 4 m. Recalculate the force acting between the two objects:

(b) What happened to the magnitude (size) of the force between the two objects when r was doubled?

`` Again we can show the effect calculated above using some algebra and rearrangement of the equation. This time: F2 = G

M1 M2 (2r)2

`` First we must expand the brackets involving the radius: F2 = G `` And rearrange to solve in units of G: F2 = ¼G

M1 M2 r2

M1 M2 22r2

=G

. Substituting F1 for G

M1 M2

4r2 M1 M2 r2

we get: F2 = ¼F1.

(b) What happens to the force if the mass of both objects is doubled?

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8. (a) What happens to the force if you triple the mass of one or other object?

9. (a) What happens to the force if the distance between the two objects is tripled?

(b) What happens to the force if the distance between the two objects is halved?

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10. The inverse square law also applies to the amount of illumination provided by a source that is a "single" point of light. The Earth is approximately 150 million km from the Sun, whereas Mars is approximately 228 million km from the Sun. (a) How would the light intensity of the Sun differ on Mars compared to Earth?

(b) Calculate the approximate difference in the Sun's light intensity on Mars compared to Earth:

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`` The rearrangement of the equations for gravity on the previous page apply in the same way to Coulomb's law, we simply use different notation (k instead of G for example). The questions below refer to Coulomb's law.

11. (a) What happens to the force when one of the charges is doubled?

(b) What happens to the force when the distance between the charges is doubled?

(c) What happens to the force when both charges are doubled AND the distance between the charges is doubled?

(d) What happens to the force when one of the charges is quadrupled AND the distance between the charges is doubled?

12. What can you say about the way in which Newtonâ&#x20AC;&#x2122;s law of gravitation and Coulombâ&#x20AC;&#x2122;s law work?

`` Unlike the equation for gravity, which only ever deals with positive numbers, Coulomb's law may deal with positive and negative numbers (e.g. positive charge and negative charges). This means we may get answers that are positive or negative.

13. Use Coloumb's law to answer the following:

(a) Is the force produced positive or negative when two positive charges are brought together?

(b) Would these charges attract or repel each other?

(c) Is the force produced positive or negative when two negative charges are brought together?

(d) Would these charges attract or repel each other?

(e) Is the force produced positive or negative when a positive charge and negative charge are brought together?

(f) Would these charges attract or repel each other?

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14. What can be said about the sign (positive or negative) in front of the force value in relation to charges attracting or repelling each other?

`` Coulomb's law is important in understanding how charged particles interact. For example, why does the compound sodium chloride have a different melting point to lithium fluoride? We can answer this if we know a little about the charge the particles carry and the distance they are apart from each other.

`` The particles in sodium chloride and lithium fluoride are called ions. To understand their properties we must first

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understand the structure of the atoms from which they originate. We will explore this in the following activity.

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15 Atomic Structure and Bonding

ENGAGE: Atomic models

`` Atoms are depicted in many different ways in books or on the internet. Sometimes this is done to make the atom shown easier to understand. At other times, it is simply an artistic exercise.

PR E O V N IE LY W

1. In the space below, choose six models or depictions of atoms in books or on the internet. Draw them or print and paste them into the space below. Describe the similarities and differences between them:

EXPLORE: Atomic structure

`` Earlier we studied how charged objects interact. Objects carrying charge of the same sign repelled while objects

carrying charge of the opposite sign attracted. To understand the origins of the charge carried by different materials we need to examine the atoms they are made from.

`` An atom is composed of three types of subatomic particles: positively charged protons (+) found in the nucleus, neutral neutrons (0) found in the nucleus, and negatively charged electrons (â&#x20AC;&#x201C;) orbiting the nucleus.

`` Although electrons and protons are vastly different in physical size, the charge they carry is equal in size but opposite in sign.

`` Atoms are neutral. They have no overall charge because they have equal numbers of protons and electrons. `` A difference between the number of protons and electrons in an atom will result in the atom having an overall charge.

Electron Negatively (â&#x20AC;&#x201C;ve) charged

`` Protons are secure in the nucleus and remain constant in any one type of atom (element, e.g. carbon). Changing the number of protons changes the element (e.g. removing a proton from carbon produces boron).

Neutron No charge

`` In contrast, electrons can be lost or gained under certain conditions.

`` Gaining or losing electrons causes an

`` We will save the workings of the

nucleus for a later chapter. To understand electrostatics, we need to concentrate on understanding electrons.

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Nucleus

overall negative or positive charge in the atom, producing an ion.

Proton Positively (+ve) charged

`` Electrons are found in shells. The

1st electron shell

higher the atomic number, the more electrons and shells an atom has.

2nd electron shell

SC

SF

SPQ

P

PS2.B

PS1.A

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76 Electrons

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`` Electrons are the negatively charged particles of the atom. Together, all of the electrons of an atom create a negative charge that balances the positive charge of the protons in the atomic nucleus.

2. (a) If a neutral atom has 18 protons how many electrons would it have?

(b) If a neutral atom has 10 protons how many electrons would it have?

3. What would happen to the charge of an atom if it were to: (a) Lose an electron?

(b) Gain an electron?

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4. (a) If an atom had 3 protons but only 2 electrons how would this atom be affected?

(b) If an atom had 16 protons but 18 electrons how would this atom be affected?

EXPLAIN: Electrons, atoms, and ions

`` The electrons dictate the chemical behavior of an atom, and most importantly it is the electrons in the outer shell

(the valence shell) that are gained or lost when an atom becomes an ion. The electrons in the valence shell also take part in chemical reactions.

`` Electrons are arranged around an atom's nucleus in specific ways (below). Electron shells only hold a certain

number of electrons. The first shell can hold 2 and the second and third can hold 8 each. The diagram below shows an atom with 20 electrons.

1 Two electrons are

3

found in the 1st (inner most) electron shell.

Any remaining electrons are added to the 4th electron shell.

Nucleus

Electrons have a property called spin (either up or down). When an orbital is more than half full of electrons, the electrons pair up, cancelling out the spins.

Although electrons are often shown neatly aligned (as in the diagram left) in reality that is not the case. Electron shells represent places where there is a probability of the electron being found. The diagram below shows the electron cloud for the inner most electron shell.

2 A maximum of eight

electrons are found in the 2nd and 3rd shells.

Nucleus

Electrons are most likely to be found here

`` Atoms with full valence shells are chemically stable (e.g. helium). They do not undergo chemical reactions. An atom

without a full valence shell will undergo a chemical reaction in order to obtain a full valence shell. During the reaction electrons may be gained, lost, or shared between atoms, depending on the number of electrons in the valence shell.

6. Use the diagram above to predict the following:

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5. What is the valence shell of an atom?

(a) Will lithium (3 protons) gain or lose electrons in a reaction?

(b) Will chlorine (17 protons) lose or gain electrons in a reaction?

(c) How reactive would you expect an atom with 18 electrons to be?

(d) How many electrons would oxygen (8 protons) need to gain to become stable?

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Forming ions `` Remember neutral atoms have equal numbers of electrons and protons. Since the number of protons in an atom does not change, fewer or extra electrons can create a charged atom called an ion.

`` Cations have fewer electrons than the original neutral atom and therefore have an overall positive charge. `` Anions have more electrons than the original neutral atom and therefore have an overall negative charge.

`` Ions are not the same as the neutral atom. They have different properties due to carrying a charge and so behave differently.

PR E O V N IE LY W A cat-ion

An-ion

During a sodium/ chlorine reaction an electron is exchanged.

Sodium

Chlorine

Wilco Oelen Creative Commons Attribution-ShareAlike 3.0 Unported License. http://woelen.homescience.net/ science/index.html

atom. The sodium atom loses an electron, which is donated to the chlorine atom. The sodium atom now has one less negative charge than positive charges and so becomes a positive ion. The chlorine atom gains one extra negative charge and so become a negative ion.

Drawings F.Hicks

`` In the example below, a sodium atom reacts with a chlorine

Chlorine reacting with sodium

7. Explain why sodium loses an electron during a reaction:

8. Explain why chlorine gains an electron during a reaction:

9. (a) Draw a diagram showing the magnesium ion (12 protons) (as above):

(b) Draw a diagram showing the oxide ion (8 protons): (as above)

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10. In Investigation 2.5, when we rubbed the balloon with the wool/synthetic fabric, what was happening with the electrons between the two materials to produce the reactions we observed?

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11. Over time, the charges dissipated. What was happening with the electrons for the materials to neutralize?


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EXPLAIN: Atoms, ions, and the periodic table

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`` The periodic table is arranged in a specific way so we are able to gain a lot of information about an atom of an element just by looking at its position in the table. Group

Period

Non metals

Metals

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Atomic number (= number of protons = number of electrons)

Lanthanoids Actinoids

`` Elements are arranged numerically based on the number of protons in an atom of that element’s nucleus (hydrogen has one proton, helium has 2, carbon has 6, and oxygen has 8 for example).

`` Elements are arranged in rows called periods which tells us how many electron shells the atoms have (the 1st period has one electron shell, the 2nd period has two, the 3rd has three and so on).

`` Elements are arranged in columns called groups. All the atoms in a group have the same number of electrons in their valence shell.

`` Elements on the left side of the periodic table (the metals) become positively charged ions (cations) and elements on the right side (the non metals) become negatively charged ions (anions).

12. (a) The atoms in group 1 of the periodic table form an ion with what charge?

(b) The atoms in group 2 of the periodic table form an ion with what charge?

(c) The atoms in group 17 of the periodic table form an ion with what charge?

(d) The atoms in group 16 of the periodic table form an ion with what charge?

(e) Would you expect the elements in group 18 to form ions? Explain:

`` The number of valence electrons determines whether the atom is likely to gain or lose electrons to achieve a full valence shell.

`` The fewer valence electrons an atom has, the more likely it is to give up an electron. 13. Which would you expect to be more reactive: Sodium or magnesium? 14. Complete the following paragraph about chlorine by filling in the blank spaces:

Chlorine has an atomic number of _____. It has ____ protons and _____ electrons. The first orbital around chlorine’s

nucleus has _____ electrons, the second has _____ electrons, and, the third orbital has______ electrons for a total of _____ electrons. When chlorine forms an ion it will ________ __________________ ion.

______ electron to become a

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`` The closer the atom is to having a full valence shell, the more likely it is to gain an electron.

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EXPLAIN: Bonding and electrostatics

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`` Atoms are rarely found on their own. In fact only the noble gases (group 18 elements He, Ne, Ar, Xe, and Rn) are found as single atoms. This is because they have full valence shells are do not need to react with other atoms to gain or lose electrons.

`` Other atoms react together to form complete valence shells. During the reaction, the atoms form bonds that hold the atoms together. These bonds are between atoms in the same molecule (or compound) so they are called intramolecular bonds.

`` Intramolecular bonds may be ionic (formed by ions), covalent (atoms sharing electrons), or metallic (metal atoms bound by mobile electrons).

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Ionic bonds `` To study an ionic bond, we will use the reaction of sodium metal and chlorine gas as an example. When a sodium atom reacts with a non-metal atom it forms a sodium ion (Na+). It has one less electron than its atomic number.

`` The sodium ion now has only 10 electrons. It has a complete valence shell and the same number of electrons as neon (Ne), but it behaves very differently because it has a positive charge.

`` Because it is positively charged, other electrically charged atoms (ions) of the opposite charge (negative) have a

Wilco Oelen Creative Commons Attribution-ShareAlike 3.0 Unported License.

Wilco Oelen Creative Commons Attribution-ShareAlike 3.0 Unported License.

natural attraction to the sodium, e.g. the chloride ion formed when chlorine gains an electron. Together the sodium ion and chloride ion form sodium chloride (NaCl), table salt (below).

In its pure form, the element sodium is a silvery metal. Its atoms share their mobile electrons and are held together by metallic bonds. It is a very reactive metal.

Sodium chloride (table salt) is a highly stable, non-toxic crystal made of sodium and chloride ions held together by ionic bonds.

Chlorine is a gaseous element with a yellow tinge. In its pure form, the atoms are found covalently bonded together in pairs. Chlorine is highly toxic and reactive.

`` The positively charged sodium ion can combine with any ion with a negative charge. Together, ions of opposite

charge balance out the charges created by the loss and gain of the electrons in the atom. Much like negatively charged electrons balance their positively charged proton counterparts, positively charged cations balance their negatively charged anion counterparts.

15. (a) Positive ions are attracted to ___________________ ions.

(b) A cation with a charge of 2+ would need ____ anions with a charge of 1– or one anion with a charge of _____ to balance its total charge.

(c) A Mg2+ ion needs _____ Cl– ions or _____ O2– ion to balance its 2+ charge.

16. (a) Predict what would happen if two lithium ions were near each other:

(b) Predict what would happen if two fluoride ions were near each other:

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17. Predict what would happen if a lithium ion were near to a fluoride ion:

18. Use electrostatics to explain the differences between the behavior of the ions in Q16 and Q17 above:

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19. A crystal of sodium chloride has a ratio of 1 Na+ ion to 1 Cl– ion. What would the ratio of Al3+ to O2– ions be in a crystal of aluminum oxide?


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20. Coulomb's law can be used to explain differences in the strength of ionic bonds. Consider the two ionic substances MgO and NaCl. The melting point of MgO is 2852°C whereas the melting point of NaCl is 801°C. Use Coulomb's Law to explain why there is such a large difference between the melting points of NaCl and MgO:

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Covalent bonds

`` Covalent bonds are formed when non-metal atoms share one or more pairs of electrons. Remember, non-metals want to gain valence electrons to reach a stable arrangement. If there are no metal atoms around to give them electrons, non-metal atoms share their valence electrons with other non-metal atoms.

`` Since the atoms are using the same electrons they are held together in a neutral particle called a molecule, e.g. two oxygen atoms share electrons in an oxygen gas molecule. A molecule is a neutral particle of two or more atoms covalently bonded together.

`` Molecules may contain atoms of the same element such as N2, O2, and Cl2, or they may contain atoms of different elements like H2O, NH3, or C6H12O6.

`` Covalent bonds form when atoms have similar electronegativities (so electrons are shared, rather than gained or lost to form ions). The covalent bonds in an individual molecule are very strong compared to the bonds between those molecules in a substance, so covalent compounds tend to be gases, liquids, or low melting point solids. However, some covalently bonded substances (such as diamond and quartz) form covalent networks, which are very strong.

`` The electrons in covalent bonds are not always shared evenly between atoms. Some atoms attract electrons more than others. This means that, in a molecule, electrons may spend more time around one atom than others. This results in polar covalent bonds.

`` Molecules with polar covalent bonds can be non-polar overall if they have a symmetrical shape e.g. CO2. Molecules that are not symmetrical will have a polarity, e.g. water (H2O). d+

e- e-

ee-

O

e- e-

d–

e- e-

e- ee- e-

O

ee-

e- e-

Non-polar molecule: Both oxygen atoms attract the electrons with the same force. Electrons are shared evenly. There is no polarity in the bond or the molecule.

e- e-

O

e- e-

d–

e- ee- e-

e- e-

C

e- ee- e-

O

e- e-

Non-polar molecule. Oxygen attracts the electrons more than carbon, so each C=O bond is polar. However the molecule is symmetrical and so the molecule is non-polar overall.

d–

ee-

e- e-

O

e- e-

H

d+

H

d+

ee-

Polar molecule: The oxygen atom attracts the electrons more than the hydrogen atom. Electrons are shared unevenly resulting in a slightly negative (d–) end and a slightly positive end (d+) (a dipole).

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21. Imagine two substances made of molecules of roughly the same size. One substance is polar and the other is non-polar. Use your knowledge of electrostatics and the information about covalent bonds above to predict which one would have the higher melting point. Explain your answer:

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22. Covalent bonds require a lot of energy to be broken. What is happening to the molecules in a molecular substance (such as propane, methanol, or water) when it melts or boils? What bonds or forces are being overcome?

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INVESTIGATION 2.8: Polarity

See appendix for equipment list.

1. Fill a 50 mL burette with distilled water. Fill another burette with cyclohexane. 2. Rub a glass rod with a silk or polyester towel. This removes electrons from the glass.

3. Turn on the burette containing water so that it flows into a beaker. 4. Hold the rod close to the burette and observe the effect.

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5. Repeat with the burette of cyclohexane and observe the result.

23. (a) What was the effect of holding the rod close to the stream of water?

(b) What was the effect of holding the rod close to the stream of cyclohexane?

(c) Now look at the structure of water and the structure of cyclohexane below. Use your knowledge of electrostatics to explain (a) and (b) above:

Water

Cyclohexane

Metallic bonds

`` Metallic bonds form between multiple metal atoms. Most metal

atoms have only one or two valence electrons and these are not tightly bound to the atoms. In a piece of metal, these loosely held valence electrons do not belong to any single one of the atoms but are able to move freely through the structure from one atom to another.

`` Metals can be thought of as positive ions (all of the atom except the valence electrons) in a “sea” of loose (delocalized) valence electrons. The mutual attraction of each metal atom to the others’ valence electrons forms the metallic bond.

`` The metal ions line up in a regular repeating pattern (a crystal lattice) and their loose valence electrons move through this crystal acting as an electron glue. Each of the ions is strongly attracted to all of the loose electrons surrounding it so the whole metal holds together as a crystal.

Gold is particularly valuable metal

`` While the attraction between the "electron glue" and the ions is strong, the attraction between the ions themselves has some "flexibility" (unlike the ionic bond between a sodium and chloride ion which is very rigid).

(a) Electrical conductivity:

(b) Conductivity of heat:

(c) The ability of metal to be shaped (its "malleability" and its "ductility"):

(d) The melting points of metals:

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24. From the information above predict the following properties of metals:


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EXPLAIN: Intermolecular forces

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`` Molecules interact with each other via intermolecular forces. These are very weak compared to the intramolecular forces that bond the atoms within molecules together.

`` Collectively intermolecular forces are called van der Waals forces. Two important van der Waals forces are hydrogen bonding and induced dipole-dipole forces.

Hydrogen bonds

Induced dipole-dipole forces

`` When hydrogen forms a covalent bond with either

`` Electrons are always in motion around an

atom, even in atoms covalently bonded to other atoms. The motion is random and this results in instances where there are more electrons on one side of the molecule than another. This results in a slight polarity from one side of the molecule to the other (below).

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oxygen, nitrogen, or fluorine, those atoms attract the electrons much more than the hydrogen, producing a polar covalent bond. The dipole that forms allows other similar molecules to be attracted. Hydrogen bonds are the strongest intermolecular force.

d+

Hydrogen

Hydrogen bond between d– oxygen and d+ hydrogen

Cl

Cl

d–

Even distribution of electrons

d–

Cl

Cl

d+

Instantaneous uneven distribution of electrons

`` The instantaneous dipole can affect nearby molecules, so that they also form dipoles, resulting in temporary attractions between the molecules (below):

Polar covalent bond

Oxygen

d+

d–

d–

d+

d–

Water molecule

d+

d–

d+

d–

d+

d–

d+

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Scientists have been inspired by the gecko's feet to create dry glues that can be used multiple times or sticky pads that can be used to hold objects to a wall. In 2014, scientists at Stanford University created an adhesive device the size of a human hand and based on gecko's feet, that allowed a 70 kg man to climb a vertical glass wall (right).

Biomimetics and Dexterous Manipulation Lab, Stanford University

Van der Waals forces play an important role in sticking things together. The ability of geckos (above) to walk up seemingly smooth surfaces is due, in part, to van der Waals forces. The small effect is multiplied millions of time over by the microscopic hairs on the gecko's feet.

Biomimetics and Dexterous Manipulation Lab, Stanford University

25. Explain why water is a liquid at 25°C but oxygen must be cooled to less than –183°C before it forms a liquid:

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16 Magnetism

ENGAGE: Magnetism

`` Like gravitational forces and electrostatic forces, we find that magnetic forces also act at a distance. We will explore

this further in this activity. You will probably have some idea about what magnets are. It is very likely you have some on your refrigerator at home holding up pictures and lists.

1. Why donâ&#x20AC;&#x2122;t magnets stick to standard drywalls?

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2. Why are magnets attracted to some things and not others?

`` Many people think magnets are attracted to all metals, but that is not necessarily true.

INVESTIGATION 2.9: What is affected by magnets?

See appendix for equipment list.

1. You will need the following materials: aluminum foil, pure iron, pure copper, paper clips, copper penny, a nickel or dime (or other "silver colored" coins), stainless steel, brass, minerals (such as quartz, hematite, calcite, pyrite etc.), other materials, including pvc plastic, styrofoam, wood, paper etc. 2. For each material predict what will be attracted to the magnet before you test it. Fill in the table below with your prediction and the actual result:

Result: attracted / not attracted

Reason

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Prediction: attracted / not attracted

P

PS2.B

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Material

PS1.A


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3. Separate the items into two piles based on if they are attracted to the magnet or not. What observations can you make about the objects attracted to the magnet?

EXPLORE: Magnets and charge

`` In investigation 2.8 you explored electrostatic charges. These attract or repel each other. Can these charges

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interact with magnets in the same way?

INVESTIGATION 2.10: Charges and magnets

See appendix for equipment list.

1. Rub a plastic ruler with wool and balance it on a small bottle lid.

2. Now rub a second ruler and bring the rubbed end of this second ruler near to the rubbed end of the first ruler. Observe the result. 3. Rub the first ruler with wool again, and again balance it on the small bottle lid. Bring the wool used to rub the ruler near the rubbed end of the ruler. Observe the result. 4. Now bring a magnet near the rubbed end of the ruler balancing on the bottle lid and observe the result. Try both ends of the magnet. 5. Try rubbing the ruler again with the wool and reintroduce the magnet.

4. (a) What happened when the rubbed end of the second ruler was brought close to the rubbed end of the ruler balancing on the bottle lid?

(b) What can you say about the two ends of the rulers based on this observation?

(c) What happened when the piece of wool was brought close to the rubbed end of the ruler balancing on the bottle lid?

(d) How did the rubbed end of the ruler and the magnet interact?

EXPLORE: More on magnets

`` Magnets are interesting in that they affect certain materials without actually touching them. Other objects, such as

the Sun also affect objects without touching them. In the case of the Sun, gravitational force affects another object. In the case of magnets, it is magnetic force that affects other objects.

5. Magnets have a north (N) and south (S) pole. The diagrams below show various alignments of magnets. Predict how these magnets will behave:

N

S

N

N

S

S

N

S

N

S

N

(a)

S

N

S

(b)

(c)

(d)

6. Describe what you would feel If you were to push two south poles together:

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S

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N

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INVESTIGATION 2.11: Magnetic fields

See appendix for equipment list.

1. Place an index card (or ruled card) in a clear sandwich bag and then place a teaspoon of iron filings into the bag.

2. Lay the sandwich bag down on the bench and gently shake the bag back and forth so there is a thin layer of iron filings on the index card. Sketch what you see in the appropriate box below. 3. Carefully lower the center of the sandwich bag on top of a bar magnet. Sketch what you see in the appropriate box below.

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4. Place a second bar magnet under the sandwich bag, lining up the two like poles opposite each other and sketch what you see in the appropriate box below. 5. Finally, reverse the second bar magnet, lining the two opposite poles and again sketch what you see. Iron filings with no magnet

Iron filings with 2 magnets (like poles aligned)

Iron filings with one magnet

Iron filings with 2 magnets (opposite poles aligned)

7. (a) How would you explain the patterns of iron filings you see when there is a magnet in place?

(b) What do the patterns reveal about attraction and repulsion between the magnets?

(c) How do the patterns of the iron filings relate to the magnetic field of the bar magnet?

(d) What happens to the pattern of iron filings when two like poles are placed next to each other?

(e) What happens to the pattern of iron filings when opposite poles are placed next to each other?

(f) Can you tell by the patterns where the force of the magnetic field is strongest? Weakest?

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86 `` You have just observed magnetic field lines produced by a

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magnet acting on iron filings through a plastic sandwich bag and index card. Like gravitational fields, magnetic fields can pass right through materials and affect objects on the other side.

`` How is the strength of a magnetic field affected by the distance from the magnet? Is it the same at any distance? Does it get less or more?

`` From the result of placing the iron filings around a magnet earlier, you should be able to guess the answers.

INVESTIGATION 2.12: Strength of a magnetic field

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See appendix for equipment list.

1. Place a piece of paper between a magnet and a metal paper clip. One at a time, continue placing additional pieces of paper in between the magnet and the paper clip.

2. Record how many pieces of paper can be placed between the magnet and the paper clip before the magnet no longer affects the paper clip.

8. (a) Why does the magnet attract the paper clip even though it is not in direct contact with the paper clip?

(b) How does the magnetic force acting on the paper clip change as you increase the number of pieces of paper between the magnet and the paper clip (what can you say about the effort it takes to pull the magnet and paper clip apart as the number of pieces of paper increased)?

(c) Would the force on the paperclip change if the paper was removed but the distance between the magnet and paperclip stays the same?

EXPLAIN: Electromagnetism

`` For a long time, it was believed that electricity and magnetism were completely separate phenomena. After all,

as you saw earlier, there is no observable reaction between a charged ruler and a magnet. It wasnâ&#x20AC;&#x2122;t until Michael Faraday showed that an electric current can create a magnetic field in 1831 that the two phenomena were shown to be related. Together, magnetism and electricity are linked through the theory of electromagnetism.

`` You have seen that when objects carry opposing charges, they are attracted to each other. However, over time, the charges can dissipate and the objects are no longer attracted to each other.

`` This occurs because there will eventually be a flow of electrons from the area of high concentration to the area of low concentration until the charges are balanced. This means that the net charge on each object gets smaller and (from Coulomb's law) if the charges are smaller, then the force will be weaker.

`` We call a flow of electrons electric current. In nature, most electron

flows occur rapidly (static shock) and sometimes violently (lightning).

`` Magnetic fields arise from the movement of any charged particles.

In most cases these moving charged particles will be electrons. This means that when lightning strikes or a static shock is given, there is a magnetic field. However, since these natural phenomena are virtually instantaneous, so are the magnetic fields. Magnetic fields are more easily observed when there is a continuous flow of electrons. This is why compasses show incorrect readings near any wires carrying currents.

Lightning results from an imbalance in charges between rain clouds and the ground. Electrons begin flowing towards the ground and make contact with positive charges flowing upwards from the ground. When contact is made, electrons flow up at about 1/3 the speed of light between the ground and the cloud, producing a giant spark.

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obtain through electric wires to run our everyday appliances (e.g. lights). This electricity is a current, a steady flow of electrons, which originates from a power plant.

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`` When we think of electricity, we often think of the electricity we

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9. Recall in the previous activity a magnet was placed near the charged end of a ruler. Knowing that there is a relationship between electric current and magnetism, can you explain why there was no observable reaction from the ruler to the presence of the magnet?

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10. Permanent magnets, like the one you used earlier, have (not surprisingly) permanent magnetic fields. However magnetic fields arise from the movement of electrons. Suggest how permanent magnets produce their magnetic field:

11. Can you explain why iron is magnetic but copper is not?

ELABORATE: Understanding magnetism

`` The model of the atom you have studied earlier shows several important things:

• Electrons fill an atom’s energy shells with electron shells near the nucleus filled first. • Electrons have a property called spin, either up or down.

• When orbitals are more than half full, electrons pair up. The spin of the electrons in these pairs is always opposite (i.e. one up one down). It is impossible for both electrons in a pair to have the same spin. • Electrons are in constant motion around the nucleus.

12. How could the electrons moving around the nucleus produce a magnetic field?

`` Spinning electrons produce tiny magnetic fields. Paired electrons, spinning in opposite directions, cancel out these magnetic fields.

13. Which atom would produce the greater magnetic field: one with all paired electrons in the valance shell, or one with no paired electrons in the valence shell?

14. (a) The metals iron, nickel, and cobalt can all be magnetized. What does this tell us about their valence electrons?

(b) Substances made of these elements are rarely magnetic on their own (not already a magnet). Suggest why:

`` In ferromagnetic materials, the magnetic fields of individual atoms can face in any direction. For this reason, even ferromagnetic materials may not show magnetic properties until exposed to an existing magnetic field (from another magnet or an electric current in a coil).

Neodymium magnets (right) are an alloy of neodymium, iron, and boron (Nd2Fe14B). They are the strongest commercially available permanent magnets. ©2019 BIOZONE International ISBN: 978-1-927309-75-9 Photocopying Prohibited

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attracted by magnets and can become magnets themselves. Iron, cobalt, and nickel are not the only ferromagnetic elements. They are simply the most common elements to demonstrate this property and are easily identified. The strongest magnets are actually made from elements such as neodymium (Nd) and other rare-earth metals.

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`` Ferromagnetic is a term used to describe materials which are


88 `` The magnetic field produced by the magnet causes the ferromagnetic material with an opposite field direction

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(north attracts south and south attracts north) to line up, instead of being oriented in random directions. This means there is always an attractive force between the ferromagnetic material and a magnet.

``INVESTIGATION 2.13: Making a magnet

See appendix for equipment list.

1. You will need a large nail, needle (or other iron object) and a bar magnet. 2. Mark a center point on the nail.

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3. Using one pole of the magnet, stroke the nail from the center out to one end. Repeat this process several times, moving the pole well away from the nail and then to the center to begin each stroke. 4. Repeat step 3 but use the opposite pole of the same magnet and stroke from the middle to the opposite end.

S

N

S

5. Test your nail on other iron objects (or a compass) to see if you have created a magnet. If it is not magnetized yet, repeat steps 3 and 4 several more times and test again.

N

Nail

`` Atoms in the iron object have magnetic fields, but they are not arranged in any particular order. The random

arrangement of the magnetic field directions results in an object that does not appear to have a magnetic field.

`` Dragging the north end of a magnet over the surface of the object encourages the atoms with opposite alignment to arrange themselves towards the north magnet. The same for the south end of the magnet.

15. Use electromagnetic forces to explain how this method produces a magnet out of a ferromagnetic material such as iron:

16. Notice that the materials that make magnets are the same as the materials magnets are attracted to. Why is this?

17. Some coins are ferromagnetic, some are not. Can you explain why?

18. Research and describe some different uses of magnets:

The Earth produces a magnetic field, which can be detected by simple compasses.

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Magnets are used in the storage of information, from magnetic tapes to computer hard drives.

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Horseshoe magnets are bent so the north and south poles are close together, creating a strong magnetic field.

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17 Applications of Electromagnetic Forces

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ENGAGE: Use of materials

`` In groups discuss why or why not the materials mentioned in the following situations are or aren't used. Summarize your ideas in the spaces provided:

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1. (a) Why is a standard bicycle frame made out of metal instead of concrete?

(b) Why is a competition bicycle (e.g. for velodrome cycling) made of carbon fiber instead of metal?

(c) Why is rubber used to make tires instead of iron (also why do trains use iron wheels instead of rubber tires)?

(d) Why is copper used in electrical wiring instead of nylon?

EXPLORE: Properties of materials

`` In the following investigation, you will explore similarities and differences in the properties of various materials: ``INVESTIGATION 2.14: Patterns in materials

See appendix for equipment list.

1. The materials you will investigate are: a metal paperclip, a plastic paperclip, thin block of wood, a (small) block of concrete or a brick, length of nylon, length of cotton, a stone, a nail, glass, natural quartz crystal.

2. Use a magnifying glass or dissecting microscope to study the structure of the material. Record any patterns or observations about the structure of the material in the table below.

3. Use a conductivity meter (or simple circuit) to test the electrical conductivity of the material. Record the results in the table below.

4. For each object, write down adjectives that describe the material's properties (e.g. hard, soft, shiny, transparent etc). You can test some of these by manipulating the materials, e.g. try bending the stone.

5. Now sort the materials into two groups based on opposites (e.g. hard or soft, shiny or dull). Record the materials in each group. 6. Regroup the objects four more times based on categories of your choosing. Record your groupings in the tables provided on the next page.

SC

SF

SPQ

P

PS2.B

Adjectives that describe the object

PS1.A

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Conductivity (yes/no)

Structure

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Material


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Structure

Conductivity (yes/no)

Adjectives that describe the object

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Material

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Groupings

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2. Are the same materials grouped together over and over again or are the groups different every time?

3. (a) Are some materials more likely to be grouped together than others? If so, which materials are they?

(b) What does this tell you about the material these objects are made of?

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4. Look at the metal paper clip, the plastic paper clip, and the wood:

(a) Describe the differences between the three materials:

(b) Do you think these differences in the material affect its uses? Explain:

5. (a) Metal and plastic paper clips perform the same function. However which performs better? Could the paper clip be changed to hold a large stack of papers? At which point would it fail? Try it and discuss your findings:

(b) What difference would there be between a metal paper clip and a wooden paper clip if both were used to hold a very large stack of papers? Why?

(c) What do these findings tell us about the atomic structure of the materials?

6. From your observations on the properties and behavior of the various materials, can the materials be separated based on the dominant form of atomic bonding (refer to the previous activity)? Explain:

`` Each element has distinct properties based on its structure: number of protons, electron configuration, etc.

`` Likewise, every molecule and compound has its own distinct

`` For example, hydrogen is highly flammable, extremely light, and a gas at room temperature. Oxygen is a reactive gas at room temperature. When they combine, they form water, which is completely non-flammable and a liquid at room temperature.

â&#x20AC;˘ The space shuttle's main engines burned liquid hydrogen and oxygen, producing water vapor as the exhaust (right).

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NASA

making them up.

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`` Molecules can have very different properties to the atoms

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properties based on the bonding forces and atoms used to make up the molecule.


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EXPLAIN: Properties of metals

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`` Earlier you were asked to predict various properties of metals. It is now useful to review those predictions and try to explain why metals have certain properties. The diagram below shows a general diagram of the atomic structure of a metal:

+

+

+ + – – – – – + + – + + + – – – – + + + + + – – – – + + + + – + – – – – + – + + + + – –

+

+

+ –

+

+

+ – +

+ –

+

+ + – – – + + + + + + – – – – – + + + + + + – + + – – – – – – – + + + + + + + + + – – – – + + + – – Atomic structure of a + + + – – – metal that has been bent. + – + + – +

+ –

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+

Metal ion

– +

– – +

+

+

Delocalized electrons

+ –

+

7. Explain the following properties of metals:

(a) All metals conduct electricity:

(b) Metals are good conductors of heat:

(c) Metals are able to be shaped:

(d) Metals have relatively high melting points (with a few exceptions, e.g. mercury, which has full orbitals):

EXPLAIN: Metals and alloys

`` Alloys are metals made from a mixture of different elemental metals and/or other elements to give the original metal different properties.

`` Both physical and chemical properties change. The atomic structure and the electric fields change due to the presence of new elements.

`` Carbon steel (or plain steel, the most common form of steel) is iron (Fe) with up to 2% addition of carbon (C). Plain steel is much stronger than iron, but is still ferromagnetic and rusts (the same as iron).

`` But why is steel so much stronger than iron? What is the carbon doing to give steel its strength?

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8. (a) How many valence electrons does carbon have? (b) How could it fill its valence shell?

(c) If carbon is added to iron, how could carbon get the electrons it needs to have a full valence shell?

(d) What would this do to the charge of the carbon atom?

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93 (e) Iron is made of Fe ions surrounded by loose or delocalized electrons. The Fe ions are able to move because they are not attracted to any one Fe ion more than any other. What would happen to this ability to move if the Fe ions were strongly attracted to another kind of negative ion?

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(f) Draw a diagram in the space below to show how Fe ions and carbon interact. Use your diagram to explain why adding carbon makes steel stronger than iron.

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9. (a) Based on the physical properties of iron and steel, explain why steel is a much more desirable material than iron for making structures:

(b) Explain any difference you might observe if you were to hammer iron opposed to steel:

(c) How does Coulomb's law explain the differences between iron and steel when hammered?

(d) By mass, steel is often only 1 â&#x20AC;&#x201C; 2% carbon. Different types of steel use different quantities of carbon. Can you make any predictions about how the physical properties (malleability, ductility, etc) of steel might change as more carbon is added? Explain what you think is happening:

EXPLAIN: Properties of ionic substances

has the formula NaCl. Note the cubic structure of the crystal.

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`` The photo on the right shows a crystal of the ionic substance sodium chloride. It

(b) Why would this happen?

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Hans-Joachim Engelhardt CC 4.0

10. (a) What do you think would happen if this crystal was hit very hard with a hammer? How does this compare to hitting a metal with a hammer?


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`` Recall that ions formed by gaining an electron have a net negative charge (anions) and ions formed by losing an election have a net positive charge (cations).

11. (a) Ionic bonds are very strong, yet many ionic substances, including sodium chloride, dissolve in water. Recall that water is a polar molecule, but the effective charge on the opposite ends of a water molecule is small compared to the charge of a ion. The diagram below shows a sodium ion and a chloride ion. Draw water molecules onto the diagram to show how the water molecules would arrange themselves around each ion:

Cl–

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Na+

(b) Explain why sodium chloride dissolves in water:

12. Solid sodium chloride is an electrical insulator, but molten sodium chloride and dissolved sodium chloride can conduct an electrical current. Explain these properties:

EXPLAIN: Properties of molecular substances

Discrete molecules `` Recall that molecules are formed when atoms share pairs of valence electrons creating covalent bonds.

`` The covalent bonds in molecules form only between the atoms in the molecules. The forces holding the individual molecules together are much weaker.

`` Discrete molecules are ones which have a fixed number of atoms per molecule e.g. NH3 (ammonia) always has 4 atoms per molecule.

`` The photos below show the substances propane (C3H8) and propanol (C3H7OH). Propane is a gas at 25°C and has to be kept in a cylinder with thick steel walls. Propanol is a liquid and can be kept in a lidded bottle. C atom

OH group

H atom

Propane

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Propanol

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13. Study the diagrams showing the molecular structure of propane and propanol. Notice that they are virtually the same sized molecule, but that propanol has an OH group at the end. Explain why propane is a gas at 25°C whereas propanol is a liquid:

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95 `` The graph below shows the melting and boiling points of a family of molecules called the alkanes. The simplest

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alkane is methane which has the formula CH4. The alkanes have the general formula CnH2n+2 when n is the number of carbon atoms. Thus the next alkane is ethane with the formula C2H6, followed by propane C3H8. In their simplest form the alkanes are long single chained molecules. 300

Boiling point Melting point

200

Methane

150

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Melting point or boiling point (°C)

250

100 50

Ethane

0

-50

-100 -150 -200

Propane

1

2

3

4

5

6 7 8 9 10 11 Alkane (by number of carbons)

12

13

14

15

14. (a) What is the structural difference between each successive alkane from CH4 to C15H32?

(b) In general the boiling point and melting point of alkanes increase as the molecules become bigger. Why might this happen?

Network molecules `` Network molecules have no limit on the number of atoms in the molecule. For example silicon dioxide (quartz) has the formula SiO2, but this simply shows the ratio of atoms in the molecule, not the number of atoms in the molecule.

C atom

`` In SiO2, every atom is covalently bonded to its neighbor and there can be any number of Si and O atoms bonded together. Other examples of network molecules include diamond and graphite.

`` Diamond (right) is made of only carbon atoms covalently bonded together. It is the

hardest natural substance known and, as such, diamonds (usually made synthetically) are embedded in diamond saws used for cutting materials such as concrete.

Diamond

(b) "The only thing that can cut a diamond, is another diamond." Explain:

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15. (a) Use your knowledge of bonding to explain why network molecules have very high melting points, usually over 1000°C:


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16. Fill in the table below with the particles, forces, examples, melting points (very high to very low) and characteristics of the substances listed:

Substance

Particles

Attractive forces involved

Examples

Melting point

Characteristics

Ionic lattice

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Giant covalent network

Metal

Polar

Discrete molecular

Non-polar

EXPLAIN: Choosing the correct material

`` We don't use salt to build houses or rubber to make plane wings. Clearly, certain materials are suited to certain tasks. Why?

INVESTIGATION 2.15: What is used where

See appendix for equipment list.

1. Carry out a survey around the school and sports fields. Look at different objects and what they are made from (e.g. chairs, bench seats, fences, etc). Are they made from wood, steel, aluminium, etc? 2. Record these in a table on a note pad. Staple your record to this page.

17. (a) From your survey, what materials were used to make chairs?

(b) Can you think of any materials used to make chairs that you did not find at school?

(c) What properties did these materials share that made them useful for constructing a chair?

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18. From your survey in Investigation 2.15, select three objects made of different materials. For each one, describe the properties of the material that make it suitable for constructing the object:

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19. New materials are being invented all the time for various purposes. An example of this would be polar fleece for light, yet warm clothing. Can you think of another material that was invented for a specific purpose? Do a little research if needed and describe the materialâ&#x20AC;&#x2122;s uses and why it was invented for that purpose:

20. Many different types of metals and metal alloys are used by humans. Some of these are: iron, aluminum, copper, zinc, chromium, tin, brass, steel, silver, and gold.

(a) Work in small groups of three or four. Each person in the group should pick three different metals or metal alloys, research their uses in industry, and explain why they are used in that way. Summarize your own findings about your three metals/metal alloys below.

(b) As a group, collaborate to make a digital presentation to your class about what you have learned. You can either present it to the class or share it electronically.

(a) Airplane wing:

(b) Cup:

(c) Knife blade:

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21. For each of the following structures, identify a suitable material for its construction and how that material could be used:


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18 Let's Go Climbing Revisited

`` At the beginning of this chapter we looked at some tall mountains and buildings and thought about the factors that might limit their height.

`` With what we have learned in this chapter, we can now revisit those factors and make some calculations and predictions on the maximum height of mountains (and buildings).

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1. Think back to the previous chapter when you were introduced to the concept of pressure. In terms of pressure, suggest why structures with a conical shape can be higher than those going straight up with vertical sides?

2. Mountains erode due to the effects of weathering. Rocks crumble and tumble down mountains even as the mountain rises. What force pulls the eroded parts of a mountain down the mountainside?

3. Recall that in the first chapter we looked at compressive strength and pressure. In this chapter, we have looked at how electrostatic forces hold materials together. How does the strength of the electrostatic forces in a material affect its compressive strength?

4. Explain why gravity and electrostatic forces limit the height of a structure:

`` Calculating the maximum height of a mountain requires a

few generalizations, but these can be made based on what we observe in nature. Most mountains are roughly conical.

`` The weight of the mountain can be found if we then find the density of the rocks that make it up (e.g. granite)

`` The pressure of the mountain on the ground is important.

The more massive the mountain, the greater the pressure it puts on the underlying rock.

`` One last thing we need to know is the compressive strength (s) of the rock that makes up the mountain. Granite has a compressive strength of about 1.3 x 108 N/m2.

`` When we put all these factors together, we get an equation

from which we can calculate a mountain's maximum height:

Most mountains tend to have a conical shape

h = 3s / rg

Where h = height in meters, s = compressive strength, r = density of the rock, and g = the strength of gravity.

`` Putting in some numbers we get: (3 x 1.3 x 108) / (3000 x 9.8) = 13,500 m = 13.2 km.

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5. At the start of the chapter you were told that the tallest mountain on Earth was Mauna Kea at 10.2 km high. (a) How does the height of Mauna Kea fit with our calculated maximum height of 13.3 km (above)?

(b) You were also told earlier that Olympus Mons on Mars was the tallest mountain in the Solar System at 22 km tall. Given that the strength of gravity on Mars is 3.7 m/s2, what is the maximum possible height of a mountain on Mars (assuming it is made of granite)?

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19 Summative Assessment

`` Part A. Mountain size is affected by three main factors (there are more): electrostatic forces, gravity, and shape. 1. Electrostatic interactions:

(a) Explain how electrostatic interactions at the atomic level affect the properties of a material:

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(b) What kind of material properties do you think would be optimal to construct a tall, stable structure like a building?

(c) What kinds of materials would have the properties you described?

(d) The following is a table of the properties of various rocks:

Material

Compressive strength Strength (Ď&#x192;) (N/m3):

Density (r) (kg/m3):

Limestone

41,000,000

2700

Sandstone

55,000,000

2100

Marble

69,000,000

2800

Granite

130,300,000

3000

i. Explain why a limestone mountain will not be able to obtain the height of a marble mountain:

ii. What is the maximum height of a sandstone mountain on Earth given that g = 9.8 N/kg and height (h) = 3s / rg?

2. Gravity also influences the shape of a planet or asteroid. The images (right) show the asteroid 101955 Bennu and the dwarf planet Ceres. 101955 Bennu has a diameter of 492 meters and a mass of 6 x 1010 kg. Ceres has a diameter of 950 km and a mass of 9.4 x 1020 kg. Note that 101955 Bennu is shaped almost like a spinning top, whereas Ceres is spherical.

Explain why 101955 Bennu and Ceres have such different shapes:

Both images: NASA

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101955 Bennu

Ceres

SC

SPQ

P

ESS1.B

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PS2.B


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3. The shape of a mountain also influences it height. Study the three dimensional shapes below:

(a) Which shape would you expect to be able to be built to a greater height?

(b) Explain why:

`` Part B.

4. Use electrostatics to explain the following:

(a) Why does water vapor in the air form clouds instead of just dispersing evenly throughout the atmosphere?

(b) Why when oil (such as cooking oil or paraffin oil) is added to water, it forms droplets that do not mix with the water:

5. In the water stream below, draw the orientation of water molecules as they pass by the charged glass rod:

Burette of water

+

Water stream

q1q2 r2

Na+

F–

Na+

I–

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F=k

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6. The diagram below shows the sizes of two ions from the ionic substances NaF and NaI. Use Coulomb's law to explain why NaF has a higher melting point than NaI:

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7. The table below lists some properties of three metals: iron (as steel), aluminum, and titanium, which are used for various purposes: Property

Metal Iron (as carbon steel)

Aluminum (alloy 6061)

Titanium (grade 5)

Strength (MPa)

841

300

950

(g/cm3)

7.58

2.7

4.5

Resistance to corrosion

Medium-low

High

Very high

Price per tonne (approx)

$500

$2000

$30,000

63,000

82,000

6,600

Easy

Difficult

Difficult

Density

Abundance in crust (ppm)

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Ease of refinement from ore

Using the table above, explain why the metals are used in the following ways:

(a) Iron is commonly used in the construction industry to build large scale buildings (e.g. factory sheds or sky scrapers):

(b) Aluminum and titanium are commonly used in the aerospace industry (e.g. building parts of planes):

`` Part C

8. Below is a model of a distant solar system. The star in the center is one solar mass (it is the same size as our Sun). The distances from the center of the star to the orbits shown is to scale. It has been determined that the innermost planet takes 123 Earth days to orbit the star. Use this data to calculate the distance from the star to the other three planets along their semimajor axis, and the time they take to orbit the star.

2

Star

+

3

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1


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9. The diagram below shows the path of a comet with an eccentric orbit about a star. Use the diagram to explain the motion of the comet as it moves around its orbit at point A and B:

A

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B

A.

B.

10. The exoplanet Kepler-186f orbits the red dwarf star Kepler-186. It takes 129.9 days to orbit the star and is about 0.40 AUs from it. Calculate the mass of the star Kepler-186 in solar masses:

11. Use Newton's law of gravity to compare the size of the gravitational force experienced by each pair of orbiting objects:

F=G

M1M2 r2

r

2r

M=2

M=2

M=4

M=1

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12. The average distance from the Earth to the Sun is 1.5 x 1011 m. The mass of Earth is 5.97 x 1024 kg, and the mass of the Sun is 1.99 x 1030 kg. G = 6.673 x 10â&#x20AC;&#x201C;11 Nm2 /kg2. Calculate the force acting between the Earth and Sun:

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13. A space probe reaching Neptune was placed into orbit 45,000 km from the center of the planet. Calculate the orbital period of the space probe in hours (note Neptune has a mass of 1.024 x 1026 kg):

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Energy Conversion and Renewable Energy

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Instructional Segment 3

103

Activity number

Anchoring Phenomenon

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The winds of change! The role of renewable energy sources in the present and future.

20 27

How do power plants generate electricity?

c

1

Identify and describe different methods of electricity generation from both renewable and non-renewable energy sources. Describe the benefits, limitations, and environmental impacts of each. Recall the first law of thermodynamics. Electricity generation involves changes in energy within a system. Where does the energy for different methods of electricity generation come from and where does the energy go?

21

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2

Analyze data from maps of the pollution in your community and ask questions about the source of these pollutants and their effects. How have the methods for electricity generation in the USA and in California changed in the last 5-10 years? What do you think these changes mean for environmental health indicators such as the release of CO2 and pollutants?

21

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3

A power plant is essentially a system in which energy flows out in the form of electricity. Investigate the power generation capacity and fuel source of a power plant in your area and then calculate the amount of fuel needed to operate the plant for a set period of time (knowing the electrical energy flowing out of the system). How is the electricity generated? Develop and use a model to show that the sum of kinetic and potential energy of component particles must equal the total bulk energy measured at the macroscopic level. Now apply this understanding to explain how power plants convert thermal energy into kinetic energy and how this kinetic energy is converted into electricity. At each stage in the process, communicate the form of energy at the microscopic and macroscopic level. Explain why this process is not 100% efficient.

22 28

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4

Electric generators are an essential component of nearly all types of electricity generation. Investigate this by building a model of a simple power plant to demonstrate that the turning of the generator produces electricity. You can understand how the electric current is generated by investigating and modeling the relationship between electricity and magnetism and using a magnetic field to induce directional electron flow.

23 28

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5

Use what you have learned through your own investigations to explain the principles of electricity generation and to design and build an electrical generator in which there is a constant flow of electricity.

23

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6

Solar panels convert light to electricity. Unlike most electricity generation, the production of an electric current by photovoltaic cells does not involve a generator. Use your understanding of the properties of different elements and their position on the periodic table to explain the role of semiconductors in the construction of photovoltaic cells and the use of light to generate an electric current. Communicate your understanding of the processes involved to others using a kinetic or visual presentation.

24

What engineering designs can increase the efficiency of electricity production and reduce the negative impacts of using fossil fuels?

7

You should now have a good understanding of the principles of electricity generation. Recall the sources of renewable energy you explored earlier in this chapter. Use mathematics to compare the power output from different renewable sources of energy (hydroelectric and wind power, and the energy produced by a photovoltaic cell). Next, work in groups to come up with a design solution to provide the population of a specified region with electricity using only renewable energy sources. You must account for the efficiency of the energy conversions involved because only a proportion of the energy will be converted into electricity. Present your plan to your class, providing data to support it .

25

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Use your understanding of energy conversion devices to design and build your own energy conversion device, with the goal being to provide affordable electricity without the problems associated with fossil fuels. Work within engineering limits to generate the largest power output you can while taking account of prioritized criteria and trade-offs. Refine your device to maximize efficiency.

26

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Use what you have learned through the activities so far to create a computational simulation to show how the management of resources (e.g. energy resources), human sustainability, and biological diversity are related.

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20 The Winds of Change

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104

ANCHORING PHENOMENON: The role of renewable energy sources in the present and future

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We take electricity for granted but it is an extremely important aspect of modern civilization and our everyday lives.

`` Electricity is central to our lives and how we produce it is becoming increasingly important, especially in highly

developed, industrialized societies with high power demands. As demand for electricity has increased, we have come to recognize the environmental damage done by large scale power plants, especially those that use fossil fuels.

`` Technology now provides the means for people to meet their own needs for power generation more easily without relying on commercial suppliers. Many people find this independence appealing.

1. Think of the activities you do throughout the day. Which ones require electricity? Start from when you wake up in the morning and walk yourself through the day:

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2. Imagine your life without electricity. How would things be different?

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3. With the rapid growth of human population and our increasingly electricity-driven lives, there is a huge demand for more energy. How do you think we can prepare for the energy demands of the future?

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21 Electricity in Daily Life

ENGAGE: What methods are used to generate electricity?

`` How many of the following methods for electricity generation can you identify? Briefly answer the following questions relating to the corresponding photograph:

1. (a) Electricity generation method:

(c) Benefits:

(d) Limitations:

Conn, Kit cc 3.0

(b) Environmental impact:

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(b) Environmental impact:

(c) Benefits:

(d) Limitations:

David Monniaux cc 3.0

2. (a) Electricity generation method:

(b) Environmental impact:

(c) Benefits:

(d) Limitations:

USAF public domain

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3. (a) Electricity generation method:

EM

ESS3.A ESS2.D

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4. (a) Electricity generation method:

(b) Environmental impact:

(c) Benefits:

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(d) Limitations:

5. (a) Electricity generation method:

(b) Environmental impact:

(c) Benefits:

(d) Limitations:

(b) Environmental impact:

(c) Benefits:

(d) Limitations:

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6. (a) Electricity generation method:

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7. Go back and research any questions you could not answer. Which of the six methods of electricity generation do you think is the most preferable for where you live and why?

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EXPLORE: Conservation of energy

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Law of Conservation of Energy `` Energy can neither be created nor destroyed. It can only be transformed from one form to another. This is also known as the First Law of Thermodynamics.

`` This energy has to come from somewhere and, when we are finished with it, the energy has to go somewhere. Where does the energy come from? `` Most energy sources ultimately originate from the Sun (except nuclear fission, tidal, and geothermal). How the Sun's energy is utilized

Solar

Light energy excites electrons in solar panels resulting in an electric current.

Wood

Produced by plants through photosynthesis using sunlight.

Petroleum and natural gas

A fossil fuel formed by the fossilized remains of prehistoric organisms that settled in the oceans.

Coal

A fossil fuel formed by the fossilized remains of prehistoric plants buried in swamps.

Hydroelectric

Sunlight evaporates water from the oceans, which falls as rain and snow on top of mountains, and then returns to rivers. Water collected in dams stores potential energy.

Wind

Globally, winds are caused differential heating by the Sun between the equator and the poles.

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Energy source

`` How is sunlight energy involved in the formation of these

energy sources? Let's look at wood as an example. Photosynthesis traps light energy and stores it as chemical energy found in the chemical bonds of wood.

• U nbalanced equation for producing wood using photosynthesis: CO2 + H2O + energy (sunlight) → C6H10O5 (wood) + O2

• B alanced equation for producing wood via photosynthesis: 6CO2 + 5H2O + energy → C6H10O5 + 6O2

• Burning the wood releases this stored energy in a reversal of the photosynthesis equation:

Wood + O2 → CO2 + H2O + energy

`` Energy from combustion originates from the energy of

sunlight. The energy is stored in the chemical bonds between atoms in molecules. When we burn fuels, we are converting the chemical energy stored in chemical bonds to heat energy.

`` In power plants, we are able to convert some of this heat

energy into electrical energy. In addition to energy, fossil fuel combustion results in carbon dioxide and water (assuming complete combustion). If incomplete combustion occurs, then carbon (soot) and carbon monoxide can also be produced.

Energy from the Sun is stored in the chemical bonds in the molecules that make up wood.

CA EP&Cs III: Human practices can alter cycles and processes in natural systems (III c)

`` The carbon dioxide released in combustion of wood and fossil fuels does not have a direct health impact but contributes to an increase in atmospheric carbon dioxide and so global climate change (global warming).

(a) Combustion of fossil fuels:

(b) Hydroelectric power:

(c) Solar power:

(d) Wind power:

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9. Why is it important to consider the unwanted by-products of energy generation?

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8. For each method of producing useful energy below, predict what unwanted by-products result during the conversion of energy sources into useful energy. Do not consider wastes produced in making the energy conversion device:


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10. Produce a diagram that shows the flow of energy from its source to its end point through a food chain involving a herbivore (plant eating animal) and a carnivore (meat eating animal):

EXPLORE: Our carbon footprint

`` If you have watched the news, or seen or read almost any news media, you will be familiar with the term carbon footprint. What exactly does this mean?

11. When you think of the term ‘carbon footprint’, what do you think of?

12. Is our carbon footprint something important we should be worried about? Why or why not?

13. Just by living, we are producing carbon dioxide (CO2). Our bodies use oxygen to convert the food we eat into usable energy and CO2. How does this CO2 production fit into the idea of having a carbon footprint?

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14. In addition to the processes in our body, humans utilize a lot of additional energy. We burn wood to release heat energy to keep us warm when it is cold. Power plants produce electricity to do a variety of tasks from keeping our food cold to listening to music. We travel in vehicles, which convert the chemical energy from burning fossil fuels into mechanical energy to take us places quickly. How does this additional energy use influence your thoughts on your carbon footprint?

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15. What would the effect on your carbon footprint be if you used renewable energy sources instead of fossil fuels? Explain:

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EXPLORE: Electricity generation and pollution

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`` Electricity is a form of energy that is easy to transport (via wires). Humans have learned to use primary sources of

energy (such as solar or coal) to produce electricity. The ability to produce and use electricity is one of the greatest of human inventions. We can even store energy to be converted back to electrical energy at a later time.

`` Devices that use electricity are so common now that we

CA EP&Cs IV: The by-products of human activity are not readily prevented from entering natural systems and may be beneficial, neutral, or harmful.

simply take them for granted. However, the amount of energy needed to operate all the electrical items we use is almost inconceivable. In 2018, the Earth's human population used over 26,700 terrawatt hours (TWh) of electricity (2.67 x 1016 Wh).

`` Most of this electricity is generated in thermal power plants by

`` Humans use a variety of fuels to provide

energy. When these are burned they may release harmful chemicals into the air that may then affect nearby populations.

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burning fossil fuels, mainly coal. Coal is an ideal fuel source because it is energy dense, relatively easy to obtain, and simple to store, transport, and use.

`` However it costs energy to obtain coal. Mining coal can produce

down eight coal and oil fired power plants. In 2018, medical researchers showed that this was associated with a reduction in pre-term births (births before 37 weeks) from mothers living within 12 km of a power plant, with the rate dropping from 7.0% to 5.1% (graph right).

2

Joan A. Casey et al 2017, American Journal of Epidemiology

`` For example, between 2001 and 2011, California shut

Changes in pre-term births

Mean difference in % of pre-term births

a lot of environmental damage and burning it can release dangerous pollutants, such as sulfur, which are trapped in the coal. Modern power plants have processes to remove these pollutants either before or after burning, but some pollutants (in addition to CO2) are still released.

0

-2 -4

1

5 10 15 Distance from power plant (km)

20

16. On a computer or other device, go to the California Power Map website. The link can be found on the BIOZONE Resource Hub. On the website, you can investigate the distribution and output of natural gas and bioenergy power plants for various parts of California. You can also investigate the pollution burden of these power plants. Use the drop-down menu to select your county. How many power plants are present? What type are they? What effects do they have on air quality? Use the CalEnviroScreen to find out how many of the power plants in your county are in disadvantaged communities. Is the pollution burden higher for these communities? Discuss your findings and what they mean in terms of the California Environmental Principles and Concepts.

EXPLORE: Renewable and non-renewable energy sources

`` When the earliest human ancestors discovered how to make fire, they went from being able to use only the energy

their body provided to being able to use more energy than any one person could produce. Later humans learned to use wind energy to sail and cross large expanses of water and to use animals to provide mechanical power.

`` Energy sources which cannot be replenished in a short period of time are called non-renewable energy sources (below). These sources include fossil fuels and radioactive elements, e.g. uranium. Radioactive elements are left over from the formation of the Earth and deposits of these elements are limited. The Earth's supplies of fossil fuels took hundreds of millions of years to form through biological and geological processes, and these processes are too slow to replenish what we have used. What's more, the conditions that produced these vast stores are no longer present. If these energy stores are used up, they can never be replaced.

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Oil is mostly used to fuel the transport industry, but its other uses include in the production of plastics, cosmetics, and clothing.

Radioactive elements are used to fuel nuclear power plants. No greenhouse gases are produced, but there are many issues associated with safety and disposal of radioactive waste.

Coal is important as a fuel for thermal power plants, but it produces a lot of air pollutants and CO2. It is also used in the production of iron and steel.

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Natural gas is often extracted along with oil. It is used to fuel combined cycle power plants and is a much cleaner fuel than oil or coal.


110 `` There is a movement towards using energy sources that can be replenished. These are called renewable energy

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sources (below). Sources for renewable energy include solar, wind, hydroelectric, geothermal, and biomass. These are energy sources that will be available for the foreseeable future, although they may still require careful management (water for example). The Sun will continue to shine, providing light and heat, and driving our weather systems. This means the wind will continue to blow and the water cycle will continue, providing water for dams. Wind turbines need to be located in places with near constant wind. There are many environmental and aesthetic issues around the placement of wind farms.

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Solar power plants capture energy from sunlight in numerous different ways, including photovoltaic cells and "power towers".

Development of wave power, ocean thermal, and tidal power plants is ongoing. A few sites are in operation, but the harsh environments of the oceans makes suitable sites difficult to find.

Hydroelectric power plants use the energy of falling water to drive turbines attached to generators.

17. What makes some energy sources renewable and others non-renewable?

18. Why are renewable energy sources a better long term option than non-renewable energy sources?

EXPLORE: Energy consumption in the USA

`` Most energy in the United States comes from non-renewable resources. However, renewable methods of

generating electricity are becoming more popular (and efficient) and contribute increasingly to electricity production with each successive year.

19. The approximate percentages of sources of electricity generation for the United States in 2015 are provided below. The numbers do not come to exactly 100% because of rounding errors. Use various websites to investigate how much of each source is used today (or as close to the current date as you can possibly find) in the United States, your state, and your county (if the data is available). The BIOZONE Resource Hub has some links that you may find helpful:

Coal

32.63

Oil

0.68

Natural gas

32.49

Solar

0.60

Hydroelectric

6.01

Wind

4.6

Geothermal

0.38

Biomass

1.5

Nuclear

19.24

Other

1.8

US: present (%)

Your state: present (%)

Your county: present (%)

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US: 2015 (%)

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Energy source

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20. What trends do you notice about the sources of energy for electricity generation in the US from 2015 to today?

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21. Make a prediction about the energy sources for electricity generation over the next several years. Why do you think this?

22. How do the energy sources for electricity generation used by your state compare to those used by the US as a whole? Why do you think this is?

23. How is electricity produced for your county? Why are these sources used and not others (think about geographic limitations and availability of energy sources in your area)?

EXPLORE: Sources of energy

Oil and natural gas `` Oil and natural gas are formed from the remains of algae and zooplankton that settled to the bottom of shallow seas and lakes about the same time as the coal-forming swamps (300-400 million years ago). These remains were buried and compressed under layers of non-porous sediment. The amount of pressure and heat, together with the composition of the biomass, determined if the material became oil or natural gas. Greater heat or mainly algal biomass produced natural gas.

(b) Why is oil considered to be a non-renewable energy source?

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24. (a) Are the processes that produce oil still happening today?

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The formation of oil


112 Coal

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`` Almost all of the coal available today comes from the Carboniferous period (358.9 to 298.9Â mya). At the time, there

existed vast tropical swamps and the plants in them had a new organic structural material called lignin. Organisms capable of breaking down this material had not yet evolved, so dead plant material accumulated more quickly than it could decay. Deep burial subjected this plant material to heat and pressure, which over time transformed the plant material into a hard black rock. The first stage of coal formation is peat (partly decomposed plant material). Deeper burial and increasing temperature and pressure produced lignite (brown coal), bituminous coal (soft black coal), and finally anthracite (hard black coal).

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The formation of coal

25. Compare the processes that create coal to those that create oil.

(a) How are they similar?

(b) How are they different?

26. Why is coal considered a non-renewable resource?

Biomass

`` Biomass is possibly the oldest external energy source used by humans, excluding the Sun. It consists of any organic matter that can be burned to produce energy. While the earliest humans probably only burned wood, sources of biomass fuels now include landfill wastes, animal dung, specialized crops, biofuels, and even dried seaweed.

comes from photosynthetic organisms trapping radiant energy from the sun. This energy is stored in the chemical bonds of complex organic molecules such as sugars, carbohydrates, and their derivatives.

Drying dung for fuel

Claude Renault

`` All the energy available from biomass energy sources ultimately

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27. Why is energy from biomass sources considered renewable?

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28. What would the long-term consequences be if our demand for biomass energy sources exceeded our ability to replenish those sources?

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29. Recall the equation for photosynthesis from earlier in this chapter. Combustion of the products of photosynthesis produces the reverse reaction.

(a) What molecules are produced from the combustion of the products of photosynthesis?

(b) Write the equation for the combustion of the products of photosynthesis. Include the energy in and energy out:

Hydroelectric

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`` The Sun provides a continuous influx of energy to the Earth. This energy warms the Earth's surface and the

warming and cooling of the atmosphere produces the wind and weather. This sunlight energy also drives the water or hydrologic cycle (below). Atmospheric water vapor

Evaporation from the oceans

Precipitation

(rain, snow, hail, fog, sleet)

Transpiration (90% of water vapor produced on land is from transpiration)

Evaporation from the land

Oceans

Lakes and rivers

Infiltration into soil

Percolation (movement through soil and rock)

Groundwater

`` Energy from the Sun excites liquid water molecules on the

surface of the Earth (oceans, rivers, lakes, etc), causing them to become water vapor. When the water vapor reaches the cooler air in the higher atmosphere, it condenses to form clouds and eventually falls as precipitation (e.g. rain) back to Earth. Once back on the surface in liquid form, water flows downhill due to gravity, forming moving rivers and streams that flow until they reach the ocean.

The Hoover dam impounds Lake Mead on the Colorado River.

cycling of water, producing electricity by using the movement of water to do work. As long as the water cycle continues (for as long as the Sun is around), and we manage water supplies appropriately, we will not run out of this source of energy.

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`` Hydroelectric power plants take advantage of this continuous

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30. Outline the energy transformations that occur during the water cycle. Start with light energy acting on liquid water on the surface of the Earth:


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31. Describe any limitations you think hydroelectric power has an energy source?

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32. Are there any environmental concerns associated with using hydroelectric power plants to produce electricity? What are they and how do they affect the environment?

Wind

harness from the wind ultimately comes from the Sun. Wind is simply moving air. When the Sun shines, it heats up the Earth, but it does not heat up all of the Earth at the same rate. Not only does land heat up faster than water but the intensity of the Sun is greater at the equator than the poles. Even at different times of the day, the Sunâ&#x20AC;&#x2122;s intensity varies leading to more or less heating. As the air warms, it expands and rises into the atmosphere. Heavier, cooler air rushes in to replace the rising air. This continuous movement of the air due to this uneven heating is the wind.

Hurricanes near the equator

NOAA

`` As is the case for hydroelectric power, the energy we

33. Why is wind considered a renewable energy source?

34. Do you think wind is equally available as an energy source everywhere? Explain your answer:

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36. What do you think would happen to the wind at night? Explain:

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35. Wind occurs because warm or high pressure air moves to a zone of cold or low pressure air. Sea breezes occur because of the difference between temperatures of the land and the nearby sea. During the day, the land heats up faster than the water. On the diagram below draw arrows to show the movement of the air due to this difference in heating:

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115 Solar

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`` The Sun is the ultimate source of energy on Earth. It has been calculated that it will continue burning for another 5Â billion years. That is a long-term source of renewable energy (in effect, "endless")!

`` Solar energy has been used for centuries. As early as the 7th century BCE, people used simple magnifying

USAF

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glasses to concentrate the light from the Sun to set wood on fire. Much later, people created solar water heaters. Producing electricity from solar energy is a much newer technology developed in the past few decades.

Using solar energy can be as simple as heating water cycled up from a house's hot water cylinder.

Photovoltaic cells convert sunlight directly to electricity. Their efficiency is currently about 50%.

A simple structure such as a greenhouse uses sunlight to heat the air, but traps the heat, keeping the structure warm.

`` More energy reaches the Earth as solar radiation everyday than we use in a year. However, the amount of energy

a specific location receives depends on many factors including latitude (total daily radiation is greater at the equator than at the poles), time of year, time of day, and location (e.g. in a valley or elevated).

37. Think about the limitations on the solar energy falling to Earth in the area where you live. What factors would influence the solar energy available in your location. For each factor, how much would it influence the solar energy available?

38. For each of the following explain how it might limit the amount of solar energy that might be available: (a) Latitude:

(b) Time of year:

(c) Time of day:

(d) Location:

Geothermal

`` Geothermal energy comes from the heat generated within the Earth itself. Unlike the other energy sources we have looked at so far, geothermal energy does not originate from the Sun.

`` The use of geothermal energy to generate electricity

is limited to places where geothermal activity occurs relatively close to populations. However, because its output is almost constant, geothermal power is useful as a base load provider that continuously supplies electricity to the electricity grid.

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About half the energy in the Earth is left over from the formation of the planet. The other half comes from the decay of radioactive elements found in the Earth (which were formed during the supernovae of a giant star).

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`` The heat in the Earth's interior comes from two sources.


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39. Do you expect geothermal energy is viable in the area where you live? Explain:

40. What are some advantages of geothermal power?

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41. What are some disadvantages of geothermal power?

Nuclear `` Like geothermal energy, nuclear energy does not originate from the Sun but rather from the radioactivity of elements in the Earth. These radioactive elements are mined and used in fission reactors where the heat produced by their decay is used to generate electricity in a similar fashion to any thermal power plant.

`` An advantage of nuclear power is that carbon dioxide is not

produced as a result of the electricity generation process. However the highly radioactive wastes need to be contained and stored or buried in safe places for thousands of years.

42. Why is nuclear fuel (uranium) considered a non-renewable energy source?

43. What are some advantages of nuclear power?

44. What are some disadvantages of nuclear power?

EVALUATE: Which is best?

Create a presentation, which you will present to the class explaining why you chose this energy source. Note: you will need to do additional research on the various sources of energy as only introductory information was provided for you in this chapter. Make sure you: • Clearly list the advantages and disadvantages of your selected energy source. • Compare your energy source to each of the other available sources and explain (using advantages and disadvantages) why your selected energy source is preferable/more advantageous. • Compare your selected energy source to that currently being used to provide electricity to your community. • Explain why or why not your energy source is currently being used in your location. Make a list of the energy sources your classmates chose:

`` Power plants need to be

located in places where there is accessible fuel, and environmental and social impacts are not extreme. They should be relatively near where the electricity is to be used (within acceptable parameters of energy loss over distance transmitted).

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CA EP&Cs V: Decisions affecting resources and natural systems are based on a wide range of considerations and decision-making processes (V a,b)

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45. Now that you have been introduced to some of the energy sources used to generate electricity, it is time to evaluate the data. In groups of three, study the energy sources and decide which energy source is the best for electricity generation in your city (alternatively, groups can be assigned to argue the case of a preassigned method of electricity generation).

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22 How Do Power Plants Work?

ENGAGE: Get to work!

`` In physics, work is the amount of energy transformed from one type to another. It follows that work must have the same units as energy itself: joule (J).

`` Work is done when an object moves in the direction of the force that is being applied, so work (W) = force (F) x distance (d). But force (F) = mass (m) x acceleration (a). Thus work (W) = mass (m) x acceleration (a) x distance (d). In symbols: W = m a d, which is probably true outside of physics as well!

`` 1 J is the energy required for a 1 N force to move an object 1 m (or a 2 N force to

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move an object 0.5 m or a 0.2 N force to move an object 5.0 m and so on).

`` Anything that possesses energy has the capacity to do work. Thus, a simple definition of energy is the capacity to do work.

1. (a) A 200 kg rock at the top of a cliff breaks loose and falls 55 m to the ground, where it shatters. How much work did the Earth do on the rock (remember g = 9.8 m/s2)?

(b) Where did the energy for the work come from?

(c) How much potential energy did the rock have at the top of the cliff?

(d) How much potential energy did the rock have at the bottom of the cliff (the moment before impact)?

(e) How did the energy of the rock at the top of the cliff change by the time it reached the bottom of the cliff?

(f) Where did the energy go the moment after impact?

(g) How could some of the energy have been harnessed to do something useful?

EXPLORE: Work and energy

`` Heat can do work. The image on the right shows a piston at a low and a

high temperature. At a low temperature the gas particles in the piston are moving slowly and collide with the piston with little energy. Adding heat to the system (e.g. from a flame) increases the speed at which the gas particles are moving. They collide harder with the piston forcing it upwards.

`` Because heat is a form of energy, it can used to do work and is measured in joules. Another unit for measuring heat (and energy) is calories.

`` One calorie (cal) is the heat required to raise the temperature of 1 gram of water by 1°C. 1 cal = 4.184 J (rounded to 4.2 J).

`` Nutritional information on a food container is often shown in food calories (C), which is actually a kilocalorie (kcal). The energy in food may also be shown in kilojoules (kJ).

Cold

Hot

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2. (a) How many calories are there in a kilocalorie?

(b) How many grams of water would a food calorie be able to raise by 1°C?

(c) In a typical hamburger, there are 257 Calories (C or kcal). 1 liter (L) of water weighs 1 kg. How many kilograms of water (and therefore how many liters of water) could be raised by 1°C from the energy in the burger?

(d) How many joules of energy are there in the burger? EM

SSM

PS3.B

PS3.A

CL

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118 `` Kinetic energy (Ek) is the energy due to motion. A vehicle in motion has energy due to its movement. If it were to

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collide with a stationary object (below) then some of the original kinetic energy would become kinetic energy of the second object as well as heat and sound energy in the resulting crash. Kinetic energy can be calculated using the equation Ek = ½mv2, where m = mass (kg) and v = velocity (m/s).

3. A 1500 kg car has a speed of 2.0 m/s. What is its kinetic energy?

4. A boy pushes with a horizontal force of 400 N on a 20 kg box at rest on a level, slightly rough floor. (a) How much work has he done by the time the box traveled 10 m?

(b) What happens to the work done by the boy?

(c) What theoretical speed will the box have, when it has traveled 10 m?

(d) The box only reaches a speed of 15 m/s. Explain:

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5. Water in a river running down a hill or over a waterfall has kinetic energy.

(a) What makes the water move down the hill?

(b) Is the water more or less capable of doing work at the top of the hill than at the bottom?

(c) Name a device that could harness the energy in the water as it flows down the hill:

`` Potential energy (Ep) is stored energy which has the potential to be used to do work. The energy stored due to an object's position above the ground is call gravitational potential energy (Egp).

`` Objects on top of a desk have greater gravitational potential energy than objects on the ground. If the desk were to disappear, the object would fall to the ground converting the potential energy into kinetic energy and then heat and sound energy.

`` Potential energy can also be seen in electromagnetism. A steel bar and a magnet are being held apart. If the bar is released then the potential energy is converted to kinetic energy as the magnet and steel bar come together and becomes sound and heat energy when they join.

`` The bonds between atoms store energy. The energy can be released during a chemical reaction. This is why we obtain energy from the conversion of large molecules such as sugars to smaller ones such as CO2 and water.

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6. (a) Returning to the rock at the top of the cliff in question 1 on the previous page. What kind of energy does the rock have at the top of the cliff?

(b) The moment before impact with the ground, all of the energy the rock had at the top of the cliff has been converted into what kind of energy?

(c) Write a simple equation to shown how the two types of energy in 6(a) and 6(b) are related:

(d) Where does all this energy end up?

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EXPLAIN: Interconversion of mechanical energy

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`` If friction is negligible, then the total mechanical energy (Ep + Ek) of a

system is constant. This means any change in Ep is equal and opposite to any change in Ek.

`` In the diagram right, as the 20 kg mass falls, it loses Egp and gains Ek.

However some of the Egp the 20 kg mass loses also goes into a gain of Egp and Ek for the 10 kg mass.

Pulleys 20 kg

`` So: Egp(lost by 20 kg) = Ek(gained by 20 kg) + Egp(gained by 10 kg) + Ek(gained by 10 kg) `` Then: Egp(lost by 20 kg) – Egp(gained by 10 kg) = Ek(gained by 20 kg) + Ek(gained by 20 kg)

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`` So, in this case: Ep(lost) = Ek(gained)

7. (a) Looking at the system on the side of the smaller mass, the smaller mass has no energy before the larger mass starts falling but gains potential energy. Where did the energy come from?

10 m

(b) In terms of work and energy, explain why the larger mass falls more slowly when there is a smaller mass attached to the rope on the other side of the pulley than if it were to fall on its own:

10 kg

Floor

`` Water wheels were an invention that provided mechanical work for mills by harnessing the energy in falling water. In a water wheel, falling water does work by turning the wheel. The water falls more slowly than it would ordinarily because it has less kinetic energy.

`` Total energy of the system doesn’t change.

8. Why does the water fall more slowly when in the water wheel than if it is in free fall? Where does the energy of the water go?

`` Hydroelectric power plants use falling water to

of a river, such as a deep narrow canyon, where it is easier to build a high dam which maximizes the height of water above the turbine. This can also be achieved by using the natural fall of a river where the dam is built well upstream and water is piped to a turbine well downstream.

``The turbine is attached to a generator, which produces electricity.

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`` Hydrodams are normally situated in sections

Generator

Reservoir

Turbine

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turn a turbine in the same way waterwheels use falling water. However, in a hydroelectric power plant a dam provides water storage and determines the height from which the water will fall. The greater the mass of water passing through a turbine and the greater the height of water above it, the greater the energy that will be available (E = mgh).


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9. (a) Explain how hydroelectric dams are used to generate electricity:

(b) Describe the relationship between water mass, height of the dam, and electricity production:

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EXPLAIN: Efficiency of power plants

`` Thermal power plants use the energy in steam to turn a turbine. They produce the steam by heating water. There are many different designs but all essentially work as shown in the diagram below:

10. (a) With reference to the diagram on the right, discuss where useful energy from the fuel might be lost or wasted:

Direction of water flow

Boiler

H20(l)→ H20(g)

Generator

Water pump

Fuel

Turbine

(b) Thermal power plants obviously need heat energy to make steam but in order to function efficiently they also need cooling systems. Explain why:

Condenser

H20(g)→ H20(l)

River, lake, or ocean

Cooling water intake upstream

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(c) Thermal pollution of air, rivers, lakes, and sea areas is one of the problems caused by thermal power stations. Research this and explain how this occurs:

Heated cooling water discharged downstream

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121 Work, heat, and efficiency

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`` A consequence of the first law of thermodynamics is that energy

is conserved in a closed system. This means we cannot create or destroy energy, but it can change form.

Energy figures for 1 hour of operation at a typical thermal power plant Energy input from fuel 1.5 x 1012 J

`` Thermal power plants use the heat energy from the combustion

of fuel to heat water and make steam. Nuclear power stations use heat from a nuclear fission reaction to heat water and make steam. The force of the steam on a turbine does work on a generator and produces electrical energy (electricity). Throughout this process some of the energy that originally came from the fuel is always lost to the surroundings, directly as heat energy, and also as a result of heat caused by frictional forces

Useful work (electrical energy produced)

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6.0 x 1011 J

`` The efficiency of a power plant can given as a percentage by the following calculation:

Efficiency (%) =

useful work done (electrical energy generated)

x 100

energy input from original source (fuel)

Using the diagram right:

Efficiency =

Energy lost to the system as heat

6.0 x 1011 x 100 = 40% 1.5 x 1012

9.0 x 1011 J

11. (a) Assume that a power plant produces 470 kJ of electrical energy when a mole (16 g) of methane is burned. Burning one mole of methane produces 814 kJ of (total) energy. What is the efficiency of the process?

(b) How much heat is produced?

12. Different parts of a power plant have different efficiencies of energy transformation. The boiler efficiency is about 90%, the turbine is about 75% efficient, and the electrical generator is about 95% efficient. (a) A fuel source in a power plant produces 5000 kJ of energy per kg. Use the information above to calculate the amount of work the fuel will produce:

(b) What is the overall efficiency of the power plant?

EXPLAIN: Combined cycle power plants

`` Gas powered power plants use natural gas as a fuel. However just burning the gas to heat water wastes a huge

amount of the energy in the fuel. Using the heat produced from the burning gas to do some work is more efficient.

`` The natural gas and air are mixed together and ignited. The heat produces higher pressure gases that are passed

through a gas turbine, which is connected to a generator. The hot gases are then passed though a heat exchanger to boil water to steam. The steam is passed through a steam turbine, which is connected to a second generator. Exhaust gas

Natural gas

Combustion chamber

Gas turbine generator

Gas turbine

Electricity

Water Steam turbine

Steam turbine generator

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Condenser

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Air


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13. How does the operation in a combined cycle power plant help to increase its efficiency?

EXPLAIN: More on efficiency

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`` To begin with, an important relationship involving relationship power, energy, and time.

Power = Energy ÷ Time

The unit is J/s = W (watt) but kW and MW are often used.

Energy = Power x Time

The unit is J/s x s = J (joule) but kWh (kilowatt-hour) and MWh (megawatt-hour) are often used.

NOTE: 1 kWh = 1000 Wh (since kilo = 1000) = 1000 J/s x h (since 1 W = 1 J/s, i.e. 1 watt = 1 joule per second) = 1000 J/s x 3600 s (since 1 h = 3600 s, i.e. 1 hour = 3600 seconds) = 3,600,000 J = 3.6 x 106 J = 3.6 MJ

`` EXAMPLE:

How long would a small 500 W generator take to produce 0.2 kWh of electrical energy? 0.2 kWh = 0.2 x 3.6 x 106 J = 7.2 x 105 J Time = Energy ÷ Power = 7.2 x 105 J ÷ 500 = 1440 s = 24 minutes

`` The efficiency of power plants in also measured by the heat rate. Heat rate (BTU /kWh) =

Heat energy used (BTU) per hour Electrical power output (kWh)

NOTE: The smaller the heat rate, the greater the efficiency.

`` Power plants involve massive amounts of energy, so large sized units are needed.

• Heat energy used is measured in British Thermal Units (BTU). 1 BTU = 1055 J • Electrical power out put is measured in kilowatt (kW). 1 kW = 1000 W

A thermal power plant requires 6.75 x 108 J of heat per hour from the fuel it uses to generate an electrical power output of 40 MW. Calculate its heat rate.

6.75 x 108 J = 6.75 x 108 ÷ 1055 BTU = 6.4 x 105 BTU 40 MW = 40,000 kW Heat rate = 6.4 x 105 ÷ 40,000 = 16 BTU/kWh

`` EXAMPLE:

14. Calculate the following:

(a) The joules in 2 kilowatt-hours:

(b) The joules in 45 kilowatt-hours:

(c) The power of a generator that can produce 2 MJ in 30 seconds:

(d) How long it would take to use 50 MJ if a device had a power rating of 2000 W:

(e) If 15 kWh of electricity were used in 3 hours, how many kilowatts were being used per hour?

(f) How many hours would it take to produce 20 kWh of electricity if the power output was 4 kW?

(g) How many BTU are there in 3 MJ?

(h) How many J are there in 2000 BTU?

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15. The table below shows the heat rates of various power plants in California. In the grid below the table, plot a column chart to compare the heat rate of the plants. Use different colors to distinguish the different fuel types. Write the capacity of each plant by its column. Alternatively, plot capacity for each plant alongside heat rate and use a second Y axis. Plant

Code

Primary fuel

Capacity (MW)

Heat rate (MBTU/MWh)

Agua Mansa Power Plant

AM

Natural gas

61

9.7

Bear Mountain

BM

Natural gas

47

9.1

Calpine Greenleaf 1

CG

Natural gas

72

7.0

Clearwater

CW

Natural gas

49

8.2

EN

Biomass

13

21.7

DEC

Natural gas

857

7.0

High Desert Power Project

HD

Natural gas

855

11.4

DTE Stockton

DTES

Biomass

45

13.9

Mt Poso Cogeneration

MPC

Biogas

44

16.3

Sunshine Gas Producers

SGP

Landfill gas

23

12.1

Indigo Generation

IG

Natural gas

135

10.2

Redding Power

RP

Natural gas

183

8.8

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El Nido

Delta Energy Center

16. (a) Of the fuel types used, which type appears to have the greatest efficiency?

(b) Which fuel type seems to enable a greater capacity power plant?

(c) The Delta Energy Center natural gas power plant has a heat rate of 7.0. It has a capacity of 857 MW. i.

How much electrical energy (in joules) does the power plant produce in one hour?

ii. How much energy (in joules) does it take to produce this electrical energy?

iii. What is the efficiency of the power plant as a percentage?

iv. Compare this to the El Nido biomass power plant:

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23 Generating Electricity

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124

ENGAGE: A simple power plant

`` A power plant's generator is effectively a giant electric motor operating in reverse. Instead of using electricity, it is producing it. The inner workings of a generator and an electric motor are very similar and consist of coils of wire spinning inside an enclosure of magnets or electromagnets.

INVESTIGATION 3.1: A simple power plant

See appendix for equipment list.

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1. Take two simple 1.5 volt electric motors, like those found in many battery powered models, and connect them together by wires as in the diagram below:

Drive shaft

2. Rotate the drive shaft on one of the motors. What happens to the drive shaft on the other motor?

3. Remove the second motor and add a galvanometer or center zero voltmeter in its place. Spin the motor again (as fast as possible). Try spinning the motor in the opposite direction. What happens?

4. If possible, attach a small, low voltage light bulb (e.g. flashlight bulb) instead of the galvanometer and try making your own turbine blades to attach to the motor's drive shaft. Turn on a faucet slightly and use the falling water to turn your turbine (be careful not to get water on or in the motor itself). You've built an electricity-producing water wheel!

EXPLORE: Current electricity and magnetism

`` A summary of how a power plant works might be: potential energy is converted to kinetic energy to do work and move a turbine.

`` Potential energy is often first converted into thermal energy:

Rotor blade

• Combustion: chemical potential energy (from the energy in the bonds within molecules) is converted to thermal energy and used to heat water into steam. The positions of the water particles are changed from a densely packed liquid to a gas. The fast-moving water molecules collide with the turbine transferring the kinetic energy of the water molecules (thermal energy) into movement of the turbine.

• Nuclear: nuclear potential energy (from the energy in the strong nuclear force holding the subatomic particles in the nucleus together) is converted to thermal energy and used to heat water into steam in a similar process as combustion power plants.

`` Thermal energy is not always used:

• Wind: air molecules (moving due to thermal energy being added to the atmosphere from the Sun) collide with the rotor blades (connected to the generator via the rotor shaft). The force of the wind does work on the rotor blades, causing the rotor shaft to turn.

`` However, we are missing the last part of the process. As you saw

PS3.A

PS3.B

PS3.C

CE

SSM

Wind turbines

EM

CL

earlier with the electric motors, turning the generator produces electricity. Current electricity is a flow of charged particles. In wires these particles will be electrons. We did not create electrons through energy transformations. Why did the electrons move through the wire? To answer this we need to extend our investigations of electromagnetism from the last chapter.

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• Hydroelectric: gravitational potential energy is converted to kinetic energy due to water falling. The force of the falling water is used to turn the turbine.

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INVESTIGATION 3.2: Electricity affects a compass part 1

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See appendix for equipment list.

Caution is required when doing anything with electricity. We recommend school laboratory power supplies and common 1.5 V cells are used.

1. Create a loop circuit using 1.5 volt AA single cell, insulated wire, and electrical tape. Do not attach the second end of the wire to the cell yet.

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2. The circuit you will create is essentially a short circuit of the battery so can only be turned on for short time. The short circuit produces maximum electromagnetic effects but also causes the wire to become hot. Because of the short circuit, the cell should only be connected for the minimum amount of time as it will go flat quickly. 3. Tape the wire to a piece of cardboard in a circular loop (right).

B

A

4. Connect the other open end of the wire to the cell so current begins to flow.

C

5. Bring the compass into the center of the loop.

6. Move the compass around, closer to the wire and away from the wire. 7. Sit the compass right on top of the wire, then move it along the top of the wire and observe the direction the arrow points. 8. Disconnect the wire from the cell. Careful, the wire may be hot.

9. For the second part of the experiment, reverse the cell and repeat the investigation.

1. For the first part of the experiment, describe the direction the compass arrow pointed at points A, B, and C: A: B: C:

2. For the second part of the experiment, describe the direction the compass arrow pointed at points A, B, and C: A: B: C:

INVESTIGATION 3.3: Electricity affects a compass part 2

See appendix for equipment list.

1. Take a compass and wrap three loops of wire around it as shown in the photograph. Secure the wire with clear tape. 2. Connect the cell and observe the direction the arrow points.

Compass

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3. Describe the direction the compass arrow points with respect to the wire:

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3. Reverse the cell and repeat.


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INVESTIGATION 3.4: Electricity affects a compass part 3

See appendix for equipment list.

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1. Set up a circuit as shown in photograph 1 by cutting a piece of card to a square of about 10 cm by 10Â cm and threading a wire through the middle of the card.

A

D

B

C

Photograph 1

Photograph 2

2. Fold the wire over so that about 10 cm of the wire is perpendicular to the cardboard. Fix the wire in place with tape. 3. The cardboard produces a space between the two parts of the wire and also creates a shelf for a small compass to rest on.

4. Connect the 1.5 volt cell and hold the wire upright with the cell at the bottom. You might need the help of another student to hold the circuit upright and connect the cell while you obtain compass readings in the next step. 5. Place the compass at points A, B, C, and D as shown in photograph 2. Draw a diagram in the space below left to show your results. Label the positive and negative ends of the wire: 6. Reverse the cell and repeat. Draw a diagram in the space below right to show your results.

4. (a) What happens to the direction the arrow points when the cell and therefore current is reversed?

(b) What kind of field is the electricity in the wire producing that is influencing the compass?

(c) Conventional current flows from the positive terminal to the negative terminal of a cell. What can be said about the direction of the field in Q 4(b) around a wire?

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EXPLORE: Magnetism and electricity

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`` Flows of electrons (electric currents) create magnetic fields (as seen in investigations 3.2, 3.3, and 3.4). Even a bolt of lightning creates a magnetic field – however, the field only lasts as long as the flow lasts.

`` Recall that metals conduct electricity and have many delocalized electrons. Can the effects you have just seen work in reverse? That is, can a magnetic field be used to induce these electrons to all move in one direction?

INVESTIGATION 3.5: Electricity from magnets

See appendix for equipment list.

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1. You have a length of insulated wire, a bar magnet, a cardboard tube, and a galvanometer (used to measure small electric currents).

2. You must use these objects to create a simple device or method to show that magnetism can be used to create electric current in a wire.

3. First, think about the investigations you have already done (3.1 to 3.4). Electric current (electrons flowing) produced a magnetic field. What is the reverse of this? 4. Draw a diagram of your device in the space right and describe how it will work. Check with your teacher if it will work and refine your device if needed.

5. Test out your device and record any observations:

5. A galvanometer is a device used to detect and measure small electric currents: (a) What did the galvanometer show before the magnet was introduced to the wire coil?

(b) What did the galvanometer show when the magnet was being moved back and forth between the coils?

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6. With some modifications you can turn your device in investigation 3.5 into a fully functioning generator. To do so, you only need strong bar magnets, a spool of enamelled copper wire, cardboard, a nail, and a galvanometer or low voltage light bulb (e.g. 1.5 V, 25 milliamp). Now consider the following questions: – What will you need to do to produce a continuously changing magnetic field? – How will the effects of this changing magnetic field be transferred to the copper wire? – How will you know if electricity is being produced in the wire? Design a generator that could provide continuous electrical power. Draw and label a diagram of your design (right) and describe how it would work (below):


128 `` The relationship we have explored between magnetism and electricity is what allows the generator of a power plant

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to produce the electricity we are able to use.

`` In generators, it does not matter whether it is the magnet that is turning or the coils of wire. It is the relative

movement of the magnetic field and the coil that matters. However there will be slight differences in the design to accommodate the different moving parts.

`` There are also different designs depending on whether alternating current (AC) or direct current (DC) is required. DC generator

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AC generator

Rotation

Rotation

Wire coil

Wire coil

Magnet

Magnet

AC output

Slip rings

+

– DC output

AC output

Brushes

Split ring commutator

Brushes

In an AC generator, the coil rotates through the magnetic field and current flows in the coil through to the slip rings and is passed to the brushes. Because one side of the coil first passes down through one side of the magnetic field and then up through the other side, the current alternates back and forth in the coil so each output will alternate from positive to negative.

8. On the axis below draw a graph (similar to that in Q7) for the type of generator (AC or DC) that you did not name in Q7.

Time

One cycle

Current

Current

One cycle

Time

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7. The diagram below shows an output wave for one of the generators above (AC or DC). Identify which type of generator produced the wave:

In a DC generator, the coil is connected to a split ring called the commutator. The side of the coil moving down through magnetic field is only ever in contact with the + brush, while the side moving up is only ever in contact with the – brush. This means a brush can only have either + or – output. The output rises and falls as the coil rotates through different parts of the magnetic field.

(b) What are some other ways of increasing the generator's output?

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9. (a) What would happen to the output of a generator if the number of turns of wire in the coil was increased?

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24 Converting Light to Electricity

ENGAGE: Solar power

`` Have you ever tried playing with a solar powered toy like the one shown on

the right? A photovoltaic cell on the top captures sunlight and converts it to electricity to power a small electric motor. On a really sunny day these little toy cars can reach surprisingly high speeds. Such a toy is always on. To turn it off, you simply flip it on to its roof.

PR E O V N IE LY W

1. (a) What would happen to the speed of the solar car shown right if it moved into the shade?

(b) Would the solar car run faster or slower in winter compared to in summer?

(c) Explain your answer:

EXPLORE: Comparing solar and conventional power

`` Recall that a traditional power plant converts potential energy (gravitational, chemical, nuclear) into kinetic energy used to turn a turbine. The turbine turns a wire coil or magnets inside a generator, which generates an electric current providing electricity.

`` Photovoltaic cells (photo = light, voltaic = electricity) work very differently. The diagram below shows the layers of

materials making up a photovoltaic cell. Energy from sunlight ("photons") causes electrons to be removed from their positions leaving holes behind where they used to be ("electron-hole creation"). Electrons migrate to the front contacts while holes migrate to the back contact. When an external circuit is connected between these two contacts an electric current (electrons from the front contact) can flow and supply energy to an electrical device in the external circuit. Electrons that arrive at the back contact combine with holes again ("electron-hole recombination"). This process continues as long as sufficient light energy irradiates the top surface of the photovoltaic cell. Electron flow

Electron

Photon

Front electrical contact Glass

N-type layer

OFF

ON

Depletion zone

Photon absorbed electron-hole creation

Current

P-type layer

Hole

Back electrical contact

Electron-hole recombination

2. Describe differences between a solar panel and a traditional power plant:

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3. Outline the energy transformations in a gas power plant, starting from the chemical potential energy stored in the gas to the electricity we use to keep the lights on in the classroom:

4. From the diagram of a photovoltaic cell, predict the energy transformations taking place from light to electricity:

SF

EM

CE

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PS4.B


130

EXPLORE: Conductors and insulators

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`` Materials can be classified by their electrical conductivity (how well the material conducts a current). Materials with a high conductivity are called conductors. Materials with a low conductivity are called insulators.

5. (a) What are some uses for conductors?

(b) What are some uses for insulators?

Low conductivity indicates insulators and high conductivity indicates conductors. But what about materials in between? Materials between conductors and insulators, which only have a moderate level of electrical conductivity, are called semiconductors. The unique properties of semiconductors make them important in computers and they are found in nearly all modern electronic devices.

Silicon

Germanium

Jurii CC 3.0 http://images-of-elements.com/ germanium.php

PR E O V N IE LY W

`` Electrical conductivity exists on a spectrum.

6. Look at the periodic table in activity 60 and find silicon (Si) and germanium (Ge):

(a) What group(s) are they found in?

(b) How many electrons will these elements need to fill their valence shell?

(c) Remember atoms are more stable with a full outer shell. Are silicon and germanium more likely to gain or lose electrons in order to have a full outer shell? Explain:

(d) How do the valence electrons in these elements explain why they are in between conductors and insulators?

7. (a) Atoms in conductor materials are more likely to (gain an electron / lose an electron) (circle one).

(b) Atoms in insulator materials are more likely to (gain an electron /lose an electron) (circle one).

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8. Using what you know about valence electrons, explain why electrons flow freely through conductors but not through insulators:

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9. How would expect the electron flow to be affected when a semiconductor is exposed to an electric current? Explain in terms of valence electrons:

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131

EXPLORE: The effect of light on electrons

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`` An electroscope is a device that can detect and show the effect of electrons. Simple ones consist of metal leaves

hanging on a hook attached to a metal plate. When electrons are added to the metal plate they travel down to the metal leaves. The leaves repel each other and spread out (below). Adding electrons from a charged rod causes the leaves to spread apart.

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Metal plate

Metal hook

Metal leaves Vacuum

10. The images below show a charged electroscope being illuminated by ultraviolet light over time. The plate is made of aluminium. UV light

UV light

UV light

(a) Why do the metal leaves close back together over time?

(b) How might the observation above help explain how photovoltaic cells work?

(c) Photovoltaic cells use materials that work in the infrared to visible parts of the electromagnetic spectrum. Why do you think this might be more useful than using materials that work in the ultraviolet part of the spectrum?

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132

EXPLAIN: The photoelectric effect

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`` Light can be described in two ways, as a wave and as a particle. We will study waves in chapter 5. The workings of solar panels (collections of photovoltaic cells) can be understood by describing light as a particle, called a photon.

`` When light shines on a metal, electrons are released. This is because photons collide with electrons on the

surface of the metal and knock them loose. The greater the intensity of the light (meaning more photons) the more electrons are knocked loose.

`` The frequency of the light is also important.

Light above threshold frequency Electron knocked loose

Light below threshold frequency

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Photons with short wavelengths (e.g. blue and ultraviolet light) carry more energy than long wavelengths of light (e.g. red and infrared). High energy photons are able to knock electrons loose whereas low energy photons can not.

`` Every metal has a different "threshold frequency".

No electron

Below this frequency, photons of light cannot knock the electrons loose, but above this frequency all photons can knock electrons loose.

Metal

`` Remember that moving electrons produce an

electric current. Photovoltaic cells work by capturing electrons that have been knocked loose and forcing them to travel around a circuit. They do this using semiconductors (e.g. silicon and germanium).

11. A photographic film contains various chemicals that will react to form a picture when exposed to visible light. A photographic film placed next to a strong radio transmitter or microwave oven (which produce waves with frequencies less than that of visible light) will never be affected. A developed film will simply look black. If the same film is placed next to a weak gamma ray or X-ray source (which produce waves with frequencies much higher than visible) it will bleach and produce a white image.

Use the photoelectric effect to explain this situation:

EXPLAIN: Photovoltaic cells

`` The functional part of a photovoltaic cell is two layers of silicon placed together. Each layer has a different

combination of silicon and another element that produce a certain crystal structure. These structures are what produce and capture the electrons when the cell is exposed to sunlight. In a highly simplified photovoltaic cell there are three main layers. The top layer is the N-type layer, the bottom layer is the P-type layer. The middle layer is the P-N junction. N-type

P-N junction

The P-type layer is made of silicon with a small amount of boron. Boron has 3 valence electrons, so there is one electron short, per boron atom, for the covalent bonding with surrounding silicon atoms. This creates a "hole" where an electron could be accepted. At this point the P-type region is still neutral.

2 +

+

+

+

+

3 +

+

+ +

e– e–

+

+

+

+

+

e–

e–

+

+

+ +

– –

P-N junction

P-N junction

N-type

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P-type

N-type

The N-type layer is made of silicon with a small amount of phosphorus. Phosphorus has 5 valence electrons, so one electron, per phosphorus atom, is not needed for the covalent bonding with surrounding silicon atoms. At this point the N-type region is still neutral.

P-type Near the junction, free electrons of the N-type material move across the into holes of P-type material. The makes the N-type positive and the P-type material negative.

P-type

Because two oppositely charged zones now exist, there will be an electric field from the P-type side to the N-type side. This field propels any electrons, ejected from their atoms by the photoelectric effect, towards the upper layer.

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1

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133 e–

e– e–

+

+

+

+

e–

+

+

P-N junction

– –

P-type

w n flo

+

c tr o

+ +

e–

Ele

N-type

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4

The N and P-type materials are placed between conductive plates. The negative electrons freed by the photoelectric effect are collected on the upper plate while a corresponding positive charge accumulates on the lower plate. The result is a photovoltaic cell with a voltage, just like any chemical cell or battery. It can be used to "push" an electric current through any device connected via an external circuit.

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Conductive plate

12. What are the energy transformations present in a solar panel allowing us to generate electricity (start with sunlight)?

13. Explain how the photoelectric effect is utilized by solar panels to generate electricity:

14. How are the properties of semiconductors manipulated to make them useful in producing electricity from sunlight?

15. Why do you think semiconductors are used to create the electric field in the photovoltaic cells rather than conductive metals? Explain:

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16. Working in small groups, create a visual presentation, e.g. stop motion animation or skit, to describe how photovoltaic cells produce electricity. Present it to your classmates. You may use visual props or diagrams to help but make your presentation dynamic, do not design a poster or use a powerpoint display. Use the space below to develop you ideas:


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25 Evaluating Renewable Power Plants

ENGAGE: Renewable energy sources

`` There are numerous ways of producing electricity from renewable energy sources. The three most common ways are hydroelectric power, wind power, and solar power.

1. Go to the website Energy Maps of California - California Energy Commission by following the link in the BIOZONE Resource Hub. Under the heading 'Power Plants and Energy Facilities', click on the link Power Plants in California. A map of all the power plants in California will appear. You can download this as a pdf if you wish. (a) Where are the majority of photovoltaic solar power plants in California situated?

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(b) Where are the majority of the hydroelectric power plants in California?

(c) Where are the majority of the wind farms in California?

(d) Why are the power plants located in these particular places?

EVALUATE: Renewable energy sources

`` The power produced by a

hydroelectric power plant can be approximated from the mass of water flowing past the turbine and the height of its fall.

`` The power available to a wind

• Note where water is not stored in a dam and a flow through turbine is used, the equation for power produced is the same as that for a wind turbine (water and air are both behaving as fluids).

a photovoltaic cell can be approximated using the angle of the sunlight above the horizon. A' = A x cosine (90 – q) x h

P = p/2 x r2 x v3 x r

P=hxgxQxh

• P = power (watts W), h = height (m), Q = flow rate (kg/s), and h = efficiency of the power plant (%).

`` The energy produced by

turbine can be approximated from the density of the air acting on the turbine blades and its speed

• P = power (watts W), r = radius of blades, v = wind velocity (m/s), r = air density (kg/m3).

• The efficiency h reduces the amount of power produced. Wind turbines all have a maximum rated output independent of the wind power. This is called the capacity factor (cf), which equals the % of time the turbine is actually producing power (about 40% of the time).

• A = the solar energy at the equator per square meter (about 700 W/m2 on the ground produces 0.7 kWh/m2 (700 x 60 x 60 / 3,600,000)), A' = the amount of solar energy actually received. q = the angle of the Sun in the sky at noon (0° = the horizon, 90° = directly overhead). This gives the maximum possible energy gain provided the solar panel is pointed directly at the Sun. h = the efficiency of the solar panel.

2. Resource Island is a newly discovered island (yes, somehow how we all missed it until now) located 35° South, 1540 km from the nearest large land mass. It is 80 km wide at its widest point and 1600 m above sea level at its highest point, the volcano Mount Kiilua. The prevailing winds come from the west. 70% of rainfall occurs during March to September. Currently undeveloped, Resource Island is to be colonized. Scientists think that if the island is managed carefully, it may one day be able to sustain up to 140,000 people. Useful information about important weather based phenomena on the island is shown below:

Mar

May

Jul Month

Sep

ETS1.B ESS3.A

Nov

SPQ

18 16 14 12

10 8 6

Air density = 1.2 kg/m3

4 2 0 Jan

EM

Mar

May

Jul Month

CL

Wind speed (m/s)

Angle of Sun above horizon at noon

90 80 70 60 50 40 30 20 10 0 Jan

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Average wind speed per month in Wind Valley

Angle of Sun above the horizon

Sep

Nov

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135 H er

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b

ar

N

or

t wa

p ee

D

E

Estuary of Mud

S

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Small River: average discharge rate 10 m3/s

Mt Kiilua 1600 m

Middle River: average discharge rate 15 m3/s

Lake Blue

The Field of Soil

Long River: average discharge rate 30 m3/s

Iron Sands Beach

: m ws rro ls 50 a l N fa e Th yon can

Wind valley

The Neck

The Dragon's Fangs

Mount Kiilua (1600 m)

River

10 km

Lake

Resource Island will eventually host a population of 140,000 people. The average person uses about 9,000 kWh of electricity per person per year.

CA EP&Cs II: The expansion and operation of human communities influences geographical extent, composition, biological diversity, and viability of natural systems

The new population of Resource Island have decided that they will only use renewable energy sources to provide the island with electricity. They will use solar power, hydroelectric power, and wind power.

In groups, work out how much electrical power the island will need for all its inhabitants and how you will provide that power given that resources are variable throughout the year. This may be from a combination of all three renewable energy types or maybe only one type.

You will need to research the design of various power plants, calculate their possible power output (e.g. the power output of a 1 km2 photovoltaic array) and decide which would work best on the island. Remember there needs to be land for crops, livestock, reserves, recreation areas, and at least two major towns or cities, so you can't cover the entire island in solar panels! The building of any power plants will also affect the natural environment.

`` As human communities expand

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they affect the environment both through using resources and reducing the ability of natural resources to regenerate.

Remember the conversion of any energy resource to electrical energy is not 100% efficient or 100% reliable as the amount of a resource may change from season to season. However, people are going to want a 100% reliable electricity production network. It can't drop out in the middle of winter because of a lack of sunshine! Present your plan for electricity production to your class, providing data and calculations to show how and where the electricity will be produced. Discuss any effect your plans may have on the environment.

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26 Engineering Energy Conversion Devices

ENGAGE: Capturing energy

`` Everywhere around us there is energy, some of it is stored (e.g. in food), and some it is being used (e.g. as rushing water). Being able to capture or convert this energy into a form we can use is one of the most important needs of modern civilization.

`` Although we capture and convert a huge amount of energy into electrical energy, it is not the only way we use energy in the modern world. As the human population increases, so does the need for useful energy. For this reason, energy devices that require no electricity are becoming increasingly important.

`` Solar ovens and solar water heaters are two of these devices. Using new technology and improved designs it is

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possible for these devices to cook food or heat water as easily as with an electric device.

1. In groups, list some devices that do not use electricity but can perform a similar task to an electrically powered device:

ELABORATE: Creating a device part 1

2. You will now have the opportunity to design your own energy conversion device by applying the basic principles of energy conversion and use what you have explored in this chapter. This design challenge will be done outside the classroom in groups or individually as your teacher decides. Your teacher will determine the amount of time you can take.

The goal of this design challenge is simple: you must build a device that will produce the greatest temperature change in 1 litre of water in ten minutes.

The device may not use grid electricity or electricity supplied by a commercial battery. You may build a device that produces electricity using a generator if you wish, but you do not have to. There are other (possibly more efficient) ways to heat water.

You will need to: – research and submit a design to your teacher – build and test the design – refine the design and make any changes necessary – submit a plan showing any revisions of the design to your teacher – present a report that describes how your device works, its power output and efficiency (how will you test this?), and situations where it will be best used. – provide a demonstration of the device so that it can be compared to other devices designed by your classmates. Note: Efficiency = energy in / energy out. Points will be awarded for the most efficient device as well as the one with the greatest change in temperature.

Energy out can be calculated from the temperature change in the water. 1 mL (1 g) of water requires 4.2 joules to raise its temperature by 1°C or E = m x 4.2 x DT (where m = mass in grams of water and DT = the change in temperature).

The method of calculating energy in depends on the device that you build. You may need to go back through this chapter to decide on a method or come up with a entirely new way of measuring the energy input. Discuss your idea for measuring energy input with your teacher and refine if necessary.

EVALUATE: Creating a device part 2

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3. (a) In the space below, summarize your research notes on a possible device to build:

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137 (b) Draw a schematic of your device and add labels or notes explaining the various parts and what will be needed to build them. Submit this to your teacher for review:

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(c) Note down any changes you will need to make after your discussion with your teacher:

(d) Build and test your device. Where is the energy coming from to power the device and how will you measure the energy input? Use the space below to record any measurements and refinements to your device:

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138 (e) After refining your device, repeat your measurements of energy in and energy out. Use the space below. Has your device improved? By how much?

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(f) Evaluate the efficiency of your device. Identify any components that increased or decreased the efficiency of the device. Explain how these components influenced the final results:

(g) Provide a final report to your teacher for marking, including all your designs and calculations and evaluations of the device's efficiency and practicality. Demonstrate your device to the class.

(h) After all the devices have been demonstrated, produce a short evaluation of each one. Which design proved to be the most efficient? Why?

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27 The Winds of Change Revisited

`` Many of our methods of electricity generation are based on limited resources. With our increasing population and

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higher demands for electricity, we are using these resources at increasing rates.

1. With what you have learned in this chapter, explain why electricity generation from renewable resources (e.g. wind and solar) is becoming more prevalent:

2. Think about the different methods of electricity generation:

(a) What do you think will be the primary method of electricity generation in the future for your region?

(b) Why do you think this will be?

(c) Give at least two advantages of this method over another method:

(d) What is a disadvantage?

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3. What do you think is needed to sustain the increasingly energy dependent and growing population of Earth in the future? Defend your reasoning with evidence.


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28 Summative Assessment

1. A 1 kg steel ball sits at the top of a ramp. The ramp is 1 m high. (a) Calculate the gravitational potential energy of the ball at the top of the ramp:

(b) The ball rolls down the ramp. What type of energy does it gain as it rolls down the ramp?

(c) How much of the energy in (b) does the ball have when it reaches the bottom of the ramp?

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2. A water wheel is connected to a generator that produces electricity.

(a) When the water is diverted past the wheel, a mass of 200 kg of water per second falls 5 m. What is the potential power of this diverted water?

(b) When the water is directed to flow over the water wheel so that the wheel starts turning, the generator produces 8Â kW of power. What is the efficiency of the water wheel?

(c) What has happened to the "missing" energy?

(d) Write an algebraic expression to calculate the energy output from a given energy input for the waterwheel:

3. A fire piston (or fire syringe) is a device that has been used since about the 17th century to ignite tinder (e.g. cotton wool) for making fire. The tinder is placed inside the sealed syringe and the plunger is rapidly pressed down, usually by a hammer or strong thrust of the palm of a hand.

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Chocolateoak

Explain why the tinder ignites when the plunger is pressed down rapidly in terms of the energy involved. Include a diagram to illustrate you explanation:

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4. In a thermal power plant, steam is passed through a steam turbine. The steam is used to turn the turbine. (a) What happens to the temperature of the steam as it passes through the steam turbine?

(b) Why does this happen?

(c) The steam produced by the boiler is superheated to 540°C and the waste steam is rapidly cooled by the condenser to about 25°C. How does this help increase the power output of the power plant?

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5. A wire is connected in a circuit to a galvanometer and placed into a magnetic field as shown in the diagram:

Wire

Magnetic field

Galvanometer

G

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(a) If the wire is held stationary (not moving) will a current register in the galvanometer?

(b) If the magnetic field rotates one whole revolution about the red point what would be seen on the galvanometer?

(c) If the wire rotates one whole revolution about the red point what would be seen on the galvanometer?

(d) Explain these readings:

(e) What would happen to the strength of the current in the wire if the wire was coiled so a greater length of wire was in the rotating magnetic field?

(f) What would happen to the strength of the current in the wire in the rotating magnetic field if the strength of the magnetic field was increased?

(g) What would happen to the strength of the current in the wire in the rotating magnetic field if the magnetic field was rotated at a greater rate?

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6. Build a computational simulation to show the relationship between natural resource use, human sustainability, and biodiversity.

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142

Human communities have a need for energy and electricity. However, to provide this humans have needed to use the resources provided by the Earth, be they renewable or non-renewable. In either case obtaining and using a resource has an effect on the environment. For example, mining coal affects the environment by the disturbance of the land and organisms living in the mine site. Burning coal affects air quality. Building a hydroelectric power station affects the land and water quality.

The effect of human activities on resources, biodiversity, and sustainability is complex. By looking at specific areas and simplifying their interactions it is possible to produce simple mathematical models that help to show how a sustainable energy production system might work.

Below are the parameters of a hypothetical system. Your task is to set up a spreadsheet (as shown) and use it to simulate the effect of using different types of energy resources in the environment. You will do this by entering different combinations of parameters into the spreadsheet and recording the outputs.

As part of this task you will need to find the model that produces the most amount of food and shelter while remaining sustainable. At the end of the exercise, attach all your notes, answers, and spreadsheet printouts here.

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Energy resource

Food and shelter

The system has three energy sources. The removal of the energy sources damages the biodiversity of the environment (e.g. by mining) in a different amount (i.e energy source A may be hydroelectric and the long term effect is less than that of mining and burning resource C (which might be coal). The amount of damage is the same per unit of energy mined and is an arbitrary scale. 1.0 is equal to no damage.

The two most basic human needs are food and shelter/warmth. The energy sources can be used to produce food and shelter. However the energy sources produce food and shelter with different efficiencies. Also the production of food and shelter damages the biodiversity of the environment in some way (e.g. plowing a field, or clearing land for a house, or burning fuel for heat, as shown below.

Table 1

Table 2

Energy source

Damage to biodiversity caused by extraction (per energy unit)

Energy source used

Units of energy Damage done to source needed to biodiversity during produce 1 unit of food production of food

A

1.1

A

8

1.6

B

1.25

B

6

1.2

C

1.6

C

2

1.1

An average person uses 10 units of food a day and 6 units of shelter/heat. The environment and biodiversity can replenish themselves by 15% each day.

The environment and biodiversity are given a starting health value of 1000 and are deemed to be healthy provided they remain at or above 60% of the original health value.

Energy source used

Units of energy source needed to maintain 1 unit of shelter/heat

Damage done to biodiversity during maintenance of shelter/heat

A

9

1.2

B

5

1.3

C

3

1.15

To carry out the simulation you need to set up a spreadsheet. The instructions given below are for setting up the spreadsheet using Microsoft Excel.

(b) Now enter the data for food production and shelter underneath. Be sure to take account of the cell numbers the data are being entered in to:

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(a) Open the spreadsheet and enter the energy source data shown in table 1 above, starting in the top corner (cell A1) of the spreadsheet:

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Table 3

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143 (c) Enter the number of food units and shelter/heat units used by a person per day (see below). Again, these are arbitrary. The number of units can be changed during the simulation to work out the maximum number that is sustainable.

(d) To run the simulation you must enter formulae to calculate the effect on the environment of using each energy source into the appropriate cells. Be careful to enter the formulae correctly or the simulation may not run as expected! The formulae are shown below. Make sure that when you have entered the formula that the cell is formatted to show the numerical result.

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(e) Create a cell where the original health/starting value of the environment can be entered. The rate at which the environment can replenish itself (as a percentage) must also be entered.

(f) Finally the output cells must have their formulae entered. Again make sure that each formula is entered correctly. If you change the layout of the spreadsheet then you must make sure the reference cells in the formula are correct.

(g) If you have created the spreadsheet correctly, you can now change the energy source for food production and shelter/heat. The image below shows the output for the first 4 days for using energy source A for both food production and shelter/heat, if you have entered everything in correctly.

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The sustainability value is tracking down. It will soon be unsustainable (<60% of 1000)

(h) Run the simulation by changing the food energy source (G6) and shelter/heat energy source (I6). Find the sustainability of an A and A, B and B, and C and C energy source scenario.

(i) Try combinations of energy sources (e.g. A and C or C and A) to see how sustainability and biodiversity are affected.

(j) Using these combinations, what is the maximum food units and shelter/heat units a person can use and remain sustainable? There may be many possible answers.

(k) Now try changing the rate at which the biodiversity replenishes or the value for the environment's original health. How do these affect the simulation?

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144

Nuclear processes and Earth History

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Instructional Segment 4

Activity number

Anchoring Phenomenon Powering a 15 billion km journey. What fuels Voyager 2?

29 35

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What does E = mc2 mean?

1

In this chapter, we are concerned with processes within the nucleus of an atom and the strong and weak nuclear forces that govern these processes. How do we know about the nuclear structure when its scale is too small to observe directly? How did Rutherford and his students use experimentation to modify the existing model of the atom and determine that the nucleus, with its positive charge, was at an atom's center? What does the atomic number of an element tell you about the makeup of the nucleus of an atom of that element? What does the atomic mass tell you and why is it usually not a whole number? Show how the proton number and nucleon number are expressed as a nuclide number. Use nuclide number to determine the numbers of subatomic particles in the isotopes of different elements.

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Recall the model of the atom you constructed earlier when you explored electrostatics. Why don't the protons in the nucleus fly apart as a result of the repulsive electrostatic forces between them? You will now have to modify your model of the atom to include the elementary particles that make up neutrons and protons (quarks) and the strong nuclear force that holds nuclei together.

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Use a cloud chamber to observe and measure the background radiation that is all around us. What is meant by radioactive decay? Obtain information about the discovery of radioactivity and emissions from radioactive elements. Which elements are most likely to decay and why? What force mediates radioactive decay and how does it work? Use a model of a decay chain to show that mass is conserved as unstable elements decay to more stable forms.

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How do nuclear reactions integrate conservation of energy and mass?

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Processes in the nucleus must obey conservation laws. As you saw with radioactive decay, the number of nucleons is conserved during nuclear reactions. We know that nuclear reactions release large amounts of energy. So where does the energy come from? Apply the principle of mass-energy equivalence (E = mc2) to explain the conservation of mass during nuclear processes, including fission, fusion, and radioactive decay. Develop models to show the changes to the composition of an atom's nucleus and the energy released during these processes.

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Apply your understanding of radioactive decay and mass-energy equivalence to explain why so much energy is released during a nuclear explosion. The energy released during nuclear fission is also the basis for nuclear power generation. Use a model to explain how the energy released from nuclear changes make nuclear power generation possible. How are the nuclear changes induced, maintained, and controlled in nuclear reactors? What about nuclear fusion? Where does it naturally occur and why is it so difficult to produce and control with current technology?

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You can now apply your model of microscopic radioactive decay to understanding how scientists use radiometric dating methods to determine the ages of the Earth's materials and the Earth itself. Make your own simple models of radioactive decay and apply what you learn about half lives to explain how radiometric dating works and why different elements are used for materials of different ages.

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Interpret data on the age of the Earth's rocks and ask questions about the patterns seen in the ages of rocks on its surface, both in continental and oceanic regions . Describe the role of the rock cycle and plate tectonics in making, reforming, and changing the distribution of rocks. Evaluate the evidence of past and current movements of the Earth's crust and the theory of plate tectonics to explain the ages of rocks in the Earth's crust.

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Develop a model (e.g. labeled diagram or slide show) to show how the Earth's internal and surface processes operate at different scales to form features of the Earth's surface.

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Analyze data obtained from impact cratering records, oxygen isotope ratios, and radiometric dating of meteorites, moon rocks, and rocks from Earth to provide evidence for the age of the Earth and the timing and possible mechanisms of the Moon's formation. Use the information and apply scientific reasoning to construct an account of Earth's formation and early history.

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Gregory H. Revera CC3.0

National Nuclear Security Administration

NASA

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How do we determine the age of rocks and other geologic features?


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29 Powering a 15 Billion km Journey

ANCHORING PHENOMENON: What fuels Voyager 2?

`` Voyager 2 is a space probe launched by NASA in 1977

to study the outer planets. The probe passed by and photographed Jupiter in 1979, Saturn in 1981, Uranus in 1986, and Neptune in 1989. More than 41 years and 15 billion kilometers later, the probe is still operating and sending data back to Earth, extending its mission to study the outer reaches of the solar system.

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`` It is estimated that sometime shortly after 2025, 48 years

HELIOSPHERE

Voyager 2

INTERSTELLAR SPACE

NASA/JPL

`` What fuel source has allowed Voyager 2 to operate for so long?

NASA

after its initial launch, the voyager 2 probe will no longer have enough power to operate any of its instruments.

The red pointer shows the position of Voyager 2 as at December 2018. Note the exponential scale. Termination Shock and the Heliopause mark the inner and outer boundaries of the heliosphere (the bubble-like region of space created by solar wind).

1. Think of all the sources of electric generation explored in the last chapter. Which of these sources could be used to power Voyager 2? Explain your answer:

2. If we consider fossil fuels, how much storage space do you think would be required to provide enough energy to power Voyager 2 for all this time?

3. How about renewable sources for energy? Are there any available for the probe to run on? Explain:

`` Remember the inverse square law. The further from the Sun, the less intense the light. Earth is 1 AU

(150 million kilometers) from the Sun. At 2 AUs, the intensity of the Sun is reduced by a factor of 4, at 3 AUs, by 9, at 4 AUs, by 16 and so on. At 15 billion kilometers, the Voyager 2 probe is 100 AUs from Earth.

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4. By how much is the intensity of the Sun reduced at this distance compared to the Earth? Show your working:

5. Do you think solar energy is a viable power source all of the probe’s functions at this distance from the Sun? Explain:

`` Voyager 2 needs to carry its own source of energy in order to power its operations. This energy source must be

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small for transportation and supply enough energy for the long duration of the journey.


30 A Bit More on Atomic Structure

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146

ENGAGE: A brief history of atomic theory

`` As a scientific theory, the atomic theory is an explanation of the nature of matter based on repeated testing. `` Modern atomic theory states that matter is made up of discrete units called atoms, which in turn are made up of subatomic particles.

`` Atomic theory has been refined over time, beginning as a philosophical concept in ancient Greece to the

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incorporation of quantum mechanics today.

The ideas of the Greek philosophers were proposed based on observation and thought. No experimentation was carried out. Philosophers at the time thought that problems could be solved simply by thinking about them. Religion heavily influenced theories and many ideas that were at odds with social beliefs were not accepted nor discussed openly.

A practice of experimentation and scientific observation began to arise and become common.

Gathering evidence allowed new ideas to be formed and redefined as new knowledge came to light.

Greek philosophers came up with the idea that matter consisted of discrete particles. The word “atom” itself is derived from the ancient Greek word atomos, which means indivisible.

Robert Boyle (1600s) wrote the "Skeptical Chemist" urging scientists to abandon the view that elements were mystical substances. He argued Earth could not be an element as it contained other substances (e.g. gold and iron). He helped to pioneer the scientific method.

Fire

Water

Air

Earth

Empedocles and others

In the 1700s chemists Joseph Priestly and Antoine Lavoisier began to explain chemical behavior in terms of the atom. They showed that substances could combine to form new materials.

John Dalton (1803) developed the law of multiple proportions which stated the ratios of masses of elements in a compound are small whole numbers. He proposed that each chemical element consisted of a single type of atom, which could not be reduced by chemical means. This was the start of the scientific atomic theory and the first attempt to describe all matter in terms of atoms and their properties. His work provided logical answers to many questions.

Dalton

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In the early 1900s, one of Thomson’s students, Rutherford, disproved the plum pudding model of the atom through experimentation. He found the positive charge of an atom, along with almost all of its mass, was located at the center, or nucleus, of the atom. He described a planetary model in which electrons orbited a positively charged nucleus.

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Rutherford: Planetary model

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Danish physicist Niels Bohr refined Rutherford's model (1913) by showing that electrons can only orbit the nucleus with specific angular momentums and energies. At the same time, Frederick Soddy described isotopes (atoms of one element with different numbers of neutrons) leading to James Chadwick's discovery of neutrons in 1932.

Quantum mechanics led to an atomic theory in which protons and neutrons consist of smaller elementary particles. Electrons are considered to be an elementary particle and, although they can theoretically be found anywhere in the atom, there is a greater probability that each electron will be in particular part of the atom called an orbital. However, the atom remains the smallest unit of matter that cannot be divided using chemical means.

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The atomic theory was refined and became more sophisticated as technology improved and new evidence was gathered.

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Thomson: Plum pudding model

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The scientific evidence for atomic theory became widely accepted.

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Through the 1800s and 1900s, many scientists made discoveries that helped to refine Dalton's atomic theory. It wasn’t until J.J. Thomson discovered the electron in the late 1800’s that scientists realized atoms were made up of even smaller particles. Because electrons carry a negative charge, while that atom itself was neutral, Thomson proposed the plum pudding model (1904) of the atom where electrons were embedded in a mass of positive charge.

+ -

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Bohr

Quantum mechanics (elementary particles)

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EXPLORE: Finding the nucleus

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`` The Rutherford gold foil experiments were a landmark series of experiments performed between 1908 and 1913

by Hans Geiger and Ernest Marsden under the direction of Ernest Rutherford. The experiments provided evidence that made it necessary to review the model of the atom popular at the time. Positively charged helium nuclei (alpha particles) were fired at thin gold foil and produced the pattern on a detection screen shown below. A few alpha particles were deflected at a wide angle. Occasionally alpha particles traveled backwards from the foil.

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Most alpha particles passed straight through or were only slightly deflected.

Detector

Gold foil (just a few atoms thick).

Beam of alpha particles

Radioactive material (source of alpha particles)

1. Why do you think Rutherford's gold foil experiment so was important in paving the way for the work that was to follow?

2. Recall the model of the atom in chapter 2, where we looked at electrons and electrostatic forces. Before we examine processes in the nucleus more closely, answer the following:

(b) Name the neutral particle found in the nucleus:

(c) Name the negative charged particle orbiting the nucleus:

(d) Draw a model in the space right to illustrate your answers:

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(a) Name the positively charged particle found in the nucleus:

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EXPLORE: Getting to know the periodic table

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`` An element is a substance consisting of atoms that are the same (they have the same atomic number). Elements are chemically the simplest substances and cannot be broken down by chemical means. All known elements are arranged on a table called the periodic table of elements. It has been reproduced for you in activity 60.

`` Atomic number: If you look at a periodic table, you will notice

Atomic number Chemical symbol Name

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each element has a number associated with it. This is the atomic number and represents the number of protons found in the nucleus of a single atom of that element. In a neutral atom, the positive and negative charge is balanced. This means there are equal numbers of protons and electrons, so the atomic number also tells you how many electrons there are in the energy levels around the nucleus.

`` Atomic mass: Each element also has a mass number (relative

Relative atomic mass

atomic mass). This is the total number of protons and neutrons in the nucleus of an atom of this element. It is the weighted average of all the naturally occurring isotopes (so not usually a whole number). We will explore isotopes a little later on.

`` An atomâ&#x20AC;&#x2122;s mass consists of the mass of the protons and

neutrons found in the nucleus. Electrons have such an extremely small mass that they do not contribute significantly to the mass of an atom and their mass can be ignored in most circumstances. Protons and neutrons have similar masses, each equal to 1 atomic mass unit (1 amu). Electrons have a mass of approximately 1/2000 of an amu.

Iron is in group 8 in the periodic table. It is a metal.

`` The proton number (or atomic number) (Z) is the same as the number of electrons in orbit around

a neutral atom. The nucleon number (or mass number) (A) is the number of protons and neutrons (nucleons) in the nucleus. This information makes up the nuclide number. It has the notation shown right, where X is the chemical symbol of the element. Isotopes of the same element have the same number of protons but different numbers of neutrons.

3. How many electrons would it take to equal the mass of a neutron or proton? 4. Look at the periodic table on the next page (or in activity 60).

(a) What is the highest atomic number you see?

(b) How many electrons would there be in a neutral atom of this element?

5. Knowing the mass number and the atomic number of an element, explain how you would work out the number of neutrons in the nucleus:

6. The commonly occurring isotope (variant) of the element carbon is carbon-12. Look at the periodic table in activity 60:

(a) Write the nuclide notation for carbon-12:

(c) How many neutrons are there in a carbon-12 atom?

(b) How many protons are there in a carbon-12 atom?

7. Carbon-14 is an isotope of carbon, occurring naturally in small amounts in the atmosphere. (a) Write the nuclide notation of carbon-14:

(b) How many neutrons are in a nucleus of carbon-14?

(c) What is the difference between the nuclei of carbon-12 and carbon-14 atoms?

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8. Complete the table describing the composition of various isotopes of selenium (Se):

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Se

77 34

Se

80 34

Se

Number of protons

Number of neutrons

Number of electrons

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Isotope

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9. Use the periodic table in activity 60 to complete the following table for stable (non-radioactive) isotopes. The number in the name indicates the isotope and therefore the nucleon number: Chemical symbol

Helium-4

He

Beryllium-9

Be

Nitrogen-14

N

Atomic number

Mass number

Number of protons

Number of neutrons

Nuclide notation

4

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Element and isotope

Oxygen-18

O

Phosphorus-32

P

Chlorine-35

Cl

Potassium-39

K

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EXPLAIN: Patterns in the periodic table

`` Elements are arranged numerically based on the number of protons in an atom of that elementâ&#x20AC;&#x2122;s nucleus. For example, hydrogen has one proton, helium has 2, carbon has 6, and oxygen has 8.

`` Elements are arranged in rows called periods, which tells us how many electron shells their atoms have (elements in the first period have atoms with one electron shell, elements in the second period have atoms with two electron shells, and so on).

`` The columns in the table are called groups. The elements in each group have the same number of electrons in the outer orbital (valence electrons). Elements in the same group therefore have similar characteristics. Metals

Non metals

Main block elements

Atomic number

Lanthanoids Actinoids

Alkaline Transition Earth metals metals

10. Looking at the periodic table above:

Metalloids

Basic metals

Non metals

Halogens

Noble gases

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Alkali metals

(a) What trend in the atomic radius of atoms would you expect as you move from top to bottom down a group? Explain:

(b) What trend in the atomic radius of atoms would you expect as you move from left to right across a period? Explain:

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31 Inside the Nucleus

ENGAGE: A new science

`` As early as the early 1960s, several scientists independently proposed that

`` At the time, there was no physical evidence for these elementary particles,

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and it was not until 1968 that a new technology called deep inelastic scattering (much like Rutherford scattering) provided the first convincing evidence of the existence of quarks.

A small section of the LHC

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neutrons and protons (together called hadrons) were not in themselves elementary (indivisible) particles, but were made of smaller particles they called quarks. They assigned properties to these particles, including mass, spin, and electrical charge.

`` Since then, physicists have learned much more about elementary particles through experimentation. So how do you "look" inside an atom? Of course you cannot, but you can find out about it indirectly by looking at what happens when particles collide.

`` The biggest 'piece' of experimental equipment is CERN's Large Hadron

`` Inside the accelerator, the strong magnetic field guides two high-energy

particle beams in opposite directions at close to the speed of light before they are made to collide. The results (by-products) of these collisions are detected by particle detectors. Analyzing these by-products allows physicists to test the predictions of different theories of particle physics.

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Collider or LHC (image, top right). The LHC is the world's largest particle accelerator. It lies beneath the France-Switzerland border and consists of a 27 km ring of superconducting magnets (image, bottom right) and particle accelerating structures, all housed within a concrete tunnel.

One of the quadrupole electromagnets, used to direct the particles.

EXPLORE: Inside the nucleus

`` Our model of an atom so far describes three types of subatomic particles: protons, neutrons, and electrons.

However, recall from the timeline of atomic theory that quantum mechanics recognizes protons and neutrons as being made up of elementary particles. Clearly, we need to modify our model, just as early atomic physicists did.

`` There are two types of elementary particle of concern to us. One type, the electron, we know about. Recall that it

has an electrical charge of -1. The other type is the quark. Quarks make up protons and neutrons (nucleons). There are six types ('flavors') of quarks. Two types ('up' and 'down') make up the protons and neutrons in atomic nuclei.

`` Each 'up' quark has a charge of +2/3. Each 'down' quark has a charge of -1/3. The sum of the charges of the quarks that make up a nuclear particle determines its electrical charge.

Proton

Neutron

1. Study the diagram of the composition of protons and neutrons:

(a) What quark 'flavors' make up a proton?

(b) What quark 'flavors' make up a neutron?

(c) Use the quark charges to explain why a proton has a charge of +1 and a neutron is neutral (no charge):

“up” quark

+2 e 3

Force carrier (gluon) joins the quarks

1 “down” quark – e 3

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2. From what you know about electrostatic forces and Coulomb’s relationship between charge and distance, how strong do you expect the repulsive forces between protons in the nucleus to be?

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3. With multiple repulsive forces acting on the protons in the nucleus of most atoms, what does the fact that the nucleus is stable tell you about it?

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EXPLORE: The strong nuclear force

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`` Four fundamental forces govern how the universe and all things in it behave (table below). We looked at

gravitational and electromagnetic forces in the first two chapters. In this chapter, we examine the strong and weak nuclear forces, which govern nuclear interactions.

`` You will have determined from what you

know of how forces act over a distance that the force holding the nucleus of an atom together is extremely strong. This strong nuclear force (or strong force) is the strongest force known.

Force

Action

Range

Relative strength

Gravitational

Acts between objects with mass

Infinite

Much weaker

Weak nuclear

Governs particle decay so responsible for radioactivity

Short range –within the diameter of a nucleus

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`` The strong force holds quarks together to form protons and neutrons and counteracts the tendency of the positively-charged protons to repel each other (due to the electromagnetic repulsion of like charges).

Electromagnetic Acts on electrically charged particles Strong nuclear

Infinite

Binds quarks together Short range – within 0.1% of a proton's diameter

INVESTIGATION 4.1: Modeling the strong nuclear force

Much stronger

See appendix for equipment list.

This may be best done as a demonstration by your teacher. Neodymium magnets can be brittle and break with repeated impacts. The activity will work with other magnets as well, but the most dramatic effect is achieved with neodymium magnets, which are the strongest type of readily available permanent magnet. CAUTION: Hold the magnets firmly as they can cause a painful injury if they pull together suddenly and "pinch" skin.

1. You will need an old click pen and two small neodymium magnets with central holes. 2. Take the old pen apart and remove the thin plastic tube that holds the ink and the spring from the pen case. 3. Place one neodymium magnet on to the ink tube. 4. Place the spring on after the magnet.

5. Place the second magnet after the spring so that it is attracting the first magnet. 6. You now have two magnets separated by the spring. 7. Slowly push the two magnets towards each other.

4. In your model of the forces inside a nucleus: (a) What does the spring represent?

(b) What do the magnets represent? 5. (a) What happens as the two magnets become closer? Can the spring keep the magnets apart?

(b) What happened when the magnets got really close together?

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6. Describe how this model demonstrates the forces inside the atomic nucleus, even though it is a simplification:


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EXPLORE: Star death and the origin of elements

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`` Stars fuse hydrogen into helium in their cores for most of

their lives. Two atoms of hydrogen are combined in a series of steps to create helium-4. These reactions account for 85% of the Sunâ&#x20AC;&#x2122;s energy. The remaining 15% comes from reactions that produce the elements beryllium and lithium.

`` The energy from these nuclear reactions is emitted as

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electromagnetic radiation such as ultraviolet (UV) light, X-rays, visible light, infrared rays, and radio waves. Energized particles, such as electrons, protons, alpha particles and neutrinos, are also released, making up the solar wind. A neutrino is a subatomic particle similar to an electron but it has no electrical charge and almost zero mass. of hydrogen. After this, the star can fuse helium to form progressively heavier elements, carbon and oxygen and so on, until iron and nickel are formed. Up to this point, the nuclear fusion process releases energy.

A supernova remnant consists of ejected material expanding from the explosion and the interstellar material it sweeps along with it.

`` Energy is required to form elements heavier than iron

and nickel (e.g. uranium, gold, and silver). The explosion of massive stars (supernova) provides this energy. In the explosion, all these elements are expelled out into space.

NASA

`` However, stars have a finite lifetime and eventually run out

Uranium ore (pitchblende with

`` Uranium is one of the heaviest naturally occurring elements in uranophane) is radioactive. the cosmos. Four elements were made during the Big Bang (H, He, Li, and Be) and another 86 are made by stars and supernovae. The remaining elements on the periodic table are thought to be man-made. It is likely that these elements form in nature as well, but only for a few moments before decaying into something else.

7. Find the element uranium on the periodic table.

(a) What is the atomic number of uranium?

(b) How many protons in its nucleus? 8. Go to BIOZONE's Resource Hub and access the Dynamic Periodic Table tagged to this activity.

(a) Click on the "Isotopes" tab. Click on "All". How many isotopes (versions) of uranium are there? (b) Complete the table for the six isotopes of uranium below (write mass number to nearest whole number): Element and isotope

Atomic number

Mass number

Number of protons

Number of neutrons

Nuclide notation

Uranium-232 Uranium-233 Uranium-234 Uranium-235

Uranium-238

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Uranium-236

(c) What do you notice about the uranium isotopes?

(d) What do you predict about the stability of the nucleus in the atoms of each of these uranium isotopes?

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32 Radioactivity

ENGAGE: Radioactivity that keeps you safe

`` A common type of smoke detector is the ionization smoke detector. You can think of it as an electronic nose because, like your nose, it uses chemistry to detect smoke entering the detector.

`` These smoke detectors are open to the air. A radioactive element

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(typically americium â&#x20AC;&#x201C; Am) bombards air particles entering the detector with alpha particles (essentially a helium nucleus, i.e. 2 protons and two neutrons with no electrons) turning them into positively charged ions and negatively charged electrons. These electrons and ions are attracted to opposite electrodes completing a circuit between the electrodes.

`` When smoke enters the smoke detector, the smoke particles

attach themselves to the ions and stop the electric current, blocking the circuit. The alarm sounds when the circuit is broken.

`` Photoelectric smoke alarms are becoming more common as they do not contain radioactive material and are somewhat more reliable.

1. (a) Do you have a smoke alarm in your home (you should have!)?

(b) What kind is it?

(c) Has it ever gone off? What for?

2. Ionization smoke alarms have a life span of about 10 years. Can you think why?

EXPLORE: Tracking particles

`` Cosmic rays are high-energy subatomic particles that constantly bombard the

Earth from outer space. Thousands of these particles pass through our planet (and through you) every second. This natural radiation is harmless and invisible.

Particle track

`` We can detect the tracks of these particles using a cloud chamber (right).

`` If air is saturated with water vapor and then cooled, tiny droplets of mist form

around floating bits of dust or other materials. They also form readily around ions. When a charged particle, such as a proton, passes through the chamber it leaves behind a trail of ions as it strikes molecules in the air along its path and tears away electrons. Mist droplets form around these ions, creating a cloud track.

`` Creating a cloud chamber will allow you to detect these cosmic rays in your

classroom. Some of the materials may be more difficult than others to obtain and this activity is therefore best done in large groups or as a demonstration.

INVESTIGATION 4.2: Making a cloud chamber

See appendix for equipment list.

Caution is required when handling dry ice as it can cause severe frost burns if touched with skin.

2. Fix or glue the felt to the bottom of the cup.

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1. Place the base of a clear plastic cup or clear plastic tank on a pad of felt and cut around so that the felt will fit into the bottom of the cup/tank. A tank is preferable to a cup because it is larger, but either will work.

3. Roll out and place a piece of plasticine around the top edge of the cup or tank. This will help create a seal later on. This step is particularly important if you are using a cup. 4. Soak the felt in the tank with isopropyl alcohol (propanol). Wet the felt, but it should not be dripping).

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5. Fill a polystyrene tray (or similar e.g. ice box lid) with dry ice (frozen carbon dioxide, -78.5°C) and then place a metal tray or similar on top (completely covering the dry ice so that the tray becomes cold). 6. Turn the cup/tank over and drain any excess propanol on to the top of the tray. Place the upside down cup/tank on to the tray, using the plasticine to make a seal (be careful of the cold metal). 7. Wait a couple minutes to allow the propanol to evaporate and for the vapor to fill the cup/tank. 8. Switch off the lights in the room.

SET UP

Tank

9. Turn on a flashlight and shine the light at the cloud chamber.

20°C

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Felt soaked in propanol

10. Observe and record what you see in the space below.

Vapor forming

Metal tray

-78°C

Styrofoam box containing solid dry ice

There are different types of particles making up the cosmic radiation passing through the cloud chamber. Each particle leaves a different path based on how it interacts with the molecules in the air. See how many you can identify as you watch the cloud chamber:

``The bigger fatter tracks are made from alpha particles ejected by radon atoms.

``Electrons leave curling, zig-zag tracks as they bounce off all the particles they run into.

You will also see tracks made by additional particles we have not discussed yet:

``Positrons (also known as an antielectron). These are subatomic particles with the same mass as an electron but a positive charge). They leave the same kind of curling zig-zagging tracks as electrons.

``Muons (subatomic particles with the same charge as an electron, but over 200 times more

massive. They leave long straight tracks as they plow through the vapor without being deflected.

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3. Which particles do you think you saw in your cloud chamber?

`` Isopropyl alcohol evaporates quickly at room temperature. The alcohol in the felt will evaporate into the air in the

tank. As the alcohol approaches the bottom of the tank, it will cool off. So the alcohol at the top of the tank will "want" to be a gas and the alcohol at the bottom of the tank will "want" to be a liquid. At this point, any disturbance in the gas will cause them to become liquid and a cloud will from.

`` As cosmic rays pass through your cloud chamber, they create disturbances as they ionize the gas molecules in the

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tank. The evaporated alcohol molecules clump together around ions and form tiny droplets. These droplets are seen as wispy clouds tracing patterns through the chamber (similar to the contrails seen along the flight paths of jets). ©2019 BIOZONE International ISBN: 978-1-927309-75-9 Photocopying Prohibited


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EXPLORE: Decay and high speed particles

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`` Some of the fast moving particles seen in the cloud chamber, such as alpha particles, are formed by the decay of

radioactive particles. Alpha particles are emitted by the decay of the radioactive gas radon. Despite being rare, radon can accumulate in buildings, causing a health hazard. It is usually the largest contributor to background radiation.

`` Muons come from the decay of the products of collisions of cosmic rays with gases in the upper atmosphere. `` The strong nuclear force between all nucleons stabilizes a nucleus by offsetting the electrostatic repulsion between the protons. However, if there are too many neutrons, or too few neutrons for a given number of protons, then the nucleus will be unstable. The stability of a nucleus requires the neutron to proton ratio to be about 1:1 for smaller nuclei up to 1:1.5 for the larger nuclei..

`` In unstable elements, the protons and neutrons do not stay together indefinitely. The nucleus of the atoms in these

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elements decay into different atoms by emitting particles. Radioactive decay occurs at varying rates depending on the isotope. Isotopes decay at a specific rate and these can be used for various applications including dating rocks, fossils, and many other mineral-based objects.

`` Sometimes a radioactive element will spilt to form an alpha particle (a helium nucleus) and a new element. At other times, it will produce a beta particle (an electron or positron) and form a new element or isotope.

4. (a) What is an alpha particle?

(b) What is a beta particle?

(c) Think carefully about the size of alpha and beta particles and what this might mean about their other characteristics. Which do you think would have more penetrative power (which would go further through matter)?

(d) What do you think this says about the safety of the radioactive americium in smoke detectors?

EXPLORE: A brief history of our understanding of radioactivity

`` In 1896, Henri Becquerel discovered radioactivity when experimenting with uranium salts. the first woman to win a Nobel prize (in physics), the only woman to win it twice, and the only person to win it in two different categories (physics and chemistry). Marie Curie died in 1934 of radiation poisoning. The dangers of radiation were not known at that time. The papers and workbooks Curie used are still stored in shielded boxes today due to their high levels of radioactivity.

`` Ernest Rutherford carried out many experiments in radioactivity. From 1898 until his

death in 1937 he was so prolific in his discoveries he is often called the "father of nuclear physics".

Henri Becquerel

Smithsonian Institution Libraries, public domain

`` The term radioactivity was coined by Becquerel's doctoral student, Marie Curie. She was

`` The discovery of radioactivity led to trying to turn it into a useful tool. This led eventually to building nuclear reactors to provide "electricity too cheap to meter" as it was advertised in 1954. It also led to the development of nuclear weapons.

5. Form a group of three to research Henri Becquerel, Marie Curie, and Ernest Rutherford

(choose one scientist each). What were the experiments they did to prove and explain radioactivity? Summarize what you have found out for your choice below. As a group, make a short presentation to the class to summarize the research of all three.

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Marie Curie

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Ernest Rutherford


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EXPLORE: Radioactive elements

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`` Radioactive elements are elements prone to decay to more stable states (other atoms) through the emission of radiation in the form of alpha or beta particles and gamma radiation.

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6. Research radioactive elements on a periodic table (see activity 60). Which elements are radioactive? Compare mass numbers and radioactivity of the elements, and their position on the table. Is there a pattern?

7. (a) Not all elements need to be very large to be radioactive. Technetium (Tc), which has the atomic number 43, is an element with no stable isotopes. The atomic mass of technetium is 98. How many neutrons does an atom of technetium have in its nucleus?

(b) What does the difference between the number of protons and neutrons in the nucleus of a technetium atom suggest?

(c) Many smaller elements on the periodic table may have isotopes that are radioactive. Why might different isotopes of the same atom cause that atom to be radioactive?

EXPLORE: Types of radioactive decay

`` Five types of radioactive decay are pictured below (spontaneous fission is not shown): Nuclear equation

Beta decay

Z

A Z

A Gamma decay

Positron emission (beta positive decay)

Z A Z A

Electron capture

X

X

X

X

X Z

4 2

0

–1 0 0 0

He

e g

e

+1 0

e –1

A–4 Z–2

A

Z+1 A Z

Y

A: Decrease by 4

Y

A: Unchanged

Z–1 A Z–1

Z: Decrease by 2

Z: Increase by 1 A: Unchanged

Y

A

Change in atomic/mass number

g

Y

Y

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A

Alpha decay

Model

Z: Unchanged

A: Unchanged

Z: Decrease by 1 A: Unchanged

Z: Decrease by 1

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Decay type

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157 `` Alpha decay is the only type of radioactive decay that results in an appreciable change in an atom’s atomic mass.

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Two protons and two neutrons are ejected from an atom as a helium nucleus (an alpha particle).

`` Beta decay includes the emission of an electron (negative beta decay) or a positron (positive beta decay). • When an electron is emitted, the atomic mass (A) remains the same. A neutron is converted into a proton, raising the atomic number (Z) by one. • When a positron is emitted, the atomic mass remains the same. A proton is converted to a neutron, lowering the atomic number by one. • Electron capture has the same effect on the number of protons and neutrons in a nucleus as positron emission.

`` In gamma decay, an excited nucleus emits gamma rays, but its proton (Z) and neutron count (A–Z) stay the same.

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`` Most commonly, decay occurs as alpha decay, beta decay via emission of an electron, and gamma decay.

8. (a) Uranium-238 decays by alpha decay. What is the name, atomic number, and mass number of the element it decays to?

(b) Bismuth-212 decays via beta decay (emission of a electron). What is the name, atomic mass, and mass number of the element it decays to?

EXPLAIN: Conservation of nucleons in a nuclear reaction

`` In chemistry and physics, we have numerous conservation laws. For chemical reactions, we have:

• The law of conservation of mass, which states that the mass of the products in a chemical reaction must equal the mass of the reactants. • The law of conservation of energy, which states that energy can only transform from one form to another (i.e. chemical  thermal  mechanical  electrical  and so on).

`` With nuclear reactions, we now have a new law of conservation: The law of conservation of nucleon number. This law states that the total number of nucleons (protons and neutrons) does not change in a nuclear reaction.

9. How is the law of conservation of nucleon number similar to the law of conservation of mass?

10. Explain why, during beta decay, the atomic number can change but the nucleon number remains the same:

Nuclear chain reactions

`` Nuclear fission is a type of radioactive decay and can be spontaneous or induced (as shown below). In this

reaction, instead of simply ejecting a small alpha particle or electron, the nucleus of a large atom splits in two, forming two similar sized nuclei.

`` This usually occurs as a result of a neutron colliding with a parent nucleus in the controlled conditions of a nuclear reactor or the somewhat less controlled conditions of a nuclear weapon.

`` Consider the following reaction:

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Barium-141

Neutron

Uranium-235

Uranium-236 The start of a nuclear chain reaction

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Neutron


158 `` If 235U is bombarded with a neutron, the resulting 236U produced is unstable and undergoes fission. The resulting 92Kr

and

141Ba

do not contain as many nucleons as

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elements

236U.

`` The remaining three neutrons are released as high energy particles, able to bombard other nearby 235U atoms and produce a chain reaction.

`` 1n + 235U 236U  141Ba +92Kr + 3n `` In each step, the total nucleon number is a constant value of 236. This is the same in all fission reactions. `` Now consider the fusion of helium-3 nuclei, which occurs in stars: 3He + 3He  4He + 2p. Again, the total nucleon number is the same before fusion and after.

``In any single fission or fusion reaction there is slight mass reduction. The size of the "lost' mass is far smaller than

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the mass of a single proton or a neutron so nucleon number stays constant. But where does this mass go? It is well established now that the "lost" mass has been converted to energy!

11. Experimental fusion reactors use tritium (a hydrogen nucleus with two neutrons and one proton, 3H) and deuterium (a hydrogen nucleus with one neutron and one proton 2H). These are fused to form a 4He nuclei. Draw a diagram in the space below to show this reaction:

EXPLAIN: Where does the energy come from in nuclear reactions? Chemical vs nuclear explosions

`` Explosions release energy very quickly. In traditional chemical

explosions (e.g. a stick of dynamite, C4, TNT) the energy released is associated with the electrostatic forces between atoms.

lower-energy bonds. The excess energy that was stored (potential energy) in the chemical bond is released as kinetic energy, light, heat, etc. These kinds of explosions are a type of chemical reaction called exothermic reactions (chemical reactions that release heat).

`` In nuclear explosions, the energy comes from breaking the bonds

between nucleons in the nucleus created by the strong nuclear force. Without the strong nuclear force holding them together, the electromagnetic repulsive forces between the protons causes them to separate very quickly. The binding energy (energy needed to hold the nucleons together) is released.

National Nuclear Security Administration

`` Chemical bonds between atoms are being broken to make more stable,

A chemical based (conventional) explosion

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12. Recall that, at extremely short distances, the strong nuclear force is much stronger than the electromagnetic force. How do we know the strong nuclear force is stronger than the electromagnetic force?

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13. Why is more energy released when breaking the bonds formed by the strong nuclear force than the chemical bonds formed from electrostatic forces?

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159 Nuclear energy and Einstein's equation

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`` You may have seen Einstein’s famous equation E = mc2: Energy equals mass times the speed of light squared. But what does that actually mean?

`` This equation combines mass and energy in one conservation law. `` Under normal circumstances, we know that energy cannot be created nor destroyed only

transformed from one form to another. Likewise, when we perform chemical reactions, the mass of the products is equal to the mass of the reactants in the reaction.

`` For nuclear reactions, and within the nucleus, things are quite different. `` When small nuclei are forced together (fusion) the total mass is reduced slightly and

the “lost” mass appears as an equivalent release of energy. When a large nucleus splits up (fission) the total mass is also reduced and the “lost” mass again appears as an equivalent release of energy. Einstein’s equation predicts exactly this result.

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Albert Einstein

`` In general, the quantity of energy released from a nuclear reaction

compared with the energy released by a chemical reaction (using suitable samples of similar size) is of the order of a million times greater. Why? It is because the presence of the strong nuclear force in nuclei allows enormous amounts of energy to be stored and/or released. The electrostatic forces, holding electrons in an atom and holding atoms in molecules, are nowhere near as powerful and consequently store and/or release much less energy.

A proton

Most of the mass is here... ...Not here

`` Another curious feature of nuclei is that the quarks within them do not

contribute significantly to the mass of a proton or neutron. Most of the mass is the mass-equivalent of energy stored by the strong nuclear force which holds the quarks together and the nuclei themselves together.

14. In a nuclear explosion, the mass of the atoms is less after the explosion than before, and the amount of energy after the reaction is much greater than before it. Explain what is happening. Do the laws of conservation of mass and conservation of energy account for this?

The strong force also holds nucleons together. Some mass is also here.

A proton

A nuclear explosion

`` Having seen where the energy in a nucleus is stored, it is now easier to see how a nuclear explosion produces such massive effects. The splitting of large atoms releases the binding energy of the strong nuclear force. Doing this on a massive scale results in the largest explosions humanity have created.

`` When describing the power of a nuclear explosion, it is typical to hear

it described as equivalent to a certain amount of TNT (trinitrotoluene).

`` The photo of the conventional explosion on the previous page is the

(b) What mass of dynamite would this be?

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15. (a) TNT and dynamite are common but quite different explosives. A stick of dynamite weighs about 200 grams and produces about 1 megajoule (1 MJ or 1,000,000 J) of energy when detonated. One tonne of TNT produces 4.2 x 109 joules. How many sticks of dynamite would need to be detonated to produce the equivalent explosion of the 23 kilotonne explosion shown?

National Nuclear Security Administration

equivalent of 16 tonnes of TNT. The photo of the nuclear explosion (right) is the equivalent of 23,000 tonnes (23 kilotonnes) of TNT.


160 `` Modern nuclear weapons can have extraordinarily high explosive yields. The most powerful nuclear weapon ever

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tested was the Soviet Tsar Bomba, a hydrogen bomb that used a small fission trigger to detonate the larger fusion device. It had a yield of 50 megatons of TNT (scaled down from the original design of 100 megatons). The explosion was so large the fireball was more than 8 km across and the mushroom cloud formed reached at least 65 km high. Everything within a radius of 55 km was flattened. The blast wave broke window panes up to 900 km from the test site.

`` The diagram below indicates the immense power of these kinds of explosions: 100 101 102 103

MOAB, largest conventional US bomb: 4.6 x 1010 J

1 joule

1010

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Castle Bravo: Largest US test 15 megatonnes

10

1011

Tsar Bomba 50 megatonnes

4

105

106

1012

1 stick of dynamite = 1 million joules

Hiroshima bomb 16 kilotonnes

107

1013

108

1014

1016 1017

1018

1015

109

1 tonne of TNT:4.2 x 109 J

Ivy King: Largest pure fission US test 500 kilotonnes

16. The Tsar Bomba released ~ 2.1 x 1017 J of energy. How many times more energy is released by the Tsar Bomba than:

(a) 1 tonne of TNT:

(b) MOAB:

(c) Castle Bravo:

EXPLAIN: Controlling nuclear fission

`` Just as conventional power stations generate electricity by harnessing the thermal energy released from burning fossil fuels, the thermal energy released from nuclear fission can be used to produce electricity in a nuclear power station.

`` The reactor core generates heat in a number of ways.

Fissionable material

• Heat is produced by the radioactive decay of fission products and materials that have been activated by neutron absorption. This decay heat source will remain for some time even after the reactor is shut down.

`` A nuclear reactor coolant – usually water, but sometimes a gas, liquid metal, or molten salt – is circulated past the reactor core to absorb the heat that it generates. The heat is carried away from the reactor and is then used to turn water into high pressure steam.

MK1 reactor core

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• Some of the gamma rays produced during fission are absorbed by the reactor and their energy is converted to heat.

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• The kinetic energy of fission products is converted to thermal energy when the nuclei collide with nearby atoms.

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161 Controlling the chain reaction

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`` Recall that when uranium-236 splits it releases neutrons. These can be absorbed by other nearby uranium-235

atoms which then split and so on in a chain reaction. A nuclear weapon produces an uncontrolled chain reaction. To maintain a sustained but controlled nuclear reaction, for every 2 or 3 neutrons released, only one must be allowed to strike another uranium nucleus.

`` Most reactors are controlled by using neutron poisons, which absorb neutrons and so reduce the rate at which the

chain reaction can proceed. They also use neutron moderators (such as heavy water) which slow down neutrons so that they are more easily "captured" by the nuclei and allow the chain reaction to proceed more rapidly. Nuclear reactors generally have automatic and manual systems to shut the fission reaction down if conditions are unsafe.

`` The power output of the reactor is adjusted by controlling how many neutrons are able to produce more fission

PR E O V N IE LY W

reactions. Control rods that are made of a neutron poison are used to absorb neutrons. Absorbing more neutrons in a control rod means that there are fewer neutrons available to cause fission, so pushing the control rod deeper into the reactor will reduce the reactorâ&#x20AC;&#x2122;s power output and extracting the control rod will increase it.

`` A nuclear power plant produces electricity by using the heat from the reactor to boil water to produce steam to drive the turbine (below). Reactor building

Powerhouse

Steam turbines

Control rods

Reactor core

Nuclear fuel rods

Cooling tower

Cooling tower

Generator

Heat exchanger

Water pumps

Condenser

17. What would happen to the nuclear chain reaction if, for every 2 or 3 neutrons released:

(a) Less than 1 was allowed to strike another uranium nucleus?

(b) More than 1 was allowed to strike another uranium nucleus?

18. (a) How do the control rods regulate the nuclear chain reaction?

(b) Describe the position of the reactor control rods when the reactor is effectively shut down:

(c) Describe the position of the reactor control rods when the reactor is at full power:

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19. Describe how a nuclear reactor produces electricity:

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162

EXPLAIN: Nuclear fusion

CL N AS OT SR F OO OR M US E

`` Nuclear fusion is the ultimate goal in nuclear reactor technology. Fission is relatively simple to achieve and control in that it happens at standard atmospheric pressure and temperature. In contrast, fusion requires enormous pressures and temperatures, as occur in the core of stars. Fusion technology is still in its infancy.

`` Nuclear fusion is the joining of smaller nuclei to form a larger one. This fusion of hydrogen to helium releases more

energy per nucleon than the fission of uranium. The Sun’s (stars’) energy comes from the fusion of hydrogen atoms into helium (see chapter 6).

`` Recall the law of conservation of nucleons. When hydrogen atoms are fused to create helium, the total number of

PR E O V N IE LY W

nucleons remains the same, as in the fusion of deuterium and tritium (both hydrogen isotopes): 2H + 3H  4He + 1n

`` However, the final mass is not the same as the original mass. During fusion, energy is released in the form of

gamma rays. The release of the gamma ray (high energy photon) results in a measurable reduction in the mass (about 0.7%) of the products of the nuclear fusion reaction.

20. Explain why fusion is so difficult to produce and control on Earth with our current technology:

ELABORATE: The worst nuclear accident

`` Nuclear fission power plants must be managed

`` The worst nuclear accident occurred at the Chernobyl nuclear power plant in Ukraine in 1986. A failed safety test caused the number 4 reactor to explode, exposing the reactor core and spreading radioactive material over a huge area of the then western Soviet Union and parts of Western Europe.

`` Because the radioactivity takes so long to reduce to

safe levels, a 30 km radius exclusion zone around the former reactor is permanently in place.

Radioactivity in fish from the Kiev reservior

18

Radioactivity (Bq/kg x 100)

carefully and have multiple safety systems to ensure that radioactive material does not escape into the environment in the event of an accident. There have been several major nuclear reactor accidents, all due to human error rather than a reactor fault (although faulty reactors have increased the seriousness of some accidents).

16 14

Bream (non-predatory fish) Pike (predatory fish)

12 10 8 6 4 2 0

1985 1987 1989 1991 1993 1995 1997 1999 Year

(b) From what you know about the energy of radioactive particles, suggest why high levels of radioactivity are dangerous:

CL

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21. (a) The graph shows the levels of radioactivity in fish in the Kiev reservoir. Why do you think pike have greater levels of radioactivity than bream:

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33 Radioactive Decay and Half-Lives

ENGAGE: Halving stuff

INVESTIGATION 4.3: Half-lives 1

See appendix for equipment list.

1. Take an A4 or US letter sized piece of paper. Measure length (l) and width (w). Calculate the area (l x w) and record it in the table.

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2. Cut the paper in half. Measure length (l) and width (w) of one half. Calculate the area again (l x w) and record it in the table. 3. Repeat four more times. Cuts

Area (cm2)

0 1 2 3 4 5

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1. (a) Plot a column graph of the results from your table onto the graph below:

(b) What shape graph is produced?

(c) Would the graph ever reach an area of zero if you kept on cutting?

(d) How many cuts would it take for the paper to reach 1/4096th it original area?

(e) If one cut occurred every 10 minutes, how long many would it take for the paper to reach 1/4096th its original area?

P

CL

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ESS1.C


164

EXPLORE: Probability and radioactivity

CL N AS OT SR F OO OR M US E

`` Different radioactive materials give off nuclear radiation at different rates. For example 1 g of radium emits 20 million times more radiation as 1 g of uranium in the same time-frame.

`` The activity of a sample of radioactive material is a measure of the number of times nuclei in the sample decay in a specific time.

`` There are two factors that determine the activity of a sample of material: • The size of the sample (2 grams of radium will have twice the activity of 1 gram). • The atoms that make up the material (some nuclei are more unstable than others).

PR E O V N IE LY W

Rolling the dice `` When we try to measure or describe the atom, much of what we measure or talk about is in terms of probability. In the microscopic world of atoms and subatomic particles things are not as definitive as in the macroscopic world. For example we can never know for sure exactly where an electron is in its orbital, only where it might be.

`` In the same way, when we measure radioactivity, we are measuring the probability that the nuclei of an atom will

decay. The nuclei will decay, but we can never know exactly how long that will take from any given time, only that it might decay within a certain time. However, the more unstable the nucleus, the higher the probability of radioactive decay within a certain time frame.

`` To demonstrate this probabilistic nature we can illustrate radioactive decay using dice.

INVESTIGATION 4.4: Half-lives 2

See appendix for equipment list.

1. Using as many 6-sided dice as your group has, throw the dice all at once (or repeatedly throw a small number of dice and record the cumulative results). Use at least 30 dice initially.

2. Every die represents an atom of a radioactive element. Every roll of 1 represents its decay into a new element. Each roll of all the dice represents a certain amount of time. 3. Record and remove all the dice that have the value of 1 and record the number of dice left.

4. Throw the remaining dice and again record and remove all that have the value of 1 and record the remaining amount. 5. Repeat this until you have 1 die remaining or all remaining dice turn up as 1.

Number of rolls

Number of dice rolled

Number of dice showing 1

Number of dice remaining for next roll

0 1 2 3 4 5 6 7

10

2. (a) How many sides do your dice have? (b) The probability of rolling a specific number would be:

(c) What fraction of dice would you expect to roll 1 in each roll?

CL

9

N AS OT SR F OO OR M US E

8

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165 (d) Study your table of results. Is the number of dice rolling 1 always this fraction of the total dice? Explain:

CL N AS OT SR F OO OR M US E

(e) Combine your results with the results of the other groups in the class. With a larger sample size, is the fraction rolling 1 closer to the fraction you stated in (c)? Why do you think this is?

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3. The number of 1s in each roll represents the radioactivity of your element (made up of dice).

(a) What can you say about the radioactivity of the material over time (the number of dice rolling 1 as you continued rolling)?

(b) If you had used dice with fewer sides (4-sided dice), would you expect to roll more or fewer 1s on each roll (assume the same number of dice)? Explain:

(c) How about if you used dice with more sides (8-sided dice)?

4. There were two factors influencing a material's radioactivity. How were both of these factors represented in this activity?

`` Probability is the chance of a particular outcome occurring and is a fraction between 0 and 1 (0% and 100%)

`` When rolling a die, the probability of a specific number

coming up is 1/6, but there is no way of predicting what number will actually come up with each roll of the die. However, the more frequently the die is rolled, the following ratio will tend to get closer to the expected number: The number of times a specific number comes up The total number of times the die is rolled

`` In a sample of radioactive material, there is a enormous

number of atoms. For example, in 1 g of uranium, there are approximately 2.6 x 1021 atoms. Within that sample, there will also be a huge number of nuclei decaying, so the probability of decay is relatively constant. This means that in equal amounts of time, the same percentage of nuclei will decay.

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5. If you started the previous investigation with 36 six-sided dice and you had 25 left, is it possible to work out how many times the set of dice were rolled? Explain how:

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6. If you started with 27 dice and removed all the dice that produced a 1 after each roll, how many rolls are likely to have been done if there are 13 dice remaining?


166

EXPLAIN: Half-lives

CL N AS OT SR F OO OR M US E

`` The decay of atoms is slightly simpler than dice because while dice may have six sides and so six outcomes, atoms have only two outcomes: they decay or they don't.

`` In a given number of radioactive atoms, some will decay and some will not. The time it takes for half of the atoms of

a sample of an element to decay (reducing the radioactivity to half) is called the half-life of that element. The element uranium-238 has a half-life of about 4.5 billion years. That means for any given sample size, it will take 4.5 billion years for half the number of atoms in the sample to decay.

7. The radioactive element carbon-14 has a half-life of 5730 years. Complete the following table: Fraction of 14C atoms (radioactivity) left

Number of half lives

Time elapsed

PR E O V N IE LY W

0 1 2 3 4 5

Carbon-14 and using half-lives

`` When dating organic material, scientists often use the carbon dating method. In carbon-dating, the two isotopes carbon-12 and carbon-14 are used.

12C

is the stable form of carbon •

14C

is a radioactive isotope of carbon

`` In our atmosphere, cosmic rays continuously produce 14C to replace those that

decay. Because of this replacement, the ratio of 12C to 14C in the atmosphere is relatively constant. While an organism is alive, it exchanges carbon with its environment, maintaining the same ratio of the two isotopes that exists in the atmosphere. Once the organism dies, the exchange stops and the 14C decreases due to radioactive decay. When dating organic material, scientists are comparing the 12C to 14C ratio in the specimen to the atmospheric ratio.

8. An anthropologist has discovered some human bones while digging at a site and wants to determine how old they are.

What would be the approximate age of the bones if the ratio of bones was (use the table you filled in to help if needed):

(a) One eighth of the atmospheric value?

(b) One sixty-fourth of the atmospheric value?

14C

to

12C

in the

9. Carbon-dating is only reliable for samples up to approximately 50,000 years old. 14C

(a) Approximately how many half-lives of

(b) What happens to the amount of

(c) Why do you think carbon-dating becomes less reliable the older the bones are?

14C

would this be?

in the sample as more half-lives go by?

Uranium-238

`` Uranium and other heavy elements are only formed during supernova explosions

`` Uranium-238 decays into lead-206 (a stable isotope). Comparing the ratio of

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that occur near the end of some stars’ lives or the collision of neutron stars. Any uranium on Earth was already present during the formation of the solar system.

10. If all the uranium found on Earth was present at the formation of the solar system, what could you use 238U to 206Pb ratios to calculate the ages of?

CL

Supernova as a bright spot within its host galaxy

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NASA/ESA

uranium to lead will provide an estimate of the age of a rock. The Earth's mantle contains a certain ratio of uranium to lead atoms. Newly formed volcanic rocks will have a ratio similar to this. Older rocks will have different ratios.


167

ELABORATE: Radiometric dating

CL N AS OT SR F OO OR M US E

`` Working out the age of a rock is simple if the radioisotopes have undergone a whole number of half-lives. For example, if radioactivity is 50% then one half-life has past.

`` But what if the ratios in the sample don't correspond to full half-lives (e.g. 0.5, 0.25 etc)? How do we calculate the number of half-lives passed if 80% of the radioactivity remains for example?

`` For any number of half-lives (t) the proportion of radioactive atoms left (r) is equal to 0.5t, i.e. r = 0.5t. • The proportion of radioactive atoms left gives us the half-lives that have passed: t = -1.4427 ln(r). • ln refers to natural logarithms.

`` EXAMPLE: A sample contained a ratio of 2:3 parent isotopes to daughter isotopes.

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• The proportion of parent isotope is therefore 0.4, since 2 out of every 5 atoms is a parent atom. 2/5 = 0.4 • A proportion of 0.4 means that 40% of the original sample is left. Therefore t = -1.4427 ln(0.4) = 1.32 half-lives. • If the isotope being studied is carbon-14 then 5730 x 1.32 = 7560 years have passed.

11. (a) A sample of radium has 69% of the original number of atoms are left. Radium has a half-life of 1622 years. How much time has passed?

(b) A sample of rock has a ratio of 47:3

238U

to

206Pb

atoms. 238U has a half life of 4.5 x 109 years. How old is the rock?

`` Different radioactive elements have different decay rates, so scientists must select which element and which dating

method is best for the material. Often multiple overlapping dating methods are used to confirm the ages of artifacts: Parent isotope

Daughter isotope

Half-life of parent (years)

Effective dating range (years)

Materials that can be dated

Uranium-238

Lead-206

4.5 billion

10 million billions

Zircon, Uraninite

Potassium-40

Argon-40

1.3 billion

50,000 4.6 billion

Muscovite, hornblend, biotite, volcanic rock

Rubidium-87

Strontium-87

47 billion

10 million billions

Muscovite, biotite, potassium feldspar, igneous rock

Carbon-14

Carbon-12

5730

100-50,000

Wood, charcoal, bone, tissue, shell, ice containing pockets of carbon dioxide

12. (a) Which dating method would best be used to date a human bone from an ancient Central American city?

(b) Which dating method would best be used to date a meteorite found in Antarctica?

(b) A scientist claims to have carbon-dated a bone from a tar pit to 150,000 years ago. Explain why this is highly unlikely to be an accurate date:

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13. (a) Why would using a radioisotope with a short half-life (e.g. 3000 years) be better than using one with a long half-life (e.g. 2 billion years) when dating relatively young objects (e.g. 1000 years old)?


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34 The Age of the Earth

ENGAGE: The rocks of the Earth

`` The surface (crust) of the Earth is a mixture of different rocks and minerals. Each rock and mineral is formed under characteristic circumstances and so can give information about what the environment was like when they formed.

PR E O V N IE LY W

1. Do some research, and describe the difference between a rock and a mineral:

`` Rocks are divided into three main types:

Conglomerate

Gneiss

Obsidian

M

ike

Be

au

re

ga

rd

Sandstone

Granite

Schist

Igneous

Metamorphic

Sedimentary

Formed from volcanic activity (e.g. a volcanic eruption).

Formed under extreme heat and pressure (e.g. during mountain building).

Formed from the deposition and compression of sediments (e.g. coal).

2. Research the rock types found near where you live. What does this say about the history of your area?

EXPLORE: The age of rocks

3. The map below shows the ages (in millions of years, my) of the bedrock (basement rock) around the world including the ocean floor. Study the map carefully and answer the questions below:

Ocean crust (my)

0-20

20-65

>65

Continental crust (my) 0-245

245-570 500-900

900-1600

(a) Where are the oldest rocks found?

(b) Where are the youngest rocks found?

(c) Suggest why these rocks are found where they are:

PS1.C

ESS1.C ESS2.A ESS2.B

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SC

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>2500

USGS

1600-2500

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169

EXPLAIN: Cycling of the crust

CL N AS OT SR F OO OR M US E

`` It may not seem like it, but the Earthâ&#x20AC;&#x2122;s surface is very dynamic and constantly moving. The movement is normally very slow but occasionally it can be very rapid. Rapid movement usually occurs during a large earthquake, when parts of the crust can move up to several meters in less than a minute.

`` The Earth's crust is divided into several large sections called tectonic plates. In addition to moving, these plates

are also growing and shrinking. Regions where the plates are growing are called constructive boundaries. Regions where the plates are shrinking are called destructive boundaries.

`` Where plates are moving apart they are called divergent boundaries. Where they are moving together they are called convergent boundaries.

Volcanoes form along the continental boundary of subduction zones.

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Convergent boundary (subduction zone). In a subduction zone the oceanic crust descends under the continental crust. Heat from the mantle melts the crust which can rise through cracks in the overlying continental crust and form volcanoes.

Trench

Movement of crust

Oceanic crust

Continental crust

Island arcs form on the opposing edge of a subducted plate bordered by a trench.

Hot spots: sometimes magma wells up in the middle of a plate, e.g. the Hawaiian islands.

Divergent boundary. Magma rises through cracks between the boundaries of tectonic plates, producing new crust.

4. (a) Given that oceanic crust subducts under continental crust, which type of crust would you expect to be older?

(b) How might this explain the map of the rock ages on the previous page?

5. (a) Why would rock being subducted, melted, and eventually brought back to the surface by volcanic activity have its radiometric clock "reset?"

6. (a) Is a subduction zone a destructive or constructive boundary?

(b) Is a mid ocean ridge a destructive or constructive boundary?

(c) Why do volcanoes form along the boundaries of subduction zones?

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(b) How would the cycling of the crust affect the age of the rocks likely to be found on the Earth?

CL


170

EXPLAIN: Processes that shape the Earth

CL N AS OT SR F OO OR M US E

`` Looking at other planetary bodies in the solar system, you may notice numerous craters all over the surfaces,

Far side of the Moon

Mars

Ceres

NASA

NASA

NASA

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especially on planets and bodies with little or no atmosphere and geologic activity:

Mercury

`` Craters are found on all the rocky planetary bodies (planets, dwarf planets, moons, and asteroids) in the solar

system but are apparently absent when looking at images of the Earth. It is reasonable to assume the Earth has undergone the same amount of bombardment as other bodies in the solar system over its history. Why then can we not see any craters?

`` In fact, the Earth has undergone the same kind of bombardment as other bodies in the solar system. Scientists have uncovered evidence for numerous impact sites all over the Earth as shown in the image below:

Moon crater

Mars crater

Earth crater

All images NASA

7. Compare the images below. The one on the left is from the Moon, the central image is of Mars (which has a thin atmosphere and evidence of ancient water flows), and the right image is from Earth:

(a) Suggest why impact sites on Earth are not as obvious as those on other planetary bodies:

(b) Compare of the images of the planetary bodies at the top of the page and the known impact sites on Earth. Would you expect there are more impact sites around the world scientists are not aware of? Explain:

CL

N AS OT SR F OO OR M US E

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171 Shaping the Earth

CL N AS OT SR F OO OR M US E

`` The Earth is geologically active. Its core provides heat, which drives movement of the crust. The movement of water erodes (wears away) material. The atmosphere moves both air and dust particles, which also erode structures.

`` The processes that shape the surface of the Earth can be divided into two main categories: constructive factors, which build surface features, and destructive factors, which break down surface features. Weathering

Erosion

Volcanic activity builds land. Hot fluid or semi-fluid rock welling up from deep below the crust bursts out of cracks in the crust as a volcano. Pulverized rock and lava thrown into the air by the eruption can build new land.

Weathering is the breakdown of rocks at the Earth's surface into finer particles. Weathering occurs by physical, chemical, and biological processes. Rocks do not always weather evenly, so some parts may be eroded away before others.

Erosion is the loosening and removal of weathered material. A key part of erosion is the transport of materials away from their origin so it lowers the average level of the land. Erosion may occur through the action of water, wind, or glaciers.

PR E O V N IE LY W

Volcanic activity

Tectonic activity

Mass wasting

Deposition is the process of sediments being added to a land mass. Sediments, such as sand and silt, may be carried by streams or rivers, blown by wind, carried in ice, or slide down hills as landslides.

New land can be formed by uplift during earthquakes. The seabed rising out of the sea extends the beach and adds to the land. Long term land and mountain uplift is called an orogeny.

Mass wasting, or mass movement, is the sudden movement of large volumes of rock and material, as in landslides. High cliffs and steep slopes are particularly susceptible to mass wasting.

(b) Describe the destructive factors that shape the Earth surface:

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CL

8. (a) Describe the constructive factors that shape the Earth's surface:

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Sediment deposition

G310Luke

jstuby

Erosion of differentially weathered rock

USGS

Unweathered

NASA

NASA

Weathered


172 (c) Use the information presented to draw and label a model of land formation and destruction:

PR E O V N IE LY W

CL N AS OT SR F OO OR M US E

EXPLAIN: The rock cycle

`` The processes that form the Earth's many rocks occur in a continuous cycle. Erosion of surface rocks produces

sediments. Burial of sediments transforms them into sedimentary rocks. Heat and pressure within the Earth can then transform pre-existing rocks to form metamorphic rocks such as slate and schist. Contact with magma may melt the rock, which may then form as volcanic extrusions or plutonic intrusions (igneous rock formed underground, e.g. cooling magma). Eruptions and intrusions bring these igneous rocks to the surface where the process repeats.

`` Volcanic rocks formed from lava and magma contain the same ratio of parent radioisotopes as the mantle. The

longer they are exposed, the more daughter isotopes accumulate and so the rocks can be dated from their first appearance. Sedimentary rocks are more difficult to date because they form after the erosion of igneous rocks and can be made up of sediments of different ages. Igneous rock (e.g. granite)

Rocks exposed at surface and eroded. Sediments are transported and/or buried and compressed.

Sedimentary rock (e.g. sandstone)

Rocks are buried. Exposure to heat and pressure reforms the rock.

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Rocks are buried. Exposure to heat and pressure reforms the rock.

Rocks are buried and melt on contact with the mantle. Molten rocks cool and harden following volcanic activity.

Metamorphic rock (e.g. gneiss)

CL

Rocks exposed at surface and eroded. Sediments are transported and/or buried and compressed.

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9. Identify the three rock types formed on Earth:

10. Explain how the following rocks are formed: (a) Gneiss forms from granite:

(b) Mudstone is formed from sediment:

PR E O V N IE LY W

The rock cycle and radiometric dating `` An important way to determine the age of a rock, such as the rocks on the bottom of the Atlantic Ocean, is through radiometric dating. However, radiometric dating works best when the ratio of radioisotopes in the original sample of the rocks is known.

`` When molten rock cools into igneous rocks, radioactive atoms are trapped inside. Radioactive decay is a

predictable process. This means that the time that has passed since the rock formed can be estimated from the quantity of unstable atoms remaining in the rock compared to the quantity of stable “daughter” atoms in the rock.

`` However, over time the processes of weathering and erosion break down and transport igneous rocks. The

sediments that result from these processes form sedimentary rocks. Dating these "new" sedimentary rocks by radiometric means is very difficult because they have crystals of many different igneous rocks in them and they may have been eroded and reformed many times. To date these rocks, a reference is often needed, such as an overlying lava flow, which can be dated radiometrically.

`` We would expect rocks welling up in the middle of oceans ridges to be young. Rocks further away from the ridge we would expect to be older. Using radiometric dating would prove or disprove these hypotheses.

We would expect these rocks to be older.

We would expect these rocks to be young.

Movement of sea floor.

Magma upwelling

Mid-ocean ridge

In Iceland, the rocks of the mid-Atlantic ridge can be seen on the land. The canyon here separates the North American and Eurasian plates.

11. (a) Explain why igneous rocks are most suitable for radiometric dating:

(b) Explain why dating sedimentary rocks is more difficult than dating igneous rocks:

(c) How might you determine the age of sedimentary rocks?

(d) What would you predict about the age of the rocks at equal distances on either side of an ocean ridge?

CL

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174

EXPLORE: Modeling the age of the Earth

CL N AS OT SR F OO OR M US E

`` Scientists have been modeling the Earth's age for

centuries. As techniques have become more sophisticated the models have become more refined and accurate.

100 Potassium atoms

Early models and estimates

`` Before the discovery of radioactive decay, calculating the

Time = 0 years

`` Georges Louis Leclerc (aka Comte de Buffon) developed

50 Potassium atoms 45 Calcium atoms 5 Argon atoms

PR E O V N IE LY W

age of the Earth was difficult. Most models focused on the cooling of the Earth from a molten ball of rock, but did not take into account the effect of heat produced by radioactive decay (because there was no knowledge of it). one of the earliest models for dating the Earth. In 1778 he used the cooling rate of iron spheres to model the cooling of the Earth from a ball of molten rock. Extrapolating his data he proposed the Earth was 70,000 years old, far older than the age of a few thousand years that many people believed at the time.

Time = 1.28 billion years

25 Potassium atoms 68 Calcium atoms 7 Argon atoms

`` In 1862, William Thomson (Lord Kelvin) calculated possible ages of between 20 million and 400 million years old.

`` In 1895, John Perry argued that Lord Kelvin had not

Time = 2.56 billion years

included convection currents in a molten mantle. Perry accounted for convection currents in his calculations and arrived at an age of 2 to 3 billion years.

`` In 1900, John Joly calculated the rate that the seas should

12 Potassium atoms 79 Calcium atoms 9 Argon atoms

Radioactivity offers another solution `` The discovery of radioactivity and the heat it produces in 1896 added another factor to the models of Earth's age. Heat in the Earth is being continually replaced and so the assumption that Earth simply cooled down after its formation was incorrect.

Time = 3.8 billion years

have accumulated salt to reach their current salinity. He used this to calculate the Earth's age at 100 million years.

6 Potassium atoms 84 Calcium atoms 10 Argon atoms

`` Early attempts to use radioactive decay as a way of dating

the Earth were filled with errors due to the many unknowns of the new science, but they did begin to show that the Earth had to be at least hundreds of million of years old.

`` Using the theory that uranium decays to lead following a

precise decay chain, Arthur Holmes published calculations in 1927 that the Earth was between 1.6 to 3.0 billion years old.

`` Refinements to the decay series for various radioactive

isotopes and ways of measuring isotope ratios have helped to date the age of the Earth to its currently accepted age of 4.54 billion years.

Time = 5.1 billion years

Potassium-argon dating is a commonly used radiometric dating technique. Potassium decays into calcium 89% of the time and argon about 11% of the time. Argon is inert and so is not contained in most minerals. Its mass in minerals is therefore related to the decay of potassium.

12. What assumption did many of the early models for dating the Earth make about the cooling of the Earth?

N AS OT SR F OO OR M US E

13. How did the discovery of radioactive decay invalidate many of the early models?

CL

14. Why would using the decay series of several different radioactive isotopes to date the Earth provide a more robust, accurate estimation of the Earth's age?

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175

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EXPLAIN: Methods for dating the Earth Dating Earth rocks `` The very oldest material dated on Earth is a zircon crystal found in a metamorphosed sandstone from Western Australia. It is dated to 4.4 billion years old, just a hundred million years after the Earth formed.

PR E O V N IE LY W

sample is radiometric dating. Many of the heavier elements (e.g. uranium and thorium) decay over time (their atoms break apart into smaller atoms). The rate of decay depends only on the original element's isotope. Uranium-238 ultimately decays into lead-206. The ratio of 238U to 206Pb in a sample can therefore be used to determine the time since the sample formed.

`` Zircon is a mineral and when its crystals form, it readily

The Jack Hills formation (Australia) where the oldest minerals on Earth have been found.

accepts uranium and thorium atoms in its structure but rejects lead atoms. This means any lead present in zircon has come from the radioactive decay of the uranium. The ratio of uranium to lead in the crystal is then used to date the crystal.

Evidence from meteorites `` Meteorites are solid pieces of debris (e.g. from an asteroid) that have fallen to Earth and survived impact. Meteorites originate from material that formed when the solar system formed so they can be used to estimate the age of the solar system and therefore the Earth. Most meteorites are small (a few centimeters across) but they vary in size. The largest known meteorite is the Hoba meteorite in Namibia, which is 2.7 meters across and weighs 60 tonnes.

NASA

`` One of the most accurate ways of dating a mineral

U

U

U

U

U

U

U

U U

Pb

Pb

Pb

U

U

U

U

Pb

Pb U U

Unstable atoms, e.g. uranium, change into stable atoms, e.g. lead, following a long but predictable decay series involving many radioactive elements.

`` Meteorites can be dated using the ratios of 206Pb,

and 208Pb to 204Pb. 206Pb, 207Pb, and 208Pb are all formed from the radioactive decay of uranium or thorium. 204Pb is primordial meaning it is not formed from radioactive decay. Thus the ratio of 206Pb, 207Pb, and 208Pb to 204Pb can tell us how long ago the meteorite formed (for example the ratio of 206Pb to 204Pb increases with time).

`` Because the decay rates of the parent uranium

isotopes and the radioactive lead isotopes are known, the age corresponding to each ratio of lead isotopes can be determined. These techniques have dated the oldest meteorites at 4567 million years Âą 0.01%.

Eugen Zibiso CC 2.0

207Pb,

The Hoba meteorite

15. How old is the oldest dated mineral on Earth?

16. Why would it be difficult to find rocks older that about 4 billion years old on Earth?

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CL

18. Why is lead-204 useful when radiometrically dating a meteorite?

N AS OT SR F OO OR M US E

17. Why are objects such as meteorites useful for dating the age of the Earth?


176 Evidence from moon rocks

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`` Moon rocks here on Earth come from lunar meteorites

and samples collected by the manned American Apollo and unmanned Soviet Luna missions. The Apollo missions brought a total of 380.96 kg of moon rock back from the various landing sites on the Moon.

`` The Moon has little active geology so most of the surface

PR E O V N IE LY W

`` The Moon has also suffered major impacts, some so large

they exposed the lunar mantle. This means the lunar rocks taken from the lowlands (the darker areas seen from Earth) are younger than those of the highlands (the brighter areas). Also the lunar highlands are more heavily cratered than the lowlands, indicating they are older (see "Crater counting").

Crater counting `` The amount of impact cratering created by meteorites can be used to date a surface. At its very simplest, a young surface has very few craters, an old surface has more. Different sized craters form at different rates (there are more smaller craters compared to larger craters). Therefore we can expect that ancient surfaces not only have a larger number of craters but larger sized craters compared to young surfaces.

Moon (telescope image)

Gregory H. Revera cc3.0

rocks are almost as old as the Moon. It is generally accepted that the Moon was formed when a protoplanet (named Theia) smashed into the Earth early in the development of the solar system.

Enceladus

reference point when using this method. Using the rocks brought back from the Moon, the number of craters at the sample site and the age of the surface can be compared.

NASA

`` Generally craters around 1 km in diameter are used as a

`` On a planet such as Earth, only large or very recent craters

Oxygen isotope ratios `` Oxygen has three stable natural isotopes, 16O, 17O, and 18O. It has been found that the ratios of 18O:16O and 17O:16O are unique to a planet or asteroid. However, the more closely related planetary bodies are, the closer the 18O:16O and 17O:16O ratios. The ratios are measured in terms of the deviation from the Standard Mean Ocean Water (SMOW) in parts per thousand (denoted d). When the deviations are plotted on a graph (d17O versus d18O) all the measurements from one planet or asteroid fall on their own unique line.

NASA

are visible on the surface. Smaller and more ancient craters have been eroded away by geological processes.

Mars rocks have their own unique oxygen isotope ratios

19. What is the purpose of dating Moon rocks?

N AS OT SR F OO OR M US E

20. Why are Moon rocks younger than Earth rocks?

21. Why would we expect older surfaces to have more and larger craters than a younger surface?

CL

22. The photo, middle above, shows the surface of Saturn's moon Enceladus. On the photo use labels to identify the youngest and oldest parts of the surface:

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177

ELABORATE: Dating the formation of the Earth

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`` You have been given explanations of various different techniques that can be used to date the Earth and stages

of its history. You will now use data acquired using those techniques to date important events in Earth's past and arrive at a time line of its history.

23. The data in the table below shows the age of various rocks and materials from the Earth and other bodies of the solar system. The material was dated using radiometric dating: Age (millions of years)

Error (+/-) (millions of years)

Chondrite meteorite

4568

0.3

Pb-Pb

Chondrite meteorite

4566

0.7

Pb-Pb

Dating method

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Material

4565

0.9

Pb-Pb

Mars meteorite

4428

25

U-Pb

Mars meteorite

4070

40

Ar-Ar

Mars meteorite

4040

100

U-Pb

Mars meteorite

3920

100

Ar-Ar

Moon rock highland

4426

65

U-Pb

Moon rock highland

4339

5

U-Pb

Moon rock lowland

3800

20

Ar-Ar

Moon rock lowland

3770

70

Ar-Ar

Earth - Australia

4404

68

Pb-Pb

Earth - Australia

4363

8

Pb-Pb

Earth - Australia

4341

6

Pb-Pb

Earth - Canada

3939

31

Pb-Pb

Earth - Greenland

3809

7

U-Pb

Earth - Canada

3737

23

Pb-Pb

See activity 58

(a) Plot the data above on the graph below using dot points:

NASA

Chondrite meteorite

NASA

Collecting moon rocks (Apollo 17)

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Moon rocks

Earth rocks

H. Raab CC 3.0

Mars meteorites

Chondrite meteorite

CL

Chondrite meteorites

N AS OT SR F OO OR M US E

Moon rock (Apollo 15)


178 (b) How old is the oldest rock type?

CL N AS OT SR F OO OR M US E

(c) How much older than the oldest Earth rocks is this rock type?

(d) Where might this type of rock have come from?

24. The data in the table below shows the deviations in oxygen isotope ratios (17O : 16O and different rocks and materials from the Earth and other bodies of the solar system: d17O 

d18O 

Chondrite meteorite

–3.61

1.19

Chondrite meteorite

–2.73

1.51

Chondrite meteorite

–0.91

3.52

Chondrite meteorite

0.4

5.86

Mars meteorite

2.64

4.45

Mars meteorite

2.60

4.38

Mars meteorite

2.87

4.87

Mars meteorite

2.99

5.09

from SMOW for

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Material

18O : 16O)

3.14

5.99

3.02

5.77

Moon rock lowland

2.92

5.56

Moon rock lowland

2.81

5.43

Earth rock

4.82

9.25

Earth rock

2.81

5.44

Earth rock

3.33

6.43

Earth rock

2.98

5.72

N AS OT SR F OO OR M US E

(a) Plot the data above on the graph below using dot points. Plot each group of rocks in its own color and include a key:

CL

Moon rock highland

Moon rock highland

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179 (b) Describe the shape of the plots:

CL N AS OT SR F OO OR M US E

(c) What do you notice about the Earth and Moon plots?

(d) What does this mean? 25. The data right shows the age of lunar rocks and the number of craters of diameter >1 km per km2 at the sample site: (a) Plot the data on the grid below. Try placing a curve of best fit through the points. A spreadsheet may help you.

Number of craters with diameter >1 km per km2 at sample site

Age (billions of years)

Terrae

0.35

4.35

Site

PR E O V N IE LY W

(b) Describe the shape of the graph:

(c) When was crater formation most frequent?

(d) What do you think was happening about this time?

Apollo 16

0.12

4.1

Apollo 14

0.03

3.9

Apollo 15

0.025

3.85

Apollo 16

0.025

3.85

Apollo 17

0.010

3.7

Apollo 11

0.0065

3.45

Luna 16

0.003

3.4

Apollo 12

0.004

3.2

Apollo 15

0.003

3.3

Copernicus

0.0015

0.85

Tycho A

0.00009

0.1

North Ray

0.00005

0.05

Cone crater

0.00002

0.01

See activity 57

1 x 100

1 x 10-2

1 x 10-4

1 x 10-5 5.0

4.0

3.0

2.0

Age (billions of years) Š2019 BIOZONE International ISBN: 978-1-927309-75-9 Photocopying Prohibited

N AS OT SR F OO OR M US E

1 x 10-3

1.0

CL

Frequency of craters per km2 with diameter >1 km

1 x 10-1

0.0


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26. The diagram below shows the South Atlantic ocean. Samples taken from the seabed were dated using radiometric dating. The positions of the sample and their age are shown in the table below: Sample number

Latitude

Longitude

Age of rock (millions of years)

1

14° S

23° W

62

35° S

43 W

100

25° S

7° E

80

4

41° S

6° W

40

5

11° S

11° W

20

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2

3

6

26° S

15° W

10

7

24° S

23° W

55

8

25°S

13°W

10

9

50°S

19°W

40

B

A

(a) Plot the data on the map above to show the position where the sample was taken:

(b) What happens to the age of the rock as you move from west to east across the South Atlantic?

(c) Draw a line on the map to indicate where rocks of the age 0 million years would be found:

(d) What does the position of the rocks and their ages tell us about South Atlantic ocean?

(e) The distance between point A and point B on the map is about 5,800 km. Roughly how fast are South America and Africa spreading apart?

(f) Estimate when the South Atlantic began to form:

CL

N AS OT SR F OO OR M US E

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181

ELABORATE: Information from probe missions

CL N AS OT SR F OO OR M US E

`` Due to the dynamic nature of Earth’s ever-changing surface, it is difficult to determine what the conditions were

like when the Earth was first forming. To answer some of these questions, we can look at other bodies in the solar system. Without many of the dynamics that have shaped the surface of the Earth (weathering, erosion, tectonic activity), comets, asteroids, and even the Moon provide details as to what conditions in the early solar system and consequently Earth may have been like. The Rosetta space probe was launched by the European Space Agency (ESA) in 2004. It made a gravity assist flyby of Mars, and flybys of the comets 2867 Šteins and 21 Lutetia. Rosetta then entered hibernation for 31 months before reawakening in January 2014. In August 2014 the Rosetta space probe reached comet 67P and entered orbit around it.

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Missions to comets and asteroids

Philae was released from the Rosetta space craft but failed to land correctly on the comet. It bounced along the surface of the comet and came to rest in a dark valley where its batteries ran out. Comet 67P/Churyumov–Gerasimenko orbits the Sun every 6.45 years. It is 4.3 km long by 4.1 km wide. Analysis of the comet showed that the ratio of deuterium to protium in the comet's water was three times that found on Earth. This means it is unlikely this type of comet delivered water to Earth in any significant amount.

Proton

Detecting water

Hydrogen atoms can be found as both a single proton with an electron (protium) or as a proton and neutron with an electron (deuterium). Deuterium is heavier than protium and is very rare (0.0156% of all hydrogen). In Earth's oceans there is about one atom of deuterium in 6420 atoms of hydrogen. Changes in this ratio in water molecules in comets or asteroids can be used to help answer questions about the origin of Earth's water.

Neutron

The space probe Giotto flew past Halley's Comet in 1986, becoming the first space probe to study a comet. It found the comet to be 4.5 billion years old and 80% water, 10% carbon monoxide, and 2.5% methane and ammonia.

The Stardust probe caught dust particles from comet Wilde-2 in 2004 and returned them to Earth. Analysis showed the presence of amino acids, supporting the hypothesis that comets may have brought some of the building blocks of life to Earth.

The Deep Impact space probe visited comet Hartley 2 in 2011. It was found that the comet contained water very much like Earth's, supporting the argument that comets brought at least some water to Earth.

N AS OT SR F OO OR M US E

27. (a) What evidence is there that comets may have delivered water to Earth early in its history?

(b) What evidence is there that only certain types of comet delivered the water?

(c) What is the evidence that the building blocks of life were carried to Earth on comets?

CL

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NASA

Andrzej Mireck

Electron


182

EVALUATE: Time line of the history of the Earth

CL

N AS OT SR F OO OR M US E

PR E O V N IE LY W

CL N AS OT SR F OO OR M US E

28. The Earth is about 4.5 billion years old. From the information you have studied over the last few pages you should have begun to develop a time line of the formation and history of planet Earth. Remove the next page from your book and cut out the images. Assemble them in order on pages 182 and 185 to produce a time line of the Earth's history. You will need to annotate the diagrams with as much information as you can and give approximate dates for each event based on the data on the previous pages. Use the labels as a start to help you.

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CL N AS OT SR F OO OR M US E

183

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Collision with Theia

Continents form

Earth

Moon

Comets and asteroids

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Nebula

CL

Plate tectonics

N AS OT SR F OO OR M US E

Oceans forming


PR E O V N IE LY W

CL N AS OT SR F OO OR M US E

184

CL

N AS OT SR F OO OR M US E

This page has been deliberately left blank

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CL

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N AS OT SR F OO OR M US E

PR E O V N IE LY W

CL N AS OT SR F OO OR M US E

185


186

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35 Powering a 15 Billion km Journey Revisited

`` The Voyager 2 probe was equipped

Imaging and science package

with three radioisotope thermoelectric generators (RTG).

`` Each RTG had a mass of 37.7 kg, which

High gain antenna

PR E O V N IE LY W

included 4.5 kg of plutonium-238. With a half-life of 87.7 years, the radioactive decay of the plutonium-238 provides the Voyager 2 probe with energy to power its systems.

Magnetometer

USDE

RTG

NASA

Plutonium pellet glowing under its own self-heating

1. Why was an RTG used to power the Voyager spacecraft?

2. Explain why only 13.5 kg of fuel has been enough to provide energy to the probe for the past 42 years:

3. (a) Estimate how much of the original plutonium is left in the fuel:

(b) Originally the RTGs provided Voyager 2 with a total of 470 watts of power. About how much power are the RTGs providing now?

(c) How might this affect the operation of the space craft in the long term?

N AS OT SR F OO OR M US E

4. The RTGs are mounted on a boom far away from the rest of the spacecraft. Suggest why this was done:

PS1.C

ESS1.C ESS2.A

EM

SC

CL

5. Plutonium decays by alpha emission. What element does it decay into (include atomic mass and number):

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36 Summative Assessment

1. Uranium-238 decays to lead-206 via a series of decays. The first four decays are shown below:

238 92

U

Thorium

Negative beta decay

Negative beta decay

Thorium Alpha decay

PR E O V N IE LY W

Alpha decay

Uranium

Protactinium

(a) For each of the elements shown, use the type of decay shown to calculate the atomic number and atomic mass of each of the elements shown:

Thorium:

Protactinium: Uranium: Thorium:

(b) Explain why uranium and thorium appear twice in the series:

2. Write a brief description of the strong force:

3. The diagram below shows materials needed to stop certain types of radiation produced by a radioactive source:

Relative penetrating power of alpha, beta, and gamma radiation Aluminum

Lead

Alpha Beta

Gamma

(a) Which type of radiation has the greatest amount of energy?

(b) Explain the difference in penetrating power of alpha particles and gamma rays:

(c) Why is lead shielding used to protect people from radiation?

CL

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N AS OT SR F OO OR M US E


188

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4. (a) What is the difference between nuclear decay, nuclear fission, and nuclear fusion?

(b) Nuclear fission is the most reliable of these to provide energy for producing electricity. Explain how nuclear fission is controlled and used to provide electricity:

PR E O V N IE LY W

5. When using radiometric dating to date the Earth why would using rocks from the continents be better than using rocks from the oceanic crust?

NASA

6. The image right shows Uranus's moon Miranda. Note that some parts are cratered and other parts have long streaks across them which may have formed from tidal stretching. Which event occurred first, the tidal stretching or the crater impacts? Explain your answer:

7. On the photograph below, identify, label, and describe the factors that are changing the landscape:

(a)

(d)

CL

(c)

N AS OT SR F OO OR M US E

(b)

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Waves & Electromagnetic Radiation

CL N AS OT SR F OO OR M US E

Instructional Segment 5

189

Activity number

Anchoring Phenomenon

PR E O V N IE LY W

I'm still standing: Why was the building damage during the 1985 Mexico City earthquake not uniform?

37 42

How do we know what is inside the Earth?

c

1

When you looked at energy in previous chapters, you learned that energy can be transformed from one form to another and transferred from one place to another. Think of examples of where energy is being transferred as waves. Which of your examples are mechanical waves and which are electromagnetic waves? Investigate the transfer of energy by mechanical waves. We can now ask questions about the defining characteristics of waves. How does the medium affect the speed at which energy is transferred? Use mathematical representations to describe wave travel in different media, including the relationship between wave frequency, velocity and wavelength.

38 43

c

2

Use your understanding of the behavior of mechanical waves in different media to interpret seismic information recorded at different places on the globe. How do changes in the recorded velocities of seismic waves provide evidence for the composition of the Earth's layers? Use this evidence to build on the model you developed in chapter 4 for the processes that shape the Earth's surface features. Explain how seismic waves provide further evidence for the processes occurring at destructive plate boundaries.

39 43

Why do people get sunburned by UV light?

c

3

What do understand by electromagnetic radiation ('light')? Explain how EM waves differ from the mechanical waves you explored in the first few activities of this chapter. Relate the mathematical representations of amplitude and wavelength to electromagnetic waves by comparing light of different intensities and colors. What is the relationship between changes in the wavelength of EM radiation and its color? Explain how the wavelength of EM radiation relates to how it is used both in the natural world and in technological applications.

40

c

4

Investigate two other properties unique to waves: diffraction and interference. What evidence do you have to support the idea that electromagnetic radiation can be described by a wave model?

40

c

5

Think back to the photoelectric effect in chapter 3. Recall that many metals emit electrons when light shines on them. If light acted as a wave, electrons would be emitted from frequency of light providing the wave has enough intensity (amplitude). In chapter 3, you found this wasn't the case. However the ability of light to dislodge electrons depends on its frequency (each photon has an energy proportional to its frequency). How does the photoelectric effect provide evidence for the model of light as a particle? From your investigations, evaluate the claims for the duality of light (its behavior as both a wave and a particle).

40

c

6

In the previous chapter, you explored some aspects electromagnetic radiation when you used a cloud chamber to detect the background radiation all around us. If you have ever been sunburned, you know that high energy (short wavelength) radiation harms biological tissues. However, what about longer-wavelength parts of the EM spectrum , such as microwave radiation? Apply your model of the particle nature of light from the photoelectric effect to evaluate published claims about the effects of different frequencies of EM radiation on health.

40

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How can we transmit information over wires and wirelessly? 7

Use your understanding of the properties and behavior of waves to describe how waves can encode information. Describe how technology makes use of this by (1) decoding wave interactions with media and (2) encoding signals using waves. Find out about these technologies and communicate technical information about how the properties of waves and wave interactions with matter allow us to transmit and receive information.

41

c

8

Explain the difference between digital and analog technologies. Analyze and interpret data about digital technologies and analog technologies with a similar role and assess the relative merits of each. Use what you have learned to evaluate questions about the advantages of using digital transmission and storage of information.

41

CL

c


190

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37 I'm Still Standing

ANCHORING PHENOMENON: Why was the building damage during the 1985 Mexico City earthquake not uniform?

`` On the 19th of September, 1985, at 7:17 am local time, a violent

PR E O V N IE LY W

earthquake (moment magnitude 8.0) hit Mexico City. It was followed by two strong aftershocks. The epicenter was located in the Cocos Plate subduction zone, approximately 10 km off the coast of the Mexican state of Michoacán. Although coastal regions were damaged, the most intense shaking occurred in Mexico City more than 350 km away. Was this related to the geology of the area?

`` Unlike San Francisco or Los Angeles, Mexico City is not near any

`` Most of Mexico City's downtown area sits on the old lake

USGS

fault line, but the city was originally built on an island in the middle of Lake Texcoco. The lake was drained by the Spanish leaving a foundation of silt and volcanic clay sediments.

A collapsed apartment complex sits across the sediments, which have a high water content. The regions to the west and northwest are outside the old lake margin and are built on street from a building with little damage. sands eroded from volcanic cones. They have a high water content, but not as high as the sediments of the old lake bed. The southern part of the city is built on hardened basalt lava flows with little water content.

`` As estimated 9,500 people died in the earthquake, 30,000 were

injured, and more than 100,000 became homeless as hundreds of buildings collapsed and more than 3000 were damaged. The damage costs were estimated at US$3-4 billion and sparked a change to earthquake warning systems and building regulations. But which buildings fell during the earthquake?

buildings occurred in an area corresponding to the western part of the lake zone. Buildings that were 6 to 15 stories high and built between 1957 and 1976 suffered serious damage, whereas very few of the lower buildings (1-5 stories) or those over 15 stories high were damaged.

USGS

`` 80% of the earthquake damage and nearly all the collapsed

Part of the Nuevo León apartment collapsed, whereas part of it was only slightly damaged.

1. (a) Have you ever experienced (or know someone who experienced) an earthquake?

(b) If so, was your/their house or apartment building damaged? If so, in what way?

(c) What other damage occurred?

2. How do you think an earthquake causes damage to structures like buildings and roads?

N AS OT SR F OO OR M US E

3. What factors do you think would influence the amount of damage a building suffers during an earthquake?

CL

4. In the 1985 Mexico City earthquake, some buildings collapsed while others close by were hardly damaged. Why do you think this was?

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38 The Nature of Waves

ENGAGE: The stadium wave

`` Have you ever seen a stadium wave (“the wave”)? Have you participated in one?

PR E O V N IE LY W

modern sports venues. It occurs when successive groups of spectators in a stadium briefly stand, cheer, and raise their arms. After standing up, each spectator sits back down. The result is a wave of standing spectators traveling through the crowd. Individuals do not move away from their seat.

`` Video analysis of 14 waves at large Mexican football stadia in 2002 resulted in a model of this wave behavior, which was published in the journal Nature. The videos showed that it takes the actions of a only few dozen fans to trigger a wave. Once started, it usually moves in a clockwise direction at a rate of about 12 m/s (~22 seats per second). At any given time the wave is about 15 seats wide. These observations appear to apply wherever the wave is observed.

Ken Lund from Reno, Nevada, USA [CC BY-SA 2.0

`` The wave is a common phenomenon in

The wave at Michigan Stadium, Ann Arbor, MI. It is the largest stadium in the US and the second largest in the world with a capacity of more than 110,000.

EXPLORE: The wave

`` How can we model a stadium wave? What sort of wave is it? Is the disturbance in the same direction as the wave is traveling or is it perpendicular to its travel? Let's find out more by recreating the wave in class.

INVESTIGATION 5.1: Modeling the stadium wave

See appendix for equipment list.

You will need your classmates, a recording device, and a screen to watch the video.

1. Go out into the hallway. Your teacher should direct your classmates to stand in a line. When they are given the start signal, the first person in the line will raise their hands. 2. As soon as you see the person to your right raise their hands, raise yours. After raising your hands, move them back down to your side. 3. After a practice run, your teacher will video the wave.

4. Repeat the process a few times to see how fast you can go.

5. If your teacher permits and there is enough time try some alternatives:

• When the wave reaches the end of the line, have it go back the other way. • Stand in a circle and let the wave pass around the circle a couple of times.

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PS4.A

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1. What can you say about the wave you and your classmates created?

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6. Return to the class and your teacher will play the video.


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2. What rule(s) do you need to follow to allow the wave to propagate?

3. Even though the wave moves horizontally, do you or any of your classmates move position?

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4. How do you explain the directional movement of the wave when the individuals creating it do not move in that direction?

EXPLORE: Energy and waves

`` When you looked at energy in earlier chapters, you learned that energy cannot be created or destroyed. Energy can only be transformed (changed) from one form to another. Energy can also be transferred (moved) from one place to another.

`` Some examples of energy being transferred are:

• In a power plant, heat from combustion turns water into steam. The moving molecules in steam turn a turbine to do work on a generator.

• Generators produce electric currents, which transfer electrical energy to towns, factories and homes.

• Winds blow from high pressure to low pressure regions, producing wind waves over fluid surfaces (center right) and sometimes turning turbines.

Turbine

• Seawater heated by the sun evaporates and eventually falls inland causing erosion, running down rivers, and sometimes powering hydroelectric stations.

• Tides and ocean currents (moving between temperature zones) cause the movement of huge volumes of water.

• Huge convection currents below the Earth’s crust cause the movement of crustal plates.

• Earthquakes and tsunamis are a result of energy released from sudden movements in the earth’s crust.

Ocean waves

• Light energy from the Sun travels through the solar system and reaches Earth. Light strikes air molecules and excites them, strikes the ground and heats it up, strikes the chloroplasts of plants and is trapped as chemical energy. • Electromagnetic radiation is released by excited atoms and radioactive materials which excites other atoms and releases heat.

• Musical instruments vibrate, producing detectable sounds (bottom right). • Supernova explosions in distant galaxies cause ripples in the “fabric” of space-time which can be detected here on Earth.

Sound waves

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6. What do you already know about waves that led to you choose those examples?

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5. Discuss which of the examples above are situations where the energy is being transferred by waves, then list them below:

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EXPLORE: Thunder and lightning – sound waves versus light waves

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`` A wave is an energy transport phenomenon. It transports

energy without transporting matter. Light, radiation, gravity, sound, and more all transmit energy through waves. What is it about waves that allows energy to be transported? Are all waves the same? What kinds of waves are there? What do we know about waves? Let’s explore thunder and lightning and see what we can discover…

`` The sharp flash of lightning and the loud boom of thunder are

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phenomena you will be familiar with. We briefly mentioned lightning as natural electrical discharge back in chapter 3, but there is a lot more to it than a simple near-instantaneous flow of electrons.

a spectacular lightning event when the area from Santa Barbara to LA was hit by more than 2,200 lightning strikes. The unusual event was the result of the jet stream coming further south and pushing large amounts of moisture into the area.

NOAA

`` On March 5, 2019, residents in Southern California experienced

7. Think about the last time you saw a flash of lightning.

(a) Did you hear thunder as well?

(b) Did the thunder occur at the same time as the lightning?

(c) Have you ever heard thunder occurring at the same time as lightning? Describe the situation:

8. If thunder and lightning come from the same source, why do you think you do not always hear the thunder at the same time as you see the lightning?

`` Sound waves and light waves are two different kinds

of waves even though they can arise from the same source, as is the case with lightning. As a result, these waves travel at different speeds.

• Light travels extremely fast (~300,000,000 m/s).

• Sound travels only 340 m/s in air (temperature of the air can change this speed).

`` When lightning strikes, we are able to see the flash of

light immediately. It takes longer to hear the thunder because of its slower speed. Because of the different rates that light and sound travel, we can estimate how far away a lightning bolt strikes by counting the seconds between when we see the lightning and when we hear the thunder.

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9. The circumference of the Earth is a little over 40,000 km. How long would it take a photon to travel this far?

10. Compare the circumference of the Earth to how far light can travel in 1 s. What does this comparison tell you?

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11. In 1 s, how many times can light travel around the Earth? Show your calculations:


194 `` The light from lightning is seen virtually instantaneously. Because of this, we can assume the time we see the

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lightning is the same time the lightning struck.

12. Calculate how long it takes for light to travel 1 km? Show your working:

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13. Rounding to the nearest 1 s, how many seconds does it take for thunder (the sound of lightning) to travel 1 km?

14. Based on your calculations, if you counted 9 s after seeing a flash of lightning, approximately how far away did that lightning strike? Show your working:

15. Lightning can strike up to 16 km from the storm. This is why pools and many beaches close as soon as lightning is seen. How many seconds would you need to count between seeing lightning and hearing the thunder before you can consider yourself safe? Show your working and explain your answer:

`` Visible light is an electromagnetic wave. Electromagnetic waves also include radio waves, microwaves, infrared, UV, x-rays, and gamma waves. All travel at the same speed, the speed of light (~300,000,000 m/s).

`` The medium (substance) electromagnetic waves travel through does affect their speed. Electromagnetic waves

travel fastest through matter with fewer particles. It travels through air faster than water. Light travels fastest in a vacuum, and this is the speed that is usually given for light, that is, the speed of light in a vacuum.

16. Would you expect a sound wave to travel faster through water or through air? Explain:

17. Would you expect sound to travel faster through the ground or through the air? Explain:

18. How fast would you expect sound to travel through space? Explain your answer:

pressure in the material (air, water, rocks, etc.). These waves are called pressure waves. Examples of waves resulting in variations of pressure include sound waves and seismic waves.

PHAN J. Alan Elliott

`` Many mechanical waves are the result of variation of

Pressure waves from the expansion of gases from the guns of the battleship USS Iowa can be clearly seen flattening the surface of the water.

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When lightning strikes, the sudden flow of electrons can heat the air around it to 30,000°C. This extreme heating causes the air to expand explosively creating pressure on the air immediately around it. Due to electrostatic forces between the particles in the air (recall chapter 2), the area of high pressure pushes out on the air further away. This wave of pressure continues outward away from the origin, but as the affected area increases the further away from the source, the less intense and more distorted the sound gets (recall the inverse square law).

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`` Mechanical waves are based on the movement of particles.

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19. Explain why thunder is louder the closer you are to the origin of the lightning strike:

20. Explain why you can sometimes see lightning on the horizon but never hear any thunder:

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EXPLORE: Types of mechanical waves

`` A wave can be described as an energy disturbance traveling through a medium. As waves move through a medium, energy is being passed from one particle to the next.

`` There are two types of mechanical waves: • Transverse waves

• Longitudinal waves

`` Recall the stadium wave you created with your classmates in the hall. This was a mechanical wave because it

involved the motion of particles and required a material medium (you and your classmates) for it to pass through.

`` Because the material the wave passed through moved up and down but had no movement in the direction the wave was traveling in, we call this wave a transverse wave.

INVESTIGATION 5.2: Water waves

See appendix for equipment list.

1. Fill a large plastic tray with water and allow the water to settle.

2. Place a plastic float about 5 cm square in the middle of the tray.

3. Hold a small square block of wood at one end of the tray on the water's surface.

4. Gently push down on the block of wood and release. This should produce some water waves in the tray. 5. Observe what happens to the water and the float.

6. Try pushing a little harder on the block of wood and observe again.

21. (a) How would you describe the surface of the water after you disturbed it by pressing on the block of wood?

(b) Describe the direction the waves traveled from the block of wood:

(c) Describe how the plastic float acted when the waves reached it:

(d) Did the float travel with the waves to the side of the tray or move up and down as the water waves passed underneath it? (If a little of both is true, describe which appeared to have more influence). Describe what you saw:

(e) What do you think is happening in terms of the motion of a single water molecule as a the wave reaches it and passes by?

(f) How did the motion of the float change when you pressed harder on the wood?

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196 `` Waves like you would observe on the surface of the ocean are transverse waves. This means the oscillations

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(repetitive motions) are perpendicular to the direction of the wave. The water waves in the tray were traveling from one end of the tray to the other, but the medium was going up and down causing the boat to bob in the water.

`` Likewise, in a stadium wave, the wave is traveling horizontally through the crowd (or from you to your classmates in your earlier activity) but the medium was the moving up and down motion as arms were raised above your heads.

`` Recall your stadium wave again. Imagine if the first person in

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the line collided with the next instead of simply raising their hands. The first person would transfer the energy from the collision to the second and recoil back. That second person in turn would collide with the third and so on until the energy dissipates enough that there are no more collisions.

`` You may have stood in line for an event where something like this has happened: someone trips and causes a small chain reaction of people bumping into each other. This is what happens in longitudinal waves. Molecules hit neighboring particles and then recoil. These collisions prevent the particles from moving in the direction of the wave. Only the energy is transmitted (right).

22. Think about a person in line tripping and causing a chain reaction:

(a) How might the chain reaction affect people standing closely together?

(b) How might the chain reaction affect people standing far apart?

(c) Based on your answers above, explain how the ability of a mechanical wave to travel through a material medium is related to how close the particles in the material are to each other:

INVESTIGATION 5.3: Slinky springs

See appendix for equipment list.

1. This activity needs to be done in pairs.

2. On the floor, stretch a slinky spring between you and your partner until it is taut but be careful to not overstretch it. 3. Flick the slinky sideways one time to send a single wave to your partner. Observe what happens when the wave reaches your partner’s end.

4. Now, flick the end of the slinky sideways repeatedly. Observe what happens as you vary the rate at which your hand moves.

`` When we describe waves, we use three basic characteristics.

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5. Next, create a series of waves by moving your hand towards and away from your partner. Observe this wave and how it travels.

• Frequency: the number of waves produced per second (measured in hertz, Hz)

• Wavelength: the distance between consecutive crests or consecutive troughs of a wave (in meters, m).

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• Amplitude: the displacement of a wave from the rest position. The amplitude is related to the amount of energy carried by a wave (more energy = greater amplitude).

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23. Use the three characteristics to describe your observations of the waves you produced with the slinky. (a) What happened to the frequency of the waves in the spring when you increased the rate which you moved your hand back and forth?

(b) What happened to the wavelength when you increased the rate which you moved your hand back and forth?

(c) What relationship can you draw between wavelength and frequency?

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(d) When you flicked the slinky sideways and created a wave, was the wave transverse or longitudinal?

(e) When you created a wave by moving your hand towards and away from your partner, was it transverse or longitudinal?

(f) For each wave produced, did any of the slinky coils actually travel from one end of the slinky to the other?

(g) What did travel if the wave coils did not?

(h) Describe the differences between transverse and longitudinal waves:

EXPLORE: Frequency, wavelength, and velocity 24. The diagram below shows a transverse wave:

A

B

Wavelength

Amplitude

(a) Draw onto the diagram between points A and B a transverse wave with a shorter wavelength than shown:

(b) Would your wave have a higher or lower frequency than the wave show?

(c) In a different color draw a wave with a smaller amplitude than the one shown:

(a) Mark on the diagram the three full wavelengths:

(b) How would you be able to tell what the amplitude of a longitudinal wave is?

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25. The diagram below shows a longitudinal wave. It has the same wavelength as the one shown above:


198 `` We are familiar with the concept of speed. Speed is simply the distance traveled in an interval of time (if we add a

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direction to the speed, we call it velocity) (recall v = d/t).

`` Waves transfer energy. The material the wave is traveling through is not transferring matter from one location to another.

26. If we are not measuring the movement of particles, what are we measuring when we measure the speed of a wave?

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27. When measuring a wave's speed, we can focus on the distance a point on the wave (such as a crest or trough) travels per second.

(a) If the crest of an ocean wave moves a distance of 30 meters in 10 seconds, what is the speed of the ocean wave? Show your working:

(b) If the crest of an ocean wave moves a distance of 45 meters in 10 seconds, what is the speed of the ocean wave? Show your working:

`` Sometimes a wave reaches the end of a medium that it is traveling through and encounters a new medium. In our slinky activity, for example, the wave you generated at one end of the slinky traveled through the coils to the other end where it encountered the hand of your partner who was holding their end.

`` One behavior waves exhibit when this happens, which you may have observed in the activity, is reflection. When a wave undergoes reflection, it remains within the original medium and travels back in the opposite direction.

`` Reflection is a phenomenon easily observed with sound waves. An echo is an example of this phenomenon. Sound travels through the air and when it encounters a solid object, the sound can be reflected back and heard again. Being able to yell into a canyon and hear your echo is because of the reflection of the sound waves.

28. You are standing 340 meters away from a canyon wall. You shout and hear your echo 2 seconds later. What is the speed of the wave? Show your working

INVESTIGATION 5.4: The speed of sound in air

See appendix for equipment list.

1. To start you will need tuning forks of various frequencies or a frequency generator with a speaker attached. You can download various cellphone apps that will do this and play the sound through the phone's earphones or speaker. 2. Set up the experiment as in the diagram. The PVC tube should be about 3-4 cm in diameter and about 30-60 cm in length. The cylinder of water also needs to be about this deep.

Tuning fork

Clamp stand

3. Record the frequency you are using (in hertz, Hz) (between 200 and 1000 Hz works).

5. Hold the frequency generator close to the opening of the pipe. While the sound is being generated, slowly move the pipe and the frequency generator up until you hear a loud humming in the pipe. This is called the first harmonic. 6. Clamp the pipe tight at this point and measure L (the distance from the top of the pipe to the water). Record this as L1 (in meters) in the table on the next page (L1 (m)) 7. Now with the same frequency sounding continue to raise the pipe out of the water until a loud humming is heard again. This is called the second harmonic. 8. Clamp the pipe tight and measure L again.

9. Record this as L2 in the table on the next page (L2 (m)). Repeat steps 3-9 with at least four other frequencies.

PVC tube Clamp

L

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4. Start with the PVC pipe fully down, with the top just out of the water.

Beaker or cylinder of water

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`` An alternative set up for this experiment is provided on BIOZONE's Resource Hub

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29. (a) Record your results here:

L1 (m)

L2 (m)

l L1

1/ l (L1)

l 2(L2–L1)

1/ l (2(L2–L1))

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Frequency (Hz)

(b) Using the equation l = 4L (where l is the wavelength) calculate the wavelength of sound in the pipe using your value for L1. This formula works if only one value of L is obtained. Enter the wavelength into the table above in the column labeled l L1. Do this for all your frequencies.

(c) A second formula using both L1 and L2 can be used to calculate the wavelength: l = 2(L2 – L1). Calculate the wavelength and enter it into the table in the column labeled l 2(L2 – L1). Do this for all your frequencies.

(d) We know from earlier that there is a relationship between frequency and wavelength, as one increases the other decreases. This means frequency (f) and wavelength (l) are inversely proportional so f and 1/ l will be directly proportional and will produce a straight line graph when plotted.

(e) Plot frequency (Hz) vs 1/l on the grid below. Use a key to distinguish between your different calculations of 1/ l: (f) Calculate the gradient of the graph (gradient = rise/run) for the line you produced:

(g) The equation for the gradient of your graph is: gradient = f ÷ 1/l. Rewrite the equation as multiplication:

Frequency (Hz)

(h) Frequency is measured in cycles per seconds (1/s) and wavelength is measured in meters (m). What then is the gradient of the graph measured in and what does the gradient then represent?

(i) Based on the gradients of your lines, what is the speed of sound in air?

(j) Which line is closer to the speed of sound?

1/ l

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(k) Write the equation linking velocity (v), frequency (f) and wavelength (l):

30. (a) Air particles are well spaced out and the restoring force (the force that pulls particles back into place) between the gas particles is not particular high. What do you think would happen to the speed of sound in water?

(b) Diamond is made of carbon atoms tightly bound together with covalent bonds. How would this affect the speed of sound passing through it?

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EXPLORE: Amplitude

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`` We noted there were three characteristics used to describe waves (frequency, wavelength, and amplitude). We

have explored frequency and wavelength, but what about amplitude? How does amplitude fit into our understanding of the behavior of waves?

`` Remember that a wave is an energy transport phenomenon. Energy is transported through a medium without

transporting the matter itself. In our slinky activity, when you shook the slinky back and forth you added energy to the slinky system. This energy traveled from coil to coil moving from one end to another.

INVESTIGATION 5.5: Amplitude

See appendix for equipment list.

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1. With a partner, lay a length of rope (at least 4 meters) on the ground, stretch it out and mark 1 meter intervals on the floor with masking tape.

2. At one end of the rope, reach down and give it a quick horizontal flick perpendicular to its length. 3. Observe the wave created in the rope and make sure it travels the length of the rope. If not, restraighten the rope and give the rope a harder flick.

4. Once you have determined how hard to flick the rope, straighten the rope and have your partner time how long it takes the wave in the rope to travel 4 meters. Record this information. 5. Repeat this a couple of times. Make sure you are flicking the rope with consistent amount of force.

6. Now, flick the rope a lot harder (make sure the flick is still horizontal and perpendicular to the ropeâ&#x20AC;&#x2122;s length) while your partner continues to time and record. 7. Repeat this a couple of times as well, making sure to flick the rope as consistently as possible. Speed of initial rope waves

Distance (m)

Time (s)

Speed (m/s)

Trial 1 Trial 2 Trial 3 Mean

Speed of stronger rope waves

Distance (m)

Time (s)

Speed (m/s)

Trial 1 Trial 2 Trial 3 Mean

31. (a) What happened to the amplitude (height) of the rope waves when you added more force to the flick?

(b) How was the speed of the waves affected by the change in force from your hand?

(c) What happened to the amplitude of the waves as they traveled the length of the rope? Explain why this happened:

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`` In many cases, waves propagate outwards from a single point in all directions. The energy of the wave spreads out over a greater area as it moves away from the source. This is why the energy of any point on the wave decreases significantly the further from the source it is, even though the total energy is the same.

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32. When the situation above applies, what law is likely to describe the relationship between wave intensity and distance from the source?

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EXPLAIN: Wave velocity in different media

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33. Use the equation v = fl to complete the table below for the speed of sound in different media: Frequency (Hz)

Wavelength (m)

Water

2980

0.5

Ethanol

2414

0.5

Steel

6300

0.5

Copper

4520

0.5

Polyethylene

1080

0.5

Speed of sound (m/s)

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Medium

Diamond

24000

0.5

Milk

3096

0.5

Helium

2002

0.5

Xenon

356

0.5

34. (a) What properties of the medium the wave is traveling through might affect the speed at which a wave can travel?

(b) Choose two of the above properties and explain why you think they affect the speed of the wave:

`` Electromagnetic waves do not require matter to transfer energy. This is because EM waves do not rely on collisions as a mode of energy transfer. When EM waves travel through a medium, the waves are temporarily absorbed and re-emitted by the atoms encountered.

35. (a) How might the speed of an electromagnetic wave be affected as it moves from a gas (such as the atmosphere) to a liquid (such as water)?

(b) From your answer above, explain why lead shields are used to protect from exposure to x-rays (a high frequency electromagnetic wave):

EXPLAIN: Wave period

`` The frequency of a wave is the number of waves passing a point per second. For example, in a wave with a

frequency of 5 Hz, five wavelengths pass by a point per second. Each wave must therefore take 1/5th of a second (0.2 s) to pass. This is the wave period (symbol T), ie. the time it takes for a single wavelength to pass a fixed point.

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36. (a) Use the information above to write a simple equation relating the frequency (f) of a wave to its period (T):

(b) v = fl, therefore f = v/l. Write an equation to relate T to v and l:

(c) Measurement of waves at the beach one day shows that the velocity (speed) of the waves is 3 m/s and the distance between wave peaks is 20 m. What are the frequency and wave period for these waves? Show your working:

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39 Earthquake Waves

ENGAGE: Earthquakes and waves

`` Earthquakes are caused when underground rocks suddenly break

along a fault. This releases energy stored in the stressed rocks (potential energy) and the ground moves, producing seismic waves that travel through the ground.

`` The amount of energy released and the depth of the rock fracture affects how the earthquake is felt at the surface.

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1. (a) How would the amount of energy released during an earthquake affect how the earthquake felt at the surface?

(b) How would the depth of the earthquake affect how the earthquake felt at the surface?

EXPLORE: Seismic waves

`` Seismic waves are produced by the sudden movement of a fault in the Earth. Two important wave produced are

P-waves and S-waves. P-waves are longitudinal waves (the same as sound waves). S-waves are transverse waves.

P-waves

S-waves

2. Describe the direction the wave travels compared to the movement of the medium for both P and S waves:

3. A seismogram shows the size of P and S waves in an earthquake. Study the seismogram below:

Time

(a) Which wave type arrives first and therefore travels the fastest?

(b) Which wave types arrives second and therefore travels the slowest?

(c) Which type of wave do you think would be the most destructive? PS4.A ESS2.A ESS2.B

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S-wave

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P-wave

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EXPLAIN: Using seismic waves

`` The properties of seismic waves can be used to determine the structure of the Earth. P-waves are longitudinal

waves and as such are able to travel through solids and liquids (just as sound can travel through solids and liquids). The pressure caused by moving particles bumping into each other allows the wave to propagate in the direction of the particle's movement, even in fluids and gases.

`` S-waves are transverse waves and can only travel through solid materials. Because the motion of the particles

is perpendicular to the direction the wave there is no mechanism that will translate sideways motions to forward movement in fluids and gases.

4. The diagram below shows the velocity of P and S waves in different layers of the Earth: Wave velocity (km/s)

PR E O V N IE LY W 3

5

7

9

11

Depth (km x 1000)

1 2

Lithosphere Asthenosphere Mantle

S

3

P

Outer core

4 5

Inner core

6

(a) What happens to the speed of the P and S waves as they travel deeper into the Earth?

(b) What happens to the speed of the S-wave as it reaches the outer core?

(c) What does this mean about the ability of the S-wave to travel through the outer core?

5. (a) What does the information above tell us about the state of the outer core and inner core of the Earth?

(b) Explain your answer:

`` When P and S waves from an earthquake are

mapped at seismometers around the world a diagram like that shown right can be produced:

P-waves (black)

6. Explain the patterns of P-waves and S-waves as recorded at the surface of the Earth:

No

S-waves (white)

P-w ave

S-

w

a

No

P-w

av

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No

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s ve

es

Lithosphere Asthenosphere Mantle Outer core Inner Core


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ELABORATE: Using seismic waves to locate earthquakes

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`` P and S waves move at different speeds through the Earth's crust. P-waves move at about 6-8 km/s, where as S-waves move at about 3-5 km/s.

Fault line

Epicenter (point on surface directly above the focus)

`` This time difference can be used to locate an earthquake's

epicenter, the point on the surface above where the earthquake was centered (right).

`` The difference in arrival times of P and S waves can tell us the Focus (point where earthquake occurred)

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distance away the earthquake occurred but to find direction we must use at least three different seismometer stations to triangulate where the earthquake occurred.

`` The graph below shows the travel times for P and S waves to seismometers up to 3000 km from the epicenter. P and S wave travel times

900

Distance (km)

P wave travel time (s)

S wave travel time (s)

S–P (s)

0

800

500

S-wave

1000

700

1500

Difference in travel time of 372 seconds = 2740 km

Time (seconds)

600

2000 2500 3000

500

400

The distance to an earthquake can be determined using the graph left. Either the difference in travel times can be calculated and plotted (as above) or read from the graph by finding the time between each line (as shown).

300

Another way to determine distance to calculate it directly from the travel times of the P and S waves using the equation:

P-wave

200

D=

100

0

ts - tp

1/vs – 1/vp

=

(ts - tp) vsvp vp – vs

Where D = distance, ts and tp are the travel times of the S and P waves (in seconds), and vs and vp are the velocities of the S and P waves.

0

1000

2000

3000

Distance (km)

7. (a) Use the graph above to complete the table beside the graph: (b) Plot distance and S – P on to the graph:

(c) If an earthquake occurred 600 km away, how long would it take for the P-wave to arrive?

(d) If an earthquake occurred 600 km away, how long would it take for the S-wave to arrive?

(e) What is the difference in P and S wave travel time for an earthquake 600 km away?

(f) The difference in P and S wave travel time was calculated to be 2 minutes. How far away was the earthquake?

(g) The difference between the P-wave and S wave from an earthquake was measured at seismometer A as 50 seconds. At seismometer B the difference was measured as 150 seconds. How much closer was seismometer A that seismometer B to the earthquake epicenter?

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205 `` Once distance is determined from at least three seismometers then the epicenter can be identified. Consider the

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example below:

Arrival time of P wave (hr:min:sec)

Arrival time of S wave (hr:min:sec)

Minneapolis, MN

1:30:20 pm

1:33:20 pm

Detroit, MI

1:29:56 pm

1:32:20 pm

Charleston, SC

1:30:38 pm

1: 33:48 pm

S â&#x20AC;&#x201C; P (s)

Distance to earthquake (km)

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Seismic station

8. (a) Complete the table above:

(b) The seismometer locations are shown on the map. Draw in circles to locate the earthquake epicenter using the data above and the scale on the map.

Minneapolis

Detroit

Charleston

0

(c) Why are three seismometer stations needed to locate the epicenter of an earthquake?

`` Earthquake waves has a very specific pattern, as

`` The top pattern is from a typical earthquake, with P and S waves arriving before the surface waves are detected.

`` The bottom pattern is from the underground

testing of a nuclear weapon. Note the single wave pattern. Thus nations around the world are able to monitor the nuclear tests of others and calculate the size of the weapon from the wave pattern.

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Earthquake seismogram

P-wave

S-wave

Surface waves

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shown on page 202. The ground waves produced by explosions have a slightly different wave pattern. This gives scientists a way to monitor activity around the globe. Consider the wave patterns right.

Nuclear weapon test seismogram

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500 km


206 `` Two pieces of information that are often stated about earthquakes are their epicenter and their depth. The depth of

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an earthquake can also be determined from the waves produced by the movement of a fault line.

`` Just as waves in water reflect off objects or waves in the slinky spring reflect off a hand so seismic waves can reflect of the layers of the Earth. A reflection changes the character of the wave and this can be detected in seismometers. The difference in the time of arrival of a wave and its reflection can help calculate the depth of the earthquake. Surface Seismometer

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pP-wave (reflection from surface)

Seismometer

P-wave

P-wave

Focus

`` The depth and location of the earthquake can revel a lot of information about the structure of the Earth. The data below shows the location and depth of various earthquakes around Japan's northern islands of Honshu and Hokkaido. Longitude (°E)

Depth (km)

145.0

15.9

144.5

26.1

144.0

34.8

143.5

35.7

143.0

35.9

142.5

36.5

142.0

43.6

141.5

74.9

141.0

87.2

140.5

92.4

140.0

126.0

139.5

131.4

139.0

154.2

138.5

194.8

138.0

195.9

137.5

245.9

137.0

261.2

136.5

335.9

134.5

408.8

133.5

454.2

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9. (a) Plot longitude vs depth on the grid above. Plot depth increasing down the grid: (b) What does the shape of the graph tell us about the Earth's crust off the eastern coast of Japan?

(c) Hokkaido and part of Honshu sit on the North American tectonic plate. To the east, this plate meets the Pacific plate. Is the Pacific plate moving under or over the North American plate?

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207

ELABORATE: Earthquakes, waves, and buildings

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`` All structures have a natural frequency which they will vibrate at if displaced then released. Resonance occurs

when a structure is shaken at is natural frequency. You can see this a child's swing. If you push the swing at just the right time with just the right frequency you can eventually make the swing swing very high indeed.

`` When seismic waves shake the ground beneath a building at or near its natural frequency the building will also

begin to sway back and forth in an extreme manner. This swaying can compromise the structural integrity of the building, causing it to fall. This is an important consideration when constructing buildings in areas likely to be subjected to seismic activity. See appendix for equipment list.

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INVESTIGATION 5.6: Modeling an earthquake

1. Cut out 2 strips from a Manila folder (or similar thickness card) for each of these sizes: 3 cm x 10 cm, 3 cm x 12 cm, 3 cm x 14 cm, 3 cm x 16 cm, and 3 cm x 18 cm. 2. Place the 2 same-sized strips together and clip each pair together with a binder clip at one end.

3. Label your “buildings” A through E, from shortest to tallest.

4. Evenly space all 5 strips of Manila folder between two blocks of wood. 5. Secure the blocks of wood together with tape or rubber bands, making sure they hold the blocks together tightly enough and the strips of Manila folder are secure.

6. These double strips of card represent buildings of different heights in a city. Now shake the blocks back and forth gently with a regular frequency. Observe the motions of the "buildings". 7. Now shake your blocks slightly faster and observe the reaction of the buildings. 8. Increase the speed of shaking once more and observe the results.

10. (a) Which buildings showed the greatest amount of motion for the first gentle shaking?

(b) Which buildings showed the greatest amount of motion for the second, slightly faster, shaking? Were they different from the first?

(c) Which buildings showed the greatest amount of motion for the third and fastest shaking?

(d) Describe any pattern in the movement of the buildings:

(e) Based on this activity, how is the safety of a building related to its height?

(f) How might the relationship you observed between the intensity of an earthquake and the height of the building affect how buildings might be constructed?

(g) Can you think of any ways to reduce the movement of the buildings at any given frequency of ground movement? Discuss your ideas in groups and summarize below:

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208 `` Reducing the movement of a building during an earthquake is called damping. A simple way of doing this is to

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transfer the movement of the building to something else.

INVESTIGATION 5.7: Damping a building

See appendix for equipment list.

1. Using Manila folder, again cut two strips 30 cm long by 3 cm wide.

2. Starting from one end of a strip, score and fold it at the 3 cm mark, 13 cm, 17 cm, and 27 cm. Tape your strip to a block of wood as shown in the photo.

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3. Mark the same measurements on the second strip of card. In the center 4 x 3 square draw a X across opposite corners to find the exact center. Punch a small hole through the card at this center point using a compass point or needle.

4. Thread a piece of thread or nylon through the hole. Attach the end that will be in the building to a small weight (5-10 grams). The thread should be about 4 cm long.

5. Attach the other end of the thread to the top of the building so that the pendulum you have made hangs through the middle of the building. 6. Now tape the building to the block of wood beside the first building.

7. Using a small amplitude gently shake the block back and forth at a steady frequency. Observe the difference between the two buildings.

8. Increase the frequency of shaking to reach the first building's resonant frequency and observe the difference between the buildings. 9. Experiment with different masses and lengths of the pendulum and height of the buildings. Which pendulums work best with which sized building?

11. (a) How did adding a pendulum to the building affect swaying of the building at each shaking frequency?

(b) How did changing the length of the thread or the size of the mass affect the swaying?

`` The system you have just investigated is called

tuned mass damping. It is one method to help reduce extreme oscillations caused by earthquakes, or even wind, on large structures.

which the building sits on huge isolators (like giant shock absorbers) that isolate the building from the ground, so that when the ground moves the building tends to remain still (to a certain degree).

Armand du Plessis CC 3.0

`` Other methods include base isolation in

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for Taipei 101 (Taipei World Financial Center). It is a massive 660 tonne ball held in place by massive wire ropes and sits on shock absorbers. It can move up to 1.5 meters in any direction and reduces swaying of the building by 40%.

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`` The photo right shows the tuned mass damper

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40 The Nature of Light

ENGAGE: Halos, rainbows, fogbows, sun dogs, and cloud iridescence

`` Have you ever seen unusual color phenomena in the sky? You are

probably familiar with rainbows, but what about other atmospheric optical phenomena, such as those pictured on this page.

`` The optical properties of the Earth's atmosphere cause a wide range of interesting and beautiful phenomena in the sky. Collectively, these phenomena are called photometeors.

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`` Photometeors appear when sunlight (or sometimes moonlight) creates reflection, refraction, diffraction, or interference under particular atmospheric conditions.

`` What is it about light that gives rise to these phenomena, and what

Fogbow (white rainbow), San Francisco

Cloud iridescence, Thailand

Gopherboy6956 Public domain

SC

EM

SSM

CE

PS4.B

PS4.A

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Sun dogs, North Dakota

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Halo, Nepal

Anton Yankovyi cc 4.0

Brocken Inaglory cc 3.0 c

Rainbow, Canadian Rockies

Wing-Chi Poon cc 2.5

circumstances exist to make them different?


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1. (a) Have you seen any of the photometeors pictured on the previous page? If so, which ones?

(b) For each example you have seen, describe the atmospheric conditions at the time, e.g. was it raining, cold, foggy?

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2. (a) How do you think the atmospheric conditions (weather) contributed to what you saw?

(b) What do you think might cause differences in what photometeors look like even though they are all caused by light?

EXPLORE: Energy waves

`` All waves transfer energy from one point to another and most of them can be classified into two general groups: • Mechanical waves are waves that require a material medium to pass through. The energy is passed from atom to atom, molecule to molecule, through successive collisions of the particles in the material. As such, mechanical waves are unable to travel through a vacuum. • Electromagnetic waves do not require a material medium to pass through. They are able to traverse the matterless regions of space between cosmic bodies. Electromagnetic waves are affected by the presence of matter which can slow the waves down as the energy is absorbed, transmitted, reflected etc by the particles it comes in contact with. The speed of an electromagnetic wave changes as it changes mediums.

`` We have known about electromagnetic waves for a long time and observations of their interaction with matter have

Amber Stuver cc 4.0

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been thoroughly investigated. Recently, another type of wave, that does not require a medium, has been detected. They are called gravitational waves and were predicted by Albert Einstein in 1916 as part of his theory of relativity. Gravitational waves are extremely weak, so it was 100 years later that their existence was confirmed by a largescale scientific experiment called LIGO. What little we know about gravitational waves is based on how they fit the theory of relativity and not on much observed data (yet).

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LIGO (Laser Interferometer Gravitational-Wave Observatory) is a large-scale physics experiment and observatory. The first detection of gravitational waves was made in 2015. This panoramic view shows the LIGO Livingston control room during the Advanced LIGO's first observing run. The Advanced LIGO Project began in 2008 to enhance the original LIGO detectors (which failed to detect gravitational waves). It continues to be supported by several international organizations.

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211

A: UV light

B: Sound from a turntable

C: Infrared lamp

D: Ripples on a pond

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3. Classify each of the waves above as either mechanical or electromagnetic: (a)

(c)

(b)

(d)

EXPLORE: What is light?

`` Light is a transverse wave which is composed of electric and magnetic fields oscillating at 90° to each other and at 90° to the direction of travel. It is therefore described as electromagnetic (EM) radiation.

Electric field

• EM radiation can be described by its amplitude (brightness or intensity), wavelength, frequency, and period.

λ = wavelength

etic gn d Direction a M fiel

• The energy (therefore intensity) of a wave is proportional to the square of its amplitude (I ∝ A2). If wave amplitude is doubled, it transports four times the energy. • If the intensity drops off at a rate of 1/r2 (inverse square law), the wave amplitude drops off at a rate of 1/r.

`` Electromagnetic (EM) radiation exists on a spectrum.

`` This spectrum is broadly grouped into categories based on its size. Size is measured by its wavelength. In order from shortest wavelength to longest, the electromagnetic spectrum includes:

• gamma radiation • x-rays • ultraviolet light • visible light • infrared light •  microwave radiation • radio waves Increasing frequency (f)

1024

1022

1020

γ rays

10-16

10-14

10-12

1018

1016

X rays

UV

10-10

10-8

1014

1012

IR

10-6

1010

108

106

FM

AM

Microwave Radio waves

10-4

10-2

100

104

106

f (Hz)

108

λ (m)

Increasing wavelength (λ)

600 nm

700 nm

CAUTION! We must be careful with the language we use around the EM spectrum and visible light. Sometimes the word “light” is intended to mean the whole spectrum while at other times the word “light” is used to mean only the visible part of the spectrum.

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4. Describe what happens to the frequency as wavelength on the EM spectrum changes:

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100

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500 nm

102

Long radio waves

102

Visible spectrum

400 nm

104


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Different parts of the spectrum can be distinguished by referring to their frequency or wavelength depending on the situation. When we talk about light in terms of color, we often also relate it to the wavelength (e.g. blue has a wavelength of 450 nm and green has a wavelength of 550 nm). Radio waves are referred to by their frequency. When you change the station on your car radio, you are selecting the frequency of the wavelength you want to hear. If you are tuned to 98.3, it means the frequency of that station is 98.3 MegaHertz (MHz) and its wavelength will be about 3.04 m.

EXPLAIN: The EM spectrum and the eye

`` Visible light is only a small part of the EM spectrum. This means the

information that we can access directly with our sense of sight is actually quite limited! The differences in color we can see are merely slight changes in the wavelengths within the visible spectrum.

`` If visible light is a part of the EM spectrum, why can’t our eyes detect other waves on this spectrum? Our eyes have evolved to respond to parts of the EM spectrum which are most useful to us. Of the wavelengths of light from the Sun that reach the Earth’s surface, the intensity of visible light is the highest (see diagram below). Human eyes evolved to use the most abundant type of light available.

Spectrum of solar radiation (Earth)

UV

Visible

Infrared

Irradiance (W ⁄ m2 / nm)

2.0

Sunlight without atmospheric absorption

1.5

5778 K blackbody

1.0

H2O

0.5

H2O

O2

0.0

H 2O

O3

250

Sunlight at sea level

500

750

1000

Atmospheric absorption bands H2O CO 2

1250 1500 Wavelength (nm)

1750

2000

2250

H2O

2500

EM spectrum, you will see that visible light is sandwiched between UV light and infrared (IR) light (above). Some animals’ senses allow them to detect these areas of the EM spectrum. The eyes of many insects for example are able to respond to (see) short wavelength UV light. This is useful to them because the plants they pollinate often have UV nectar guides to guide them to the nectar (right). The ability to detect the infrared part of the spectrum has evolved independently in two groups of snakes. This adaptation provides a survival advantage when hunting prey at night.

spectrum would be unlikely to provide an adaptive advantage.

Mimulus flower seen in visible light (left) and UV light (right) showing the dark nectar guide that is visible to bees but not to humans.

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`` For humans, mutations that would allow us to see outside the visible

Plantsurfer cc 3.0

`` Not all animals respond to the same wavelengths. If you look at the

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5. Suggest why eyes evolved to see the visible light part of the EM spectrum and not something like x-rays:

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6. Explain the advantages some animals have gained by extending their range of detection outside the visible spectrum:

EXPLAIN: Seeing with technology

`` Thanks to technology, we now have the ability to see

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into other areas of the EM spectrum. We are able to build devices capable of detecting these other wavelengths and transforming them into information we can detect.

• Radio receivers detect radio waves and transform them into sounds we can hear. • IR and UV glasses alter the wavelength of EM waves to allow us to see them.

• Infrared radiation is emitted by all objects with a temperature above absolute zero so thermal imaging (right) makes it possible to see the environment with or without visible light.

7. Thermal imaging utilizes wavelengths in the IR range. Explain why these images tend to use a lot of reds, oranges, and similarly longer wavelength colors of visible light:

EXPLORE: What happens when light hits an object?

`` When light comes in contact with a material substance any one of the following things (or a combination of them) can happen. The light can be absorbed, reflected, transmitted, or refracted.

`` When light is absorbed, the energy is taken in by the material.

The energy within the material increases, causing the particles to move faster. This energy eventually radiates as heat. An example of this would be heat rising from a pavement after the Sun has been shining on it for a while.

`` When light is reflected, the material fails to absorb the energy

from the light and the light rays are redirected. An example of this would be a mirror.

`` When light waves are transmitted, the incoming light passes

Air

Water

through the material unchanged. Light waves come out of the material at the same angle they entered. An example of this would be a transparent material like glass.

`` Refracted light is similar to transmitted light. The incoming

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light again passes through the transparent material, but due to differences in optical properties of materials and boundary angles, the light comes out at a different angle. An example would be when light from an object is seen after passing through a glass of water. The image is distorted.

8. Use the descriptions above and in the box above draw arrows to show what is happening to incident light when it moves from one material to another (e.g. from air to water) and is absorbed, reflected, transmitted, and refracted.

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9. Suggest why refraction is often observed as light travels through a range of different media:


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10. Different wavelengths of light are absorbed and reflected depending on the material the light hits. How does this explain the color of different objects?

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11. If you were to place a white and a black piece of paper in the Sun, which would you expect to heat up faster and why?

EXPLORE: Light – wave or particle?

`` Under specific circumstances, light acts as a wave and under others as a particle. This can be confusing when trying to determine exactly what light is.

12. Measurement of illumination at various distances from a point light source will confirm that light obeys an inverse square law.

(a) Explain this relationship using what you know about particle behavior (hint: think about spraying paint out of an aerosol can):

(b) Explain this relationship using what you know about wave behavior (hint: intensity/energy of waves is related to amplitude which will attenuate as it passes through a material. But what about light moving outwards through a vacuum?):

13. Based on your answers, do you think light acts as a wave or a particle? Explain:

INVESTIGATION 5.8: Your own double slit experiment

See appendix for equipment list.

1. Take a microscope slide and paint one side with graphite paint (or similar black paint).

4. Use plasticine or blu-tak to hold the laser pointer, and the slide, so that the laser beam is directed onto the slits and is then projected onto a wall 3-4 m beyond that.

5. Black out the room and turn the lights off. 6. Draw the pattern seen on the wall in the space provided on the next page.

Painted microscope slide with double slits

Laser pointer

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3. Make a second slit parallel, and as close as possible, to the first slit – so now there is a “double slit”.

Wall

4 3-

Plasticine

me

ters

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2. When the paint is completely dry carefully use a craft knife and ruler to make a slit in the middle of the painted side.

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215 14. Based on what you know about the nature of light, did you see what you expected to when the laser beam passed through the hole in the paper? Explain:

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Image on wall with two slits

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15. Describe what you saw when the laser beam passed through both holes:

16. Is the image on the wall consistent with what you know about the nature of waves so far? Explain:

INVESTIGATION 5.9: Investigating two properties unique to waves

See appendix for equipment list.

1. For this investigation you will work in pairs or small groups. You will need a square tray, something to generate waves with (e.g. a ruler or thin stick slightly shorter than width of the tray), and two longer and three shorter wood blocks to act as barriers. You can use masses to hold the barriers down. 2. Add water to the tray so that the depth will be about 10 mm below the top of the barriers. 3. At one end of the tray, one student holds the “wave generator” horizontally so that its lower edge is just below the water surface. Move the wave generator up and down very slightly (about a couple of mm), at a steady rate, to create a series of regular straight waves flowing across the water towards the opposite end of the tray. Important: do not touch the tray or bump the bench as this will produce unwanted ripples.

Side view of the setup

Straight wave generator

Barriers in a line across the tray

4. Place the barriers in the middle of the tank as shown in the arrangements below (viewed from above) and complete each one by drawing how the waves are affected beyond the barriers.

C

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B

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A

View of each arrangement from above


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17. In A and B, what did you observe as waves passed through the gap (especially near the edges of the gap)?

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18. Comparing A and B, what effect did the size of the gap have on what you observed?

19. In part C, what did you observe happening at the two narrow gaps?

20. In part C, what did you observe happening beyond the two narrow gaps?

21. Explain how this behavior of waves (you just observed) is related to the double slit experiment?

Wave diffraction

`` Let’s revisit the double slit experiment. As the light

from the laser pointer passes through the two slits, it begins to spread sideways. This property of waves is called diffraction and is unique to waves (nothing else known to science is able to do this).

Gap about the same size as the wavelength of the wave

Gap wide compared to the wavelength of the wave

`` Eventually, the spreading waves overlap each other

and the crests and troughs of the waves start to add together in some places and cancel each other out in other places. This property of waves is called interference and is also unique to waves.

`` Diffraction is the “bending” of waves as they pass

through gaps or pass close to edges of obstacles. This can be seen on a large scale with sea waves around harbours(right) and ships.

`` If the gaps are large relative to the wavelength then the bending is only slight.

`` If the gaps are similar in size to the wavelength (or

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AM and FM radio waves illustrate the effects of diffraction. FM wavelengths are significantly shorter than AM wavelengths. If you are operating a radio in a deep valley you will receive AM waves more easily as they will bend (diffract) over the surrounding hills more than the shorter wavelength FM radio signals.

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smaller) then the bending is very pronounced.

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217 Wave interference

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`` Wave interference occurs when separate waves traveling in the same medium overlap. As the waves pass through each other, they can combine by adding together or cancelling each other depending on how the crests and troughs of their respective waves coincide.

`` When the crests and troughs of two different waves line up, they add up resulting in a wave with greater amplitude. This is called constructive interference.

`` When the crest of one wave meets the trough of another (and vice versa), the waves cancel each other out. This is called destructive interference.

(b) Destructive interference

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(a) Constructive interference

22. Complete the diagram above to show the end result of:

(a) Constructive interference between the two waves

(b) Destructive interference between the two waves

23. Using the ideas of diffraction, explain how waves were able to overlap during your double-slit activity:

24. Using the ideas of constructive and destructive interference, explain the images you saw during your double-slit activity:

25. Explain how these explanations strengthen the idea that light is a wave?

EXPLAIN: Light and a bit more on the photoelectric effect

26. What happens when light above the wavelength threshold hits an electron:

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metal surface, electrons can be ejected from the metal. This will only occur below a unique wavelength threshold for each type of metal. Even at very high intensity, light with longer wavelengths (lower frequency) would not cause electrons to be ejected for some metals. By contrast, very short wavelengths of light are able to cause electrons to be ejected even at very low intensities.

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`` Recall the photoelectric effect from chapter 3. When light is shone on to a


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27. If light were a wave, what would happen to the energy of the electron as the wave continues to arrive and its energy continues to be absorbed?

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28. If an electron were to collect enough energy through this method, what should eventually happen? Explain:

29. Explain how your last two answers, which assume light is a wave, conflict with photoelectric effects:

30. Explain what the photoelectric effect implies about the nature of light:

`` Because of the photoelectric effect, light can be described as “particle-like” packets of energy.

`` A photon is the term we use to describe a packet of energy in light. Photons of different wavelengths possess different amounts of energy.

`` Increasing the intensity of light only increases the number of photons emitted. It does not change their energy.

EXPLAIN: The duality theory of light

`` Based on the results of various experiments and other known characteristics of light, we can see that light exhibits the properties of both a wave and a particle. This is called the duality theory of light.

31. Explain the ways in which light acts as a wave (give examples):

32. Explain the ways in which light acts as a particle (give examples):

(a) Reflection:

(b) Refraction:

(c) Diffraction:

(d) Interference:

(e) Photoelectric effect:

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33. Different effects of light can be explained in terms of waves and/or particles. State which model best describes each of the following phenomena (note: some may work with waves only, particles only, or both):

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219

EXPLAIN: The electromagnetic spectrum and health

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`` Exposure to some forms of electromagnetic radiation can lead to health problems. With the increased use of some

frequency ranges in the EM spectrum for radios, WIFI, and cell phones, it would be useful to know if they are having negative influences on our health.

`` Electromagnetic radiation can be broken down into two categories: • Ionizing radiation

• Non-ionizing radiation

Radiation effects Measurement in millisieverts (mSv). Effects are cumulative. Potentially fatal radiation sickness. High risk of cancer later in life. 10,000 mSv: Fatal within days 5000 mSv: Would kill half of those exposed in 1 month 2000 mSv: Acute radiation sickness

an electron to be ejected from a metal, a wavelength of light carrying at least a certain amount of energy is required. Anything below this had no effect. Thus, different metals had different threshold levels at which an electron would be ejected.

MODERATE

`` Recall the photoelectric effect. In order for

RI HIGH

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of a single photon to break a chemical bond. That is, radiation that carries enough energy to detach electrons from atoms or molecules, creating ions (hence the name, ionizing radiation).

SK

`` This distinction is based on the capability

No immediate symptoms. Increased risk of serious illness later in life.

1000 mSv: 5% higher chance of cancer 400 mSv: 4 h exposure would cause radiation sickness 100 mSv: Higher risk of cancer is first noticeable

`` The photoelectric effect is similar to the

`` High energy EM wavelengths such as

gamma and x-rays are ionizing and therefore quite dangerous.

No symptoms. No detectable increased risk of cancer. 20 mSv: Yearly limit for nuclear workers 10 mSv: Average dose from a full body CT scan 9 mSv: Yearly dose for airline crew 2 mSv: Average yearly background radiation in US 0.1 mSv: Single chest x-ray

TOL ERA BLE

processes involving ionizing radiation. If the energy in the EM wavelength is too low, it cannot detach an electron. Anything above a certain threshold however can.

`` If biological material (including human tissues, cells, and genes) are exposed to too much ionizing radiation then

molecules and atoms that they are made from will not function or react chemically in their usual ways. If enough atoms and molecules are affected then whole cells and organs will fail leading to sickness and possibly death.

High levels of exposure to ionizing radiation One adult chest x-ray (0.1 mSv) delivers about the same amount of radiation as 10 causes changes to DNA (genes). These days of the natural background radiation that we are all exposed to everyday. Some changes (mutations) can lead to cancer. occupations, e.g. technicians at nuclear facilities, present a higher risk than others.

34. Looking at the chart above, why do you think tolerable limits are set over quite long periods of time (e.g. a year)?

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35. Why do you think women are asked if they might be pregnant when they go to have an x-ray?

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36. The effects of ionizing radiation are well established (see diagram top). But what about the health effects of microwave radiation, which includes the frequency used by most mobile phones? Apply your understanding of the particle nature of light to evaluate the validity and reliability of published claims of the potentially damaging effects of microwave radiation. Share your findings via a collaborative web document.


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41 Waves and Technology

ENGAGE: Communicating with waves 1. You may be aware of the various types of electromagnetic waves used in communication technology. In groups discuss what you know about how each of the pieces of technology transmits or receives information: (a) AM radio:

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(b) FM radio:

(c) Cellular phone:

(d) TV satellite:

(e) Bluetooth emitter:

(f) WIFI emitter:

EXPLORE: Encoding and decoding information

`` We have seen that waves transfer energy but do not transfer matter. Using technology the basic features of waves can be manipulated so that they can also rapidly convey vast amounts of information over very large distances.

`` Waves convey information in two general ways:

• Information about a medium can be obtained simply by the way a wave is affected as it travels through that medium, e.g. seismic waves, MRIs and x-rays.

• Waves can be used as a “vehicle” for transmitting information that we want to send from one place to another, e.g. radio waves. A

first be able to encode our information into waves and then decode the waves once it has reached the receiver.

`` First let us look at how information can be encoded. One

G

of the simplest ways is something like Morse code were information is encoded as simple dots and dashes.

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N

2. Think of a short sentence. Write it out in Morse code below and see if a classmate can decode it:

B

O

U

V

C

D

I

J

P

Q

E

K

F

L

R

M

S

T

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`` For waves to transmit and receive information we must

W

X

Y

Z

PS4.A

PS4.C

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Morse code

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221

EXPLAIN: Radio waves and modulation

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`` Recall that radio waves are part of the electromagnetic spectrum. They have longer wavelengths than visible light. But how do radio waves carry information?

`` Each radio transmitting station broadcasts a radio wave, with a unique frequency, called the carrier wave. When

there is an audio signal (human voice or music) to be sent out, that signal is used by the transmitting equipment to modify the carrier wave slightly. This is called modulation.

`` You have heard of AM radio and FM radio, but what do these stand for and how do they work? What is the difference between them?

FM

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AM

Signal to be sent

Signal to be sent

Carrier wave

Carrier wave

Modulated wave

Modulated wave

AM stands for amplitude modulation. The amplitude of the carrier wave is changed. AM wavelengths are much longer than FM wavelengths. This means they are less affected by structures such as buildings or mountains and hence have a greater range.

FM stands for frequency modulation. The frequency of the carrier wave is changed. More than one signal can be transported by one carrier wave (e.g. allows stereo sound) and it enables better reproduction of the original modulating wave.

3. (a) Describe how the crests and troughs of the modulating wave are represented on an AM carrier wave:

(b) Describe how the crests and troughs of the modulating wave are represented on an FM carrier wave:

`` In wireless (WIFI) communication, the router and network cards use more complicated forms of modulation. These types of modulation allow many different signals to be conveyed by each carrier wave and can enable multiple carrier waves to simultaneously use the same bandwidth.

(b) Why do radio stations only require a simple modulation to transmit information?

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4. (a) Explain why a router would need to engage multiple carrier waves to carry information:


222

EXPLAIN: Red and blue light

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`` Radio waves can carry information. Visible light waves can also be made to

carry information. This is the basis of CDs, DVDs, and Blu-ray discs, which all use lasers (intense and highly coherent beams of light) to read and write data.

`` Visible light has shorter wavelengths (higher frequency) than radio waves.

CC2.5

This means more information can be transmitted over the same time interval with these shorter waves.

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5. Suggest why more information can be stored, read, or transmitted using shorter wavelengths of light rather than longer?

`` CDs and DVDs use red lasers (780 nm for

`` Blu-ray players use light in the blue to UV

spectrum (405 - 195 nm). A Blu-ray disc can store up to 300 GB of information depending on the format, compared to around 17 GB for DVDs and only 700 MB for a CD.

Vic Mirmow CC 4.0

CDs and 650 nm for DVDs) to read and write data. Discs store information digitally, using a sequence of pits and flat spots (called lands) arranged in a continuous line which spirals from the center of the disc to its edge. The laser reads the pits and lands to access the information on the disc. The more data that is contained on a disc, the smaller and more closely packed the pits and lands must be.

6. (a) Suggest why red lasers were used to read and write data years before blue lasers?

(b) Are there any dangers associated with using shorter and shorter wavelengths for data storage and transmission?

EXPLAIN: Digital versus analog

`` Imagine if you had to transmit information about length without a ruler, mass without a scale, temperature without a thermometer, or time without a clock.

`` In order to transmit this kind of information, you would need to make comparisons (analogies), usually to other

known objects. Length could be conveyed by comparing an object to another known object or specific marks on paper. Mass might be compared to the weight of an elephant or a small dog.

7. What kinds of things could you use for comparisons to describe:

(a) An object's mass:

(b) The temperature of water:

(c) How long it took to do an activity:

(d) The color of an object:

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223

Phrontis CC3.0

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`` A good example of the difference between analog and digital is how time is displayed on analog and digital clocks.

On an analog clock, the clock hands rotate continuously, around a continuous scale. As there are no steps in the time displayed, an analog clock can theoretically display any time at all (an infinite number of times) within the limits of our vision and the precision of the scale. In this case, the time displayed is a continuous or analog variable.

Digital clocks are programmed to change the time display once every 60 seconds (or once every second). This means the time displayed is “stepped”. Any time between these steps cannot be read from the display. Thus, within each hour there are a finite number of times that can be displayed. In this case the time displayed is a digital variable.

`` Digital devices use 0s and 1s to create a code for on and off. We call this code binary because there are only two possibilities: 1 and 0 or ON and OFF.

`` Binary code is the basis for digital information because of its simplicity. ON and OFF is achieved electronically

by transistors which can switch on and off at incredibly fast rates (typically 109 times a second). Information is encoded as a sequence of 0s and 1s, transmitted through wires or waves to devices such as our computers which decode the information and display it as characters, images, or sound for us to experience.

8. Our everyday number system uses base ten. This means there are ten symbols used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Binary uses just two symbols, 0 and 1. Table A below shows how the numbers 0 to 6 are presented in binary. Complete table A by filling in the binary numbers for 7, 8, and 9. 9. Look at the image of the digital clock. Any number is made up of seven individual LED lights, either on (1) or off (0). The seven segments of an LED clock are drawn in the space below. Each segment is labeled (A through G). Table B below shows how a number in these seven segments would be coded. Complete table B for the numbers 6, 7,8, and 9. Table A

Table B

Base 10

Binary (4 place holders shown)

0

0000

A

B

C

D

E

F

G

1

0001

1

1

1

1

1

1

0

0

2

0010

0

1

1

0

0

0

0

1

3

0011

1

1

0

1

1

0

1

2

4

0100

1

1

1

1

0

0

1

3

5

0101

0

1

1

0

0

1

1

4

6

0110

1

0

1

1

0

1

1

5

Binary code (segments)

Number displayed

6

7

7

8

8

9

9

(b) Use Table B to write down the code for each digit:

i. 1st digit:

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10. (a) The diagram below shows the blank display for a digital clock. Shade in the relevant segments to display a time of day of your choosing (hours and minutes):

3

4


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ELABORATE: Digitizing music through graphing

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`` Sound is a wave. As such it varies continuously. The information to produce music can be stored as analog or digital.

`` A vinyl record is an analog music storage device. It has a continuous

spiral groove stamped into it that rises and falls. A needle on the record player fits into the groove and vibrates as the groove passes under it. The vibrations are converted to an electric signal that is sent to the speakers.

`` Much of the music we store today is digital. The original sound wave

is a stored collection of numbers which are snapshots of points on the original wave. Music on a CD or MP3 file is nothing more than a very long sequence of 0s and 1s. The digital information is converted into an electric signal by the playing device (e.g. an MP3 player) and sent to the speakers.

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A scanning electron micrograph of the grooves in a vinyl record.

`` How do you reduce the shape of sound to a series of numbers? First the sound is received by a microphone, which converts the continuously varying sound wave to a continuously varying voltage. This varying voltage then goes to an electronic device called an ADC (analog to digital converter) which samples the voltage at very small, but regular, time intervals and produces a voltage that still varies, but in distinct steps (digitized). Each step is recorded as a unique binary number (encoded), depending on the size of its voltage.

11. Study the wave pattern on the graph below: 10 9 8 7

Voltage

6 5 4 3 2 1 0

0

1

2

3

4

5

6

7

8

9

10

Time

(a) Record the voltage to the nearest whole number for each of the times shown in table 1 below: Time

Voltage

(b) Now record the voltage to the nearest decimal place for each of the times shown in table 2 below: Time

Voltage

Time

0.0

5.5

1

0.5

6.0

2

1.0

6.5

3

1.5

7.0

4

2.0

5

2.5

6

3.0

7

3.5

8

4.0

9

4.5

10

5.0

Voltage

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0

7.5 8.0 8.5 9.0 9.5 10

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225 (c) Now plot the data from table 1 and 2 onto the grid below. Use a curve to connect the points from each table. Use a key to distinguish between the data from each table:

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(d) Compare the two graphs you just made. Which one of them best resembles the original?

(e) How could you efficiently reproduce the original graph?

12. (a) Draw a wave on the graph below, similar to the one in Q11. 8

Time

7

Voltage

6

5

4

3

2

Voltage

Time

0.0

5.5

0.5

6.0

1.0

6.5

1.5

7.0

2.0

7.5

2.5

8.0

3.0

8.5

3.5

9.0

4.0

9.5

4.5

10

Voltage

5.0

0 0

1

2

3

4 5 Time

6

7

8

9

10

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1

(b) Complete the table for your wave, entering voltage values to the nearest decimal place. Read them out to your partner. As you read them out, your partner should plot the coordinates on the graph on the following page of their book and join the points with a curved line.

(c) Once your partner has plotted your coordinates, swap over. Your partner reads out their coordinates for their wave while you plot them on the graph over the page.

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226 Plot the coordinates for your partner's graph here:

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8 7

5

4

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Voltage

6

3

2 1 0

0

1

2

3

4 5 Time

6

7

8

9

10

(d) Compare your original graph to the graph your partner created using the data points collected (your partner will also compare graphs). Describe any similarities and differences between the graphs:

(e) How could your graphs be used to argue that analog recordings are more accurate than digital recordings?

(f) If you repeated the process how could your version of your partner's graph be improved?

(g) How could your graphs be used to argue that digital sampling could be just as accurate as an analog recording (and in some ways better)?

EVALUATE: Electromagnetic waves and technology

`` The ability to use electromagnetic waves to code, decode, transmit and store information in compact digital formats

(b) Alternatively a group of four should choose one type of technology based on electromagnetic waves and research how the technology was developed, how it works, and any future possible developments or technologies based on the original technology. This should then be presented to the class as a poster, PowerPoint, or other kind of presentation.

Image from a CT scan

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13. (a) Form a group of four. Each person should select a technology based on electromagnetic waves (e.g medical imaging such as CT scans, or communication technology such as cell phones). Each person should research the topic and report back to the group on how the technology was developed, how it works, and any future possible developments or technologies based on the original technology (e.g. 5G in cell phones).

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have revolutionized the world.

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42 I'm Still Standing Revisited

`` At the start of this chapter you read about the earthquake that affected Mexico City in 1985. You found out that

while buildings between 6 and 15 stories tall collapsed or were severely damaged, buildings taller or shorter than that were relatively unaffected.

The collapsed hospital with an undamaged building behind.

Mikenorton CC3.0

USGS

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`` You should now be able to explain some of the aspects that caused this selective damage to the buildings.

The tectonic plate boundaries around Central America

1. What actually causes an earthquake?

2. What factors may have influenced the amount of damage sustained by buildings during the Mexico earthquake?

3. Explain why buildings of a specific height were damaged during the Mexico earthquake:

4. Earthquakes are not the only natural phenomenon that can damage a building. Wind can cause serious damage as well, even well below hurricane strength. (a) In what way could wind of a certain speed and gust strength or frequency affect a tall building?

(b) How would this be similar to the effect of an earthquake?

(c) How might the effect be reduced for a building in a windy city?

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43 Summative Assessment

1. (a) On the axis below draw three wavelengths of a transverse wave with a wavelength of 4 m and an amplitude of 2 m: 3 2

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1

0m

1

2

3

4

5

6

7

8

9

10

11

12

13 m

1 2 3

(b) For the wave above, the velocity of the wave was measured at 3 m/s. What is the frequency of the wave?

(c) What is the period of the wave?

2. (a) Complete the table below: Medium

Wavelength (m)

Frequency (Hz)

1

1.7

2.0

2

0.9

3

0.6

5

1.8

2.2

3.6 2.2

6

3.5

2.1

4

Speed (m/s)

2.0 2.2

(b) Based on the results above which media would have similar properties? Explain your answer:

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3. Describe the difference between a transverse and a longitudinal wave and give an example of each type:

(a) Explain why the explosion was seen before it was heard:

(b) If sound travels at 343 m/s how far away was the explosion?

PS4.A ESS2.A

CE

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4. During observation of a test explosion, the explosion was seen 2.5 seconds before it was heard:

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229 Consider the following statements: – The crust, mantle, and inner core of the Earth are all solid. – The outer core is liquid. – Subduction zones are areas of the Earth where one tectonic plate is plunging beneath another.

Explain how recording seismic waves produced by the movement of fault lines in the Earth can provide evidence for these statements. Diagrams may help your explanation:

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5.

6. To our eyes, the vast majority of plant leaves appear green. Explain this phenomenon in terms of light waves:

7. The diagram below shows two transverse waves with the same wavelength. The waves interfere with each other. Draw the resulting wave on to the diagram. 6

4

1

2 4

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3

4

5

6

7

8

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10

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0m

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2

11

12

13 m


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8. The orbital motion of water particles as a wave passes through can be modeled using PowerPoint software. This can also be done with other presentation software such as Apple KeyNote. The instructions will be similar, but you may have to search for specific features in alternative locations if you are using other software.

(a) Open PowerPoint, create a new presentation and select Blank Slide.

(b) i. Select the ‘oval’ shape and use it to draw a circle, making sure its height and width are the same (3 cm x 3 cm for example). This represents one water molecule. ii. In the ‘Format shape’ options, select ‘Solid fill’ and ‘No line’.

iii. Under the ‘Arrange’ options, select ‘align’, and then select ‘Align center’ and ‘Align top'.

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(c) i. Draw a larger circle to represent the water molecule’s orbit as the wave passes.

ii. Again, select ‘oval’ for shape and simply make sure height and width are the same.

iii. In the ‘Format shape’ options, select ‘No fill’ and ‘Solid line’ with 50% transparency. iv. Under the ‘Arrange’ options, select ‘Align’, and then select ‘Align center’ and ‘Align top’.

(d) Group your circles by clicking and dragging an area which includes both of your circles, then selecting ‘Group’ from the ‘Arrange’ pull-down options.

(e) Resize your group so you will be able to fit 25 orbits on the slide (1.3 cm x 1.3 cm works).

(f) i. Copy and paste your group to create 25 groups.

ii. Arrange the groups side by side by selecting all the groups, then under the ‘Arrange’ drop-down menu, select ‘Align to slide’, ‘Align middle’ and ‘Distribute horizontally’.

iii. If needed, you can adjust the sizes of your circles to better fit across the slide: drag and click to select all the groups, go to ‘shape format’ and adjust the ‘Height’ and 'Width’ boxes (make sure the height and width of your ovals are the same in order to make circles). Then realign to fit as needed.

(g) i. Set the groups to rotate 360° by selecting ‘Animation’ and then ‘Spin’. Each of your smaller ‘water molecules’ should rotate around their individual orbits.

ii. Once you have seen the animation work correctly, new options on the ‘Animation pane’ should be available. Select all the groups shown in the animation pane. Under the ‘Timing’ drop-down menu, go to ‘Repeat’ and select ‘Until next click’. You can also adjust the duration of the spin, but it must be the same for all groups.

(h) i. Every molecule’s position in a wave is rotated slightly relative to the previous one. You have 25 water molecules. Molecule 1 and 25 are already set to 0° and 360° (0°) respectively.

ii. The remaining 23 molecules need to be preset. Select the second molecule, go to ‘Shape format’, open the ‘Format pane’, and select the ‘Size and properties’ option (will be the image of a square with arrows on the inside and line segment on the outside).

iii. Select the ‘Size’ drop-down menu and adjust the ‘Rotation’ by typing in 15°. Select the molecules one by one, rotating each 15° more than the previous (24 x 15°= 360° for a complete circle). Since the first is 0°, the second will be 15°, the third 30°, and so on…

(j) Animate the wave as before. Once you have your wave working, you can make some adjustments until you are happy: switch between clockwise and counter-clockwise rotations, adjust the duration of the animation, adjust the transparency on the orbit to 100% so you can only see the water molecules, make the wave longer by resizing, copying and pasting all the molecules to make a second wave, etc.

(j) When running your animation, note the difference between the direction the wave is traveling and the motion of the individual particles. Describe how the two are related:

(k) Use the animation to explain why matter does not travel along the wave:

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Stars and the Origins of the Universe

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Instructional Segment 6

231

Activity number

Anchoring Phenomenon

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Hidden in plain sight. There is more to the Crab Nebula than visible light can reveal!

42

47

How do we know what stars are made of?

c

1

Look at maps of the stars and galaxies in space. What do you notice about the colors and the brightness of the stars that you can see? Use your understanding of electromagnetic (EM) radiation to find out about the light from stars. How can we measure the magnitude and luminosity of a star? What do these properties depend on and how are they related? Explain how the temperature of a star can be inferred from its color. Analyze luminosity and temperature data for a range of stars and describe any patterns you can see in the data.

43

c

2

Build on your model of atomic structure from chapter 4 to represent the multistep process by which EM radiation is absorbed by atoms and then emitted again as excited electrons return to their ground state. Use your model to explain how the bands in the EM spectra emitted from stars are used as fingerprints to identify the types and quantities of elements they contain.

43

c

3

How large is the Sun and how do we know its size? What fuels it, how old is it, and how long will it continue to shine? These questions were asked by early physicists who could not conceive of a fuel to explain the longevity of the Sun's activity. Repeat von Helmholtz's calculations for the lifetime of the Sun based on the burning of coal. What lifetime does this scale of energy release produce? Does this support the age of the Earth indicated by other lines of evidence (see Chapter 4). We now know that nuclear fusion in the Sun's core produces the Sun's heat and light. Use a model to explain how nucleosynthesis creates new atomic nuclei from pre-existing protons and neutrons and releases electromagnetic energy.

c

4

How does the heat and light from the Sun's core reach Earth? Observe evidence of convection in the Sun's outer envelope and explain the role of convection in creating variations in solar intensity. How do variations in solar output affect the Earth's climate over shorter and longer timescales?

c

5

Recall that the core of stars is the only place in the universe where nuclear fusion occurs continuously. However, even at the center of stars, conditions can change so that fusion stops. You have calculated the age of our Sun, but what did it look like when it was younger and what will it look like when it is older? We can look at other stars as examples to answer this question and see evidence that stars have a life cycle.

c

6

Use your understanding of energy conservation and nuclear fusion to explain the life cycle of stars of different mass (from their origin to end of life). Explain how counterbalancing feedback between opposing processes (gravity and fusion) accounts for the stability of main sequence stars and use this to construct a model of how fusion relates to a star's life cycle.

c

7

Create a diagram or storyboard to communicate your understanding of how stars, over their life cycle, produce the elements we find on Earth. Label your diagram to explain the way nucleosynthesis and the different elements that are created vary as a function of the star's mass and the stage of its life cycle.

c

8

Analyze the spectra of stars beyond the Sun by comparing them to known spectral lines of different elements determined in the laboratory. Explain how Doppler shifts can be used to map out the movements of stars toward or away from us. What pattern is revealed and what model could explain it? Investigate redshifts using simplified absorption lines from different galaxies and obtain information about how distance in the universe is determined. Combine your findings to describe the scale of the universe and how it is measured.

46 48

c

9

Based on your investigations, you could ask what caused the expansion of the universe and what evidence of that it exists today? Explain Big Bang theory based on astronomical evidence including the red shift vs distance of stellar spectra, the cosmic microwave background (CMB), and the measured composition of stars and non-stellar gases.

46 48

What fuels our Sun? Will it ever run out of that fuel?

NASA

44 45

44 45 48

Do other stars work the same way as our Sun?

43 45 48

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How do patterns in motion of the stars reveal the origin of our universe?

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NASA

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44 Hidden in Plain Sight

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ANCHORING PHENOMENON: There is more to the Crab Nebula than visible light can reveal! At the center of this....

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The Crab Nebula

...lies this

Photos: NASA

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The Crab Nebula was named by William Parsons in 1840, but its original appearance was first observed by Chinese astronomers in the year 1054. The image above left is a mosaic created from images taken by the Hubble Space Telescope. The image above right is an x-ray image and was produced in 2014 by the Chandra x-ray observatory. 1. In 1054 Chinese astronomers observed a "guest star" in the sky. It remained visible for about two years. As a class, or in groups, discuss what might have caused this "guest star" to appear and produce the Crab Nebula as we see it today. Bullet your discussion points below:

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SPQ

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2. The image on the right shows what is at the center of the Crab Nebula, but it can only be seen clearly through x-ray imaging. As a class, or in groups, discuss what you think the object at the center of the Crab Nebula is and what could have caused it. Why do you think we need x-ray imaging to see it clearly? Summarize your discussion points below:

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45 Star Light, Star Bright

NASA

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ENGAGE: A colorful scene

The image above was taken by the Hubble Space Telescope in 2017. It is part of the constellation of Sagittarius (the Archer). The image shows stars of many different colors. 1. (a) When was the last time you went out at night, looked up at the stars, and gave serious thought to what you saw?

(b) Did you notice any differences in the stars you observed? What were they?

2. (a) What colors of stars can you see in the image?

(b) As a class discuss what the different colors may represent:

EXPLORE: Observing stars

The wavelength of electromagnetic waves range from nanometers to kilometers. Different wavelengths are affected in different ways by Earth's atmosphere. The range of frequencies of electromagnetic radiation and their respective wavelengths and photon energies is called the electromagnetic spectrum (below). To observe them all we need a range of equipment. In physics, electromagnetic radiation is often just called light, regardless of whether or not it is visible light.

Radio waves pass through the atmosphere and can be observed using radio telescopes.

0.01nm 0.1nm

1nm

10 nm

x-rays

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100 nm

1 μm

10 μm 100 μm 1 mm

UV

EM

SSM

1 cm

Infrared Wavelength

SPQ

CE

P

10 cm

1m

10 m

Radio

ESS1.A

PS4.B

CL

Visible light can be observed from Earth but is distorted by the atmosphere. Orbital telescopes, e.g. Hubble, produce a clearer view.

γ-rays

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Infrared light is mostly absorbed by water vapor in the atmosphere, so infrared sources are best observed from space.

Visible light

Gamma rays, x-rays, and most of the ultraviolet spectrum are blocked by the atmosphere and must be observed from space.

100 m 1 km


Infrared radiation passes through dust and gas particles allowing detection of otherwise hidden features. The image above shows infrared light being emitted from the Andromeda Galaxy.

X-ray observation can help detect highly active but often invisible objects, e.g. black holes. The image above shows the x-ray light being emitted from the Andromeda Galaxy.

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Optical telescopes allow us to see extremely faint objects that emit visible light. The image above shows the Andromeda Galaxy emitting visible light.

All images NASA/JPL

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234

3. Identify the observation methods for the following types of light waves:

(a) Visible light:

(b) Gamma rays and x-rays:

(c) Radio waves:

4. Why is observing objects using infrared a useful astronomy method?

5. Why so you think it is useful to observe a celestial object using more than one part of the electromagnetic spectrum?

EXPLORE: Magnitude and luminosity

`` A star's apparent magnitude is how bright the star is to the naked eye. The scale is "backwards" and logarithmic: a magnitude 1 star is 2.5 times brighter than a magnitude 2 star. The absolute magnitude is the apparent magnitude the star would have if placed at a distance of 10 parsecs (32.6 light years) from Earth. If the distance to the star is known, then the absolute magnitude can be calculated from the apparent magnitude.

`` Luminosity and absolute magnitude are related. The more luminous a star is, the smaller its absolute magnitude. In

astronomy, luminosity is the total energy emitted over all wavelengths per unit of time (synonymous with watts (W)).

`` The table below shows the apparent and absolute magnitudes, and the luminosity of several stars: Star

Apparent magnitude

Absolute magnitude

Luminosity (Sun = 1)

Distance (light years)

Sun

-26.8

4.83

1

0

Aldebaran

0.75

-2.1

518

65

Betelgeuse

0.42

-2.9

150,000

640

-9.4

2.7 billion

3900

0.58

50

25

0.03

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VY Canis Majoris 7.9

Vega

CL

6. What is the apparent magnitude of the Sun? 7. The star Sirius has an apparent magnitude of -1.46 and an absolute magnitude of 1.4. What is meant by apparent magnitude and absolute magnitude?

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EXPLORE: Star color and temperature

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`` Temperature can be inferred, in part, from color. For example, a piece of iron heated in a hot flame will initially glow red, then orange-yellow as it gets hotter, and finally may reach white hot.

`` The temperature of stars can be determined from their color in a similar way (below). Remember short wavelengths produce blue colors, whereas long wavelengths produce redder colors. Peak power at different wave lengths By measuring the wavelength at a star's peak power density, the star's temperature can be determined using the Wien Displacement Law. b Wavelength lmax (m) = T

7000 K

20

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Power density (watts/m2)

x 1013 25

15 10

Visible

5000 K

b

4000 K

5

l

100

500

1000 1500 Wavelength (nm)

2000

T

Where

b = 2.898 x 10-3 mK

T is in Kelvin (K)

8. The image on the right shows a sparkler as it is burning.

(a) Identify and label the three bright distinct colors that can be seen on the shaft of the burning sparkler:

(b) List the colors from hottest to coolest:

9. Returning to the image at the start of this activity, list the circled stars in order of their temperature from hottest to coldest:

A

B

10. (a) What color would a star emitting its peak energy at a wavelength of 300 nm appear?

(b) Why?

C

D

NASA

11. Use the Wien Displacement Law to determine the temperature of the following stars:

Antares

934

Vega

311

Regulus

223

OTS-44 brown dwarf

1260

Sun

502

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Wavelength (m) at peak power density

Temperature (K)

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Wavelength (nm) at peak power density

CL

Star


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EXPLORE: Patterns in the stars

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12. The luminosity and temperature of stars can be plotted against each other. The data below is for a range of stars in the Milky Way Galaxy. Plot the data in the tables on to the grid below. Note that the x axis is a logarithmic scale: Temperature (K)

Luminosity (Sun =1)

Star

Temperature (K)

Luminosity (Sun =1)

Sun

5840

1.0

Epsilon Eridani

4590

0.34

61 Cygni

4130

0.15

Luyten 726-B

2670

6 x 10-5

Achernar

20,500

3150

Procyon A

6600

6.93

Alpha Centauri

5840

1.5

Procyon B

9700

5.5 x 10-4

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Star

Altair

8060

10.6

Rigel

12,140

1.2 x 105

Arcturus

4590

170

Ross 128

2800

3 x 10-3

Barnardâ&#x20AC;&#x2122;s Star

2800

4 x 10-3

Alpha Crucis

28,000

1.6 x 104

Betelgeuse

3200

105

Sirius A

9620

25.4

Capella

5150

Sirius B

14,800

1 x 10-5

Vega

9900

50

Deneb

See Activity 58

9340

1x

78

2x

105

Scatter plot of stars showing luminosity vs temperature

106

105 104

Luminosity (sun = 1)

103 102

10 1

10-1 10-2 10-3 10-4

10-5

30,000

10,000

6,000

3,000

Surface temperature (K)

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13. (a) Where are most of the stars found on the graph you have plotted?

(b) What do you notice about the outliers (data points well outside the main spread)?

(c) Predict the color of Achernar:

(d) Predict the color of Sirius A:

CL

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EXPLAIN: How do we know what a star is made of?

Hydrogen

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`` The composition of a star can be determined by its absorption spectrum. `` The very hottest inner layers of most stars emit an almost continuous

spectrum of electromagnetic (EM) radiation. When the visible section of this radiation passes through the outer layers, gaseous elements there absorb certain wavelengths, leaving dark bands in the EM spectrum that is finally emitted from the star. This pattern of dark bands can be compared with the absorption spectra, determined in laboratories, for specific elements (each element has a unique "spectral fingerprint").

Helium

Vega

`` When reaching the Earth, the light can be passed through a prism to split

The absorption spectra of hydrogen and helium and the star Vega. Vega shows hydrogen absorption lines and weaker helium lines.

PR E O V N IE LY W

it up into the spectrum of colors (ROYGBIV). Within this spectrum, black lines will indicate the "missing" wavelengths of light, i.e. those absorbed by elements in the star being observed.

Star

Dark bands at specific wavelengths indicate specific elements in a star's atmosphere.

Prism produces a spectrum of the light from the star.

Absorption by atoms The lines in a star's light spectrum are at specific wavelengths. These wavelengths correspond to the energy absorbed and re-emitted by electrons orbiting atoms in a star's atmosphere. Early in the 20th century it was established that the electrons in atoms (and ions) can only be found at certain energy levels around the nucleus. The symbol n represents the level number with the n = 1 level being the ground state (lowest level). Any energy absorbed or released by an atom must match the difference in energy between two energy levels. This is why only certain wavelengths of light (the photons corresponding to each wavelength have a unique energy) can be absorbed or emitted.

Electrons can be found only at specific energy states.

Electron Nucleus

n=1 (ground state) n = 2

Electrons are not found here.

n=3

Incoming photon

A hydrogen atom has one electron. Ordinarily it orbits the nucleus at an energy state of n = 1 (the ground state). If a photon of light with the right wavelength hits it, the electron will jump to the next level n = 2 (an excited state). The wavelength of the photon needed to do this is 121.4 nanometers. A photon with a wavelength of 103 nm will make the electron jump from n = 1 to n = 3.

Electron absorbs photon and jumps to n=2

As the electron returns to the ground state from n = 2, it emits a photon equal to what it absorbed (121.4 nm). The photon will be emitted in a random direction and is therefore unlikely to fill in the dark line of the absorption spectrum caused earlier by the absorption of a photon with the same wavelength.

n=2

n=3

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n=1

Electron emits photon and returns to ground state.

Outgoing photon

n=2

CL

n=1

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n=4

n=3


238 `` The graph below shows the absorption curves for the star Vega, the Sun, and the star Aldebaran. Vega is a blue-

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white star with a surface temperature of about 9600 K, the Sun is a yellow star with a surface temperature of about 6000 K, and Aldebaran is a orange giant with a surface temperature of about 3900 K.

`` The large dips indicated in the spectrum of Vega are consistent with the absorption lines in the visible hydrogen

spectrum. The dip at 410 nm (Hd) indicates an electron jumping from n = 2 to n = 6. Although the Sun also has large amounts of hydrogen, the dips are not as prominent. These differences are due to the stars having different temperatures and luminosities. Photons flowing from the Sun generally do not have enough energy to bump electrons in hydrogen up to higher energy states. Hd

Comparison of absorption spectra

PR E O V N IE LY W

Hg

Relative intensity (arbitrary scale)

Hb

Vega

Ha

Sun

Aldebaran

400

600 Wavelength (nm)

500

700

14. Explain briefly how the composition of a star can be determined:

15. The diagram below left shows the absorption spectra of four different elements. Use them to identify the elements present in the two hypothetical stars A and B, below right: H

A

He Li

B

Na

400

(a) A:

(b) B:

500 600 Wavelength (nm)

700

400

500 600 Wavelength (nm)

700

CL

N AS OT SR F OO OR M US E

16. All stars are made up mostly of hydrogen and helium, with small amounts of heavier elements. Explain why the absorption spectra of very hot blue stars do not generally show hydrogen lines in the visible spectrum, whereas bluewhite stars such as Vega show prominent hydrogen lines, and yellow stars like the Sun show only small hydrogen lines.

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EXPLAIN: Patterns in the stars II

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`` Previously you made a scatter plot of the relationship between the absolute magnitude of stars and their temperature. The diagram below shows a complete diagram, called the Hertzsprung-Russell diagram.

`` The position of a star on the graph tells us about that star's present stage in its life cycle. For most of their life, stars are found in the main sequence and are called main sequence stars. Main sequence stars convert hydrogen to helium by nuclear fusion in their core. During their time in the main sequence, the outward force caused by fusion balances the inward force of gravity. White dwarfs are found near the bottom left, while supergiant stars are found in the top right. As a star progresses through its life cycle, it will move off the main sequence. A star like the Sun will move to the upper right (red giants) before moving down to the lower left to become a white dwarf.

PR E O V N IE LY W

Hertzsprung-Russell diagram

106 105

A.

Supergiants

104

Luminosity (sun = 1)

103 102

Ma

in

10 1

Giants

B.

se

qu

en

ce

Sun

10-1 10-2 10-3 10-4 10-5

Red dwarfs

White dwarfs

O

B

30,000

A

10,000

F

G

K

6000

M

3000

Surface temperature (K)

17. Use the Hertzsprung-Russell diagram to determine the following:

(a) The surface temperature of the Sun:

(b) The temperature and luminosity of the star at the point labeled A:

(c) The temperature and luminosity of the star at the point labeled B:

18. Describe the position of the Sun on the diagram as it changes into a red giant and then to a white dwarf:

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19. Why are most stars found in the main sequence part of the diagram?

(a) An O class star:

(b) A F class star:

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20. Stars are classified based on their temperature and emission spectra as O, B, A, F, G, K, or M (see the horizontal axis of the graph above). What would you expect the hydrogen and helium emission spectra to look like for the following stars?


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46 The Sun

ENGAGE: Stardust

`` Almost all elements we know are formed in stars. The very lightest, hydrogen and helium, were formed during the

Carbon

USAF Staff Sgt. Jim Araos

Ravedave CC 2.5

PR E O V N IE LY W

Big Bang, at the beginning of the universe. The very heaviest natural elements, apart from small amounts produced artificially by human technology, are formed during a supernova (when massive stars collide or explode near the end of their life cycle).

Iron

Oxygen

1. People often say, "We are born of the stars". As a group discuss what you think this means. Summarize your thoughts below:

2. Edward Robert Harrison was a British astronomer. One of his best known quotes is "Hydrogen is a light, odorless gas, which, given enough time, turns into people". In groups discuss what he meant by this. Summarize your ideas below:

EXPLORE: Just how big is the Sun?

`` The Sun is a massive object. It has about 99.8% of the mass of the solar system in it. Imagining its true size can be difficult given there's clearly nothing on Earth even remotely that large.

`` We can do a simple experiment to measure the diameter of the Sun using a simple pinhole camera arrangement.

INVESTIGATION 6.1: Measuring the diameter of the Sun

See appendix for equipment list.

1. Set up a pinhole camera by using a pin to punch a small hole through piece of aluminum foil. The foil can be held flat by taping it to a cardboard frame.

2. In a sunny place, hold the aluminum foil up to the Sun allowing light to pass through the pin hole onto a sheet of paper. Move the paper back and forth until a sharp image of the Sun is formed (this image may be quite small). 3. Measure the distance between the pinhole and paper where the image formed. Measure the diameter of the Sun's image. A

D

C

Sun

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E

Sun's image

B

Aluminum foil with pinhole (cardboard frame support)

Paper

The two triangles in the diagram above are geometrically similar, therefore all corresponding sides are in the same ratio. This means the ratio of line AB÷AC is equal to the ratio of DE÷EC. The distance AC is 150 million km. Therefore:

=

DE cm EC cm ESS1.A

or

PS1.C

Diameter of Sun (km) = 150,000,000 km PS3.D

SPQ

EM

SC

Diameter of image (cm) Distance from pinhole to image (cm)

CL

AB km 150,000,000 km

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3. Record you measurements in the space below: (a) Distance between pinhole and image:

(b) Diameter of the image:

(c) Calculate the diameter of the Sun using your measurements:

(d) Compare your result to others in your class. How close are they to you?

PR E O V N IE LY W

(e) Pool your class results and find the average diameter of the Sun. Compare this to the known diameter of the Sun. How close was the class's average result?

EXPLORE: How long will the Sun shine?

`` For a long time one of the biggest mysteries in physics and astronomy was why did the Sun not burn out? By the

1850s evidence was building that Earth and the life on it had been around for hundreds of millions if not billions of years. Life clearly needed the Sun, yet no one could explain how the Sun could have lasted for so long.

`` Various scientists tried to compute the lifetime of the Sun based on known combustible material, such as coal. Two of these scientists were Hermann von Helmholtz and William Thomson (Lord Kelvin).

4. The mass of the Sun is 1.99 x 1030 kg (this can be calculated from the period of the Earth's orbit and its distance to the Sun, as described in Activity 12).

Hermann von Helmholtz first tried calculating the age of the Sun using the estimated energy output of the Sun and the known energy density of burning coal. The Sun's energy output was estimated to be around 3.6 Ă&#x2014; 1026 J/s. Coal has an energy density of about 3.0 x 107 J/kg. Calculate how long the Sun would "burn" based on these figures:

`` Helmholtz quickly dismissed the coal model and (in 1854) tried calculating the energy output of the Sun shrinking

(and thus losing gravitational potential energy as heat). He calculated an age of about 20 million years. Lord Kelvin later added to this (in 1887), estimating an age between 20 and 100 million years.

`` These estimates were made before scientists knew anything about nuclear fusion. It was not until 1925, following

Cecilia Payne-Gaposchkin's discovery, that it was realized that the Sun was mostly made of hydrogen (activity 45).

`` Knowing now that the Sun is powered by the nuclear fusion of hydrogen into helium we can calculate the age of the Sun. The Sun emits 3.8 x 1026 J/s.

5. The mass of a hydrogen proton is 1.673 x 10-27 kg. The mass of a helium atom is 6.644 x 10-27 kg. During fusion, 4 protons form the 2 neutrons and 2 protons in a helium nuclei. Calculate the mass missing from the hydrogen to helium fusion reaction:

N AS OT SR F OO OR M US E

6. The missing mass is turned into energy. We can use Einstein's equation E = mc2 to calculate the energy produced when one atom of helium is produced. Use E (joules) m (missing mass in kg) and c (speed of light, 300,000,000 m/s):

8. Calculate the mass the Sun converts into energy every second:

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7. If the Sun emits 3.8 x 1026 J/s calculate the number of hydrogen to helium reactions that occur every second:


242

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9. Nuclear fusion only occurs in the core of stars, such as the Sun. Estimates put the mass of the Sun's core at 10% of the Sun's total mass. When this mass of hydrogen is used up the Sun will begin to "die": (a) Calculate the mass of the Sun's core:

(b) What mass of hydrogen is reacted every second?

(c) Calculate how may seconds it will take for the Sun to use up this mass of hydrogen fuel:

PR E O V N IE LY W

(d) Convert this to years:

(e) Given that we know the age of the Earth to be about 4.5 billion years old (and therefore that is also presumably the age of the Sun) how many more years will the Sun shine for?

EXPLORE: What is nucleosynthesis?

`` Nucleosynthesis is the production of new atomic

nuclei from pre-existing ones. Nucleosynthesis most commonly occurs in nature by nuclear fusion in the core of stars. Nuclear fusion requires enormous energy as the nuclei must be accelerated to extremely high speeds in order to overcome the repulsive forces that normally keep them apart.

`` Elements up to iron (26 protons) are formed in the core of stars. Elements heavier than iron are formed during a supernova (when massive stars collide or explode near the end of their life cycle).

Nucleosynthesis of helium `` A star spends most of its existence converting hydrogen into helium. This stellar nucleosynthesis occurs in the core of a star where extremely high temperatures and pressures are found.

Nuclear fusion occurs in the core of stars

`` The fusion reaction shown below is called the protonproton chain reaction. Throughout each stage some mass is converted into energy and high-energy photons are produced.

Proton

Energy

2 2 A deuterium ( H) and a proton

Neutron

Energy

(1H) collide to form helium-3 and giving off more energy. Energy

Proton

1

Two protons collide. One proton decays into a neutron, giving off energy and forming deuterium.

Helium-3 nucleus

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Deuterium nucleus Helium-4 nucleus

3

Two helium-3 atoms collide to form a stable helium-4 atom. Two protons are ejected and more energy is released.

CL

10. Study the nucleosynthesis of helium diagram. How many protons are needed to form helium-4?

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EXPLORE: The structure of the Sun

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`` The Sun contains 99.8% of all the mass in the solar system. It has a diameter of 1,392,000 km and is more than

330,000 times more massive than the Earth. The Sun formed about 4.5 billion years ago and will continue to shine with little change for at least another 4 billion years.

`` When the Sun reaches about 10 billion years old, the hydrogen in its core will be exhausted. The core will shrink and the Sun will swell to form a red giant, with a diameter reaching out to the orbit of the Earth.

Solar prominence.

PR E O V N IE LY W

The core of the Sun reaches 15.6 million K. Here hydrogen is fused into helium. This process of nuclear fusion produces an enormous amount of heat and light. The core fuses 620 million tonnes of hydrogen into helium and converts 4.2Â million tonnes of mass to energy every second during this process (mass-energy equivalence).

The corona is the outermost layer. It can extend several solar diameters into space with large plumes streaming away from it. The temperature here can reach 2 million K.

Convection zone

Photons produced during fusion in the core move out into the radiation zone.

The photosphere represents the surface of the Sun (although it is not a solid surface it is the deepest layer that we can observe directly). Here the temperature is about 6000 K. From here light is radiated out into space.

11. Why is the photosphere considered the "surface" of the Sun?

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Solar flare.

CL

Sunspots are areas of magnetic disturbance in the surface of the Sun. They are about 2000 K cooler than the surrounding material and so appear darker. Sunspots move from the higher latitudes to the Sun's equator over an eleven year cycle.

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The chromosphere is a thin layer above the photosphere. It is the coolest layer of the Sun.


244

EXPLAIN: Getting energy to Earth

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`` From your earlier calculations you know the Sun produces an enormous amount of energy every second. It is also obvious that some of this energy reaches Earth – it is why the day is bright and it feels warm in the sunlight.

`` But how exactly does that energy get from the interior of the Sun and across space to Earth? Nuclei in plasma

`` Above the core is the radiation zone – an

PR E O V N IE LY W

area of ionized gas (plasma) where energy is transported out by radiation and conduction. The temperature varies from 15 million K near the interior of the zone to 1 million K near the edge. The radiation zone is very dense so photons travelling through it are subject to many collisions. As a photon travels through the radiation zone it is absorbed and remitted by nuclei at random. As a result photons can take 170,000 years to leave the radiation zone.

Arrows showing the path of a single photon.

`` Above the radiation zone is the convection

zone, where energy is transported by convection. This motion creates the Sun's magnetic field. The image of the surface of the Sun (far right) taken by NASA shows the surface to be granulated. Each of the granulations is the top of a convection cell. The brighter inner part of each granulation is where hot plasma is rising to the surface. The dark edges are where cooler plasma is descending. The darker spots are small sunspots.

`` Above the convection zone is the

Granulation on the surface of the Sun

NASA

photosphere. Here the heat and light that have been radiated and convected from the Sun's interior are released into space as electromagnetic waves (radiation).

12. (a) How do the photons emitted by the Sun originate?

(b) Why do the photons take so long to reach the surface of the Sun?

13. Why does the surface of the Sun look granulated?

CL

N AS OT SR F OO OR M US E

14. In the space below, draw a diagram showing how energy is transferred from the Sun's core to Earth:

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245

EXPLAIN: Space weather!

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`` The movement of so much plasma in the Sun combined with its rotation can cause the Sun's magnetic field to distort and affect the movements of material in the photosphere.

`` Sunspots are temporary phenomena on the Sun's photosphere where the intense magnetic activity can inhibit convection. This causes a darker, cooler spot on the surface as hot material is prevented from rising up.

`` The magnetic field lines near sunspots often tangle and reorganize, causing explosions of energy associated with

Sunspots come in pairs where the Sun's magnetic field punches through the surface, loops and plunges back through.

Solar prominences are loop shaped outbursts. They follow along the magnetic field lines of the Sun.

`` Solar flares are outbursts of electromagnetic

mass ejections) can causes many disruptions to Earth's electrical grids and electronic devices.

`` A particularly strong solar storm occurred in

1972. It culminated in an X-class solar flare (the most powerful) that caused a coronal mass ejection that reached Earth in just 14.6 hours.

`` Blackouts were reported across North America. Numerous magnetic-influence sea mines used in the Vietnam war were seen to trigger within seconds of each other.

Sunpots and solar flares

Blackout severity R5 R4 R3 R2 R1

700 600 500

250

200

150

400 300 200

100

Number of sunspots

`` Solar storms (which include flares and coronal

Solar flares are sudden releases of electromagnetic energy that can extend thousands of kilometers into space.

800

Number of blackouts (solar flares)

radiation that can interfere with radio communication and cause radio blackouts, especially in the high frequency (HF) radio band (3 to 30 MHz).

All images NASA

PR E O V N IE LY W

secondary phenomena such as solar flares, solar prominences, and coronal mass ejections. These add to the material constantly streaming from the Sun (the solar wind), sometimes disrupting the Earth's own magnetic field.

50

100

0 1976

1985

1995 Year

2005

0

2015

15. (a) Study the graph above. What happens to the frequency of sunspots over time?

(b) What is the average length of this cycle?

16. Why do sunspots appear darker than the rest of the Sun's surface?

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18. What effect do solar flares have on Earth?

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17. Explain the link between sunspots, solar flares, prominences, and coronal mass ejections:


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47 The Life of Stars

ENGAGE: Replicating a star

`` Nuclear fusion occurs continuously in only one place in the

universe, the core of stars. On Earth, the goal of many physicists is to recreate and control continuous nuclear fusion to provide energy to produce electricity.

`` Research into nuclear fusion reactors began in the 1940s but as

Plasma

Coils of the electromagnets

PR E O V N IE LY W `` Currently two main designs for fusion reactors are being tested.

The simplest is called a tokamak, which has a torus shaped reaction chamber. A more complex design (but theoretically more likely to work) is called a stellarator. Instead of simple ring shaped electromagnets, it has individually designed twisted electromagnets. The superconducting electromagnets are usually cooled by liquid helium and produce a magnetic field that confines the superheated plasma.

Tokomaks are a simple torus shape (like a donut). This causes an uneven magnetic field.

`` Although the goal of replicating a star on Earth is formidable one, progress is being made. Once sustainable reactions are obtain there is potential for enormous amounts of clean energy to be produced. The German Wendelstein 7-X stellarator has already produced plasma temperatures of up to 10 million K, although these lasted for less than a second.

Coils of the electromagnets

Plasma

Max-Planck Institut fĂźr Plasmaphysik

yet no design has been produced that has been able to produce more energy than was required to start and control the reactions. No facility has been able to sustain the reactions either.

A stellarator uses twisted electromagnets to keep the plasma in a more uniform magnetic field.

EXPLORE: Stars

`` Nuclear fusion in the core of a star produces

how long it will burn for. From this, you can conclude that the Sun is a star in middle age. But what was it like when it was younger? What will it look like when it is older? To answer this, we must look at other stars (right).

A. The Sun

B. Helix Nebula (planetary nebula)

C. Mira, a red giant

D. White dwarf (arrowed)

(c) What would happen if the temperature in a star's core increased?

(d) What would happen if the temperature in a star's core decreased?

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SSM

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(b) Which of these structures do you think is the largest?

E. Lagoon Nebula. An area of star formation.

CL

ESO CC 4.0 https://www.eso.org/public/images/eso1403a/

1. (a) The images on the right show stars that were similar to our Sun at different parts of their life cycle. Place the images in the order that you think would show the life cycle of our Sun from young to old:

All images NASA except Lagoon nebula

`` You have calculated the age of our Sun and

NASA/Hubble

a continuous stream of high energy photons, causing pressure that pushes the matter of a star outwards. However gravity, produced by the mass of the star, is always pulling the matter of the star inwards towards the core. These two opposing forces determine the size of a star and keep it in the main sequence for most of its life cycle.

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EXPLORE: Ages and sizes

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`` Just looking up at the night sky is enough to tell us there are many different types of stars. Some appear blue, others are red. Some are very bright, some seem much larger in the sky than others.

`` Some of this, of course, is because of the different distances to the stars. But some of the differences are due to the size and age of the stars.

NASA

Cygnus X-1 is an X-ray source accepted to be a black hole about 6000 light years from Earth. It is thought the original star may have been over 40 solar masses.

Proxima Centauri is a red dwarf star and the closest star to the Sun. It is just 0.12 solar masses and has a luminosity of 0.0017 that of the Sun. It is estimated to be 4.5 billion years old.

Judy Schmidt

The Pistol star (bright star center) is a blue hypergiant star and one of the most luminous stars in the Milky Way. It has a mass 27.5 times the Sun. Its age is estimated at just 4 million years.

VY Canis Majoris is a red hypergiant star and one of the largest stars known. It is thought to be 17 solar masses and to have a radius 1420 times that of the Sun. It's age is estimated at 10 million years.

ALMA (ESO/NAOJ/NRAO)/E. Oâ&#x20AC;&#x2122;Gorman/P. Kervella

Canopus is the second brightest star in the sky (after Sirius). It is a white star 8 times more massive than the Sun. Some estimates put its age at a few tens of million of years old.

All images: Nasa

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`` Consider the different examples of stars below:

Betelgeuse is a red supergiant star and the second brightest star in the constellation of Orion. It has a mass 11.6 times the Sun, and is thought to be about 8 million years old.

2. (a) Put the stars above in order from the most massive to the least massive:

(b) VY Canis Majoris has entered the final stages of its life cycle. It could explode in as little as 100,000 years. It is thought the Pistol star might explode in as little as 1 million years. Proxima Centauri is likely to shine for another trillion years. What can be said about the life time of a star and its mass?

(c) Discuss with your class why this relationship occurs:

(d) What color do old dying stars appear?

CL

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EXPLAIN: What causes the different lifetimes and life cycles of stars?

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`` We have seen that the mass of a star affects the length of its lifetime (and ultimately what happens when the star "dies"). Very large stars have short life cycles while smaller stars may shine for trillions of years.

`` At the root of this relationship is the rate at which the star uses (commonly "burns")

its hydrogen fuel. This in turn it related again to the mass of the star and pressure at the core.

`` Imagine filling a sealed syringe with gas (right). Pressing the syringe down

compresses the gas. The molecules bump into each other more often in the confined space. The pressure increases as your press down.

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3. Study the image right. It shows three stoppered syringes compressing a colorless gas (with a volume of 10 mL at room temperature and pressure).

(a) Which syringe has the higher pressure?

(b) Which syringe represents the core of a high mass star?

(c) What is likely to happen to the number of collisions of gas molecules in the syringe with the highest pressure?

(d) Using the syringes as an example, explain the relationship between the mass, pressure at the core, number of collisions, and life time of a star:

A

B

C

EXPLAIN: Forming a star

`` We have seen that the Sun burns hydrogen nuclei in its core to form helium nuclei. But before this happens two questions must be answered: where does the hydrogen come from and how do the fusion reactions begin?

`` Hydrogen is the most common element in the universe.

Hydrogen and helium (and trace amounts of other elements) are found as nebula, huge clouds of dust and gas that may be light years across.

`` A disturbance near the nebula (e.g. the shockwave from a

supernova) may cause it to begin to collapse as gas atoms are pushed closer to each other and are attracted by gravity to others.

`` Given that the gas will eventually collapse to a central point

(the eventual star) the majority of the atoms will have a very large amount of gravitational potential energy (think of something suspended a light year off the ground). This is the energy that can spark the nuclear reactions.

4. (a) What happens to the gravitational potential energy of an atom as it falls inwards to the center of a nebula?

(b) What happens to the temperature of the gas cloud as it collapses?

(c) Explain how the collapsing nebula gains enough energy to start nuclear fusion and form a star:

CL

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EXPLAIN: The end of the Sun - red giants and white dwarfs

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`` The mass of a star affects the rate of fusion in the core. It also affects what happens to the star when the hydrogen fuel in the core is used up.

`` For both sun-sized stars and more massive stars, hydrogen is fused into helium in the core of the star during the time it is on the main sequence (see the Hertzsprung-Russell diagram). Once the hydrogen in the core is used up, the core contracts under gravity. This increases the pressure in the core and the temperature increases.

`` At 100 million K, helium starts to fuse into carbon and oxygen in the core, and hydrogen in the upper layers fuses to helium in a shell around the core. The extra energy and heat produced by this new fusion causes the star to swell, forming a red giant with a diameter of up to 1000 times that of the Sun.

`` For stars up to eight solar masses the mass of the star is not enough to support fusion reactions beyond the

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formation of carbon and oxygen. When all the helium is used up, the star will die.

Sirius

Sun

White dwarf

Sirius B (white dwarf)

Temperature

As a Sun-like star nears the end of its life, it moves off the main sequence as a red giant. Over the final two billion years, the star may move back and forth about the Hertzsprung-Russell diagram as its core progressively burns hydrogen and helium in different layers.

Eventually the star runs out of hydrogen and helium. The core temperature and pressure are too low to continue fusion and a core of carbon and oxygen forms. The hot outer layers are shed into space as a planetary (ring-shaped) nebula, leaving behind a dense white hot core.

Both images: NASA

Luminosity

Red giant

White dwarfs are the left over cores of a Sun-like star. They can be a million times more dense than the original star's average density, with a density of 106 gâ&#x20AC;&#x2030;/cm3. No longer supporting nuclear fusion, the white dwarf slowly cools to a black dwarf over about a quadrillion years (1015 years).

5. Why does a star swell to a red giant when it starts burning helium in the core?

6. Explain why the surface of a red giant is much cooler than that of the original star:

7. (a) What happens to the luminosity of the star as it turns into a red giant?

8. (a) What is the cause of a planetary nebula?

(b) What is the composition of a white dwarf?

(c) Why is it unlikely there are any black dwarfs in the universe?

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(b) Why does this happen?

CL


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EXPLAIN: The bigger they are, the harder they fall–supergiants and supernovae

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`` A star greater than eight solar masses is fated to die in one of the universe's most spectacular events–a supernova. Instead of puffing off their outer layers they go out with a bang. A big one.

1

In the core, hydrogen fuses into helium. Eventually the hydrogen in the core begins to be used up. The core contracts under gravity forming a core of helium surrounded by a shell of hydrogen. As the core contracts and temperature and pressure rise, the helium core gains sufficient energy to begin fusing into heavier elements such as carbon and oxygen. The outer layers are pushed further outwards and the star forms a red supergiant.

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2

Stars greater than 8 solar masses burn very hot, up to 50,000  K at their surface, and tend to be blue or white in color.

3

H He

C

Si O Fe S

H

Fusion releases energy He C

ar ssible in a st U

Fe

Fusion not po

Pb

O 0

50

100 150 Atomic mass

200

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When a large star uses up the helium in the core, fusion does not stop. The mass of the star is enough to compress the core once more and the temperature rises until the carbon and oxygen begin to fuse in heavier elements. As this process continues, the heavy elements sink to the core where they ignite and fuse to form even heavier elements. The star may form onion like layers of heavier and heavier elements undergoing fusion. This process occurs at an accelerating rate. In the final moments of a massive star's life all the silicon in the core may fuse to iron in less than a day.

Eventually fusion in the core produces iron. The nucleus of an iron atom is extraordinarily stable. More energy is required to fuse iron atoms with other atoms (or break them apart) than is produced from their fusion. Thus when iron forms inside a star's core the process of stellar nucleosynthesis stops. The core no longer produces the outward pressure to support the outer layers. The inward force of the star's gravity takes over so the star, and its core, collapse.

Mass per nuclear particle

NASA

4

CL

9. Why do massive stars potentially end in a supernova while stars less than eight solar masses do not?

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251 The collapse of the star is cataclysmic and rapid. It has been calculated that the speed of the collapsing layers may reach 23% of the speed of light and the core reaches 100 billion K. Protons and electrons are crushed together to form neutrons. Neutrons are forced together and the core becomes so dense that the falling layers rebound outwards in a titanic explosion called a supernova. The pressures produced are high enough to cause the iron and other elements in the core to fuse into even heavier elements such as gold. This is called supernova nucleosynthesis.

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5

6

The core of the star is smashed inwards.

`` Stars with cores less than 3 solar masses

form neutron stars –  stars composed entirely of neutrons. They may have a diameter of just 20 km and a mass twice that of the Sun. A pea-sized piece of neutron star would have a mass of about 25,000,000 tonnes.

As material falls into the black hole it heats up and emits huge jets of x-rays that may reach millions of kilometers into space.

`` In stars with much larger cores, nothing

Event horizon - the point at which nothing, not even light can escape from the black hole's gravity.

is strong enough to withstand the force of gravity pulling the core inwards and it collapses to a black hole, a point with no dimensions and gravity so great that not even light can escape.

Accretion disk - material swirling around the black hole forms a disk.

Cygnus X-1 (right) was the first black hole discovered. It has a mass of about 15 times that of the Sun and an event horizon of just 44 km. As the black hole can not be seen, the image is of the x-rays emitted by superheated gas surrounding it.

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If a star is particularly massive it may not end in a supernova. These two photos were taken in 2007 and 2015 by the Hubble Space Telescope. The left image shows a circled star which is 25 times as massive as the sun. In 2009, the star's luminosity increased to a million times that of the sun, then it seemed to vanish. The right image shows a small trace of infrared light where the star once was. Where did it go?

CL

NASA

It appears that the star did not explode in a classic supernova. Instead its core was so massive that when it collapsed to a black hole the entire star fell into it as well and effectively vanished.

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NASA

NASA/ESA

Supernova 1994D (arrowed left) in galaxy NGC 4526 taken by the Hubble Space Telescope. Notice how the bright supernova easily matches the brightness of the entire galaxy beside it.


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10. Why does the formation of iron lead to the collapse of a star?

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11. How do elements heavier than iron form?

12. (a) What is a supernova?

(b) What size stars can become a supernova?

13. During the life of a massive star, what keeps the star from collapsing under its own gravity?

14. Why does a massive star form onion-like layers of elements near the end of its life?

(b) What is the event horizon of a black hole?

CL

16. (a) How does a black hole form?

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15. In the space below sketch the potential life cycle of a star. Include appropriate labels:

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48 Origins of the Universe

ENGAGE: Just how big is big?

`` One of the problems when studying space phenomena is the human limitation of visualizing the distances

between galactic and intergalactic objects. Comparisons are usually made by analogy and compressing scales into distances we can understand. Here's an example:

`` If the Sun was the size of a marble 1 cm in diameter then: • The Earth would be 0.09 mm in diameter and 1 m from the Sun • Jupiter would be 1 mm in diameter and 5.5 m from the Sun

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• Proxima Centauri (the nearest star to the Sun) would be 289 km away

• The distance to the center of the Milky Way galaxy would be 1.7 million km.

`` Even if we scaled the entire Milky Way galaxy (100,000 light years across) down to 1 cm in diameter then: • The Large Magellanic Cloud (a small galaxy orbiting the Milky way) would be 1.63 cm away • The Andromeda galaxy (the nearest large galaxy) would be 2.5 m away

• The cosmic horizon (as far as we can see with the most powerful telescopes) would be 1.3 kilometers away • The estimated diameter of the observable universe would be 9.3 km.

1. In groups discuss these scales. Do they have any real meaning to you? Work out some other scales and write them down in the space below:

EXPLORE: The shape of the universe

`` You may have heard or read about various theories on what the universe actually looks like. Something like this is difficult to comprehend as we are a minuscule part of an seemingly endless universe. Try as we may, we are unlikely to ever be able to leave it and see what it looks like from beyond.

`` At sea level, we perceive the Earth to be flat. But go high enough and we see that in fact the Earth is a sphere. Could this be the case with the universe? Can we work out the shape of universe while still inside it?

2. Take a flat piece of paper and draw a triangle on it. Measure the internal angles and add them up. What do you get?

5. How might this kind of simple geometry help us understand the shape of the universe?

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P

ESS1.A

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4. The diagram shows a saddle shape (a hyperbolic surface). What do you think the internal angles of the triangle shown on it would add up to?

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3. Now take a ball of any size and draw a triangle on it. Measure the internal angles again and add them up. What do they add up to this time?


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EXPLORE: Where we are

The solar system is approximately 10 billion km in diameter, with the Sun at the center.

The closest star to the Sun is Proxima Centauri, about 4.2 light years (LY) away. The Milky Way galaxy is about 100,000 LY across.

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`` Earth orbits the Sun. The Sun is part of the Milky Way galaxy. But where is the Milky Way? What else is out there?

Earth

The Earth is our home in the universe It measures 12,742 km in diameter at the equator and is 150 million km from the Sun.

Solar system

Milky Way Galaxy

The Local Group is part a larger cluster of galaxies called the local supercluster (or Virgo Supercluster) which is approximately 110 million LY across.

Local Group

Local Supercluster

The size of the universe

`` From the Earth we can see objects in space that emitted

The closest major galaxy is the Andromeda galaxy, 2.5 million LY away. The Milky Way is gravitationally bound to a group of about 50 galaxies called the Local Group, which is about 10Â million LY across.

The Local Supercluster is just one of many and is part of even larger filaments that span the entire universe like a tangle of giant webs (background image).

Light from distant galaxy

Movement of galaxy

light approximately 13.7 billion years ago.

`` While light from these furthest objects has taken 13.7 billion years to reach us, that does not mean they are 13.7 billion light years away. The universe has been expanding during that time.

`` This means the most distant objects are now much further

Apparent distance to UDFy38135539 = 13.1 billion LY

away than we currently see them. We are seeing them as they were 13.7 billion years ago.

`` The most distant objects seen so far have been calculated `` It is estimated that the edge of our observable universe is actually 46.6 billion light years away.

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to be at least 30 billion light years away.

Actual distance to UDFy38135539 = 30 billion LY

CL

6. Why are the distances to the furthest galaxy greater than they appear when we observe them through a telescope?

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EXPLORE: The Doppler effect

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`` It is likely you have encountered the Doppler effect, most likely out on the street. Cars moving at speed towards you

always appear to produce higher pitches (frequency) of sound than when they are moving away. This is the Doppler effect.

`` If a stationary car sounds its horn, sound waves travel out in every direction at a constant speed, frequency and wavelength as described by the equation v = fλ (see chapter 5).

`` If the car starts moving, the sound waves ahead of it continue moving at the same speed (since it is the density of the medium that affects wave propagation, not the source speed). This means that frequency and wavelength are altered.

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7. The diagram below shows a moving object emitting sound waves around it. Note: sound is really a longitudinal wave so the circles represent the crests in an equivalent transverse wave, which is easier to visualize.

(a) In the box below the circular waves draw the transverse profile of the waves, as they would appear along the dashed line:

(b) Draw an arrow on the diagram to show which direction the object is moving:

(c) Write in the boxes (left and right) where you would expect to hear a higher and a lower pitch than the original sound.

Light and the Doppler effect

`` The speed of sound is fixed with respect to the medium it is traveling in. Similarly, the speed of light in a vacuum is also fixed, but it is a universal constant i.e. it does not change no matter how it is observed.

`` The speed of light in a vacuum is 299,792,458 m/s. Because its speed is constant, when we use it in the equation v =fλ we find that frequency and wavelength are the only factors that can be manipulated.

8. The diagram below shows a moving object emitting light waves at 500 nm (green) in the visible region of the electromagnetic spectrum.

A

B

(a) If you were standing at point A what color range would you expect to see come from the object?

(b) If you were standing at point B what color range would you expect to see come from the object?

(c) Explain why you would see these color changes:

CL

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EXPLORE: Using the Doppler effect in astronomy

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`` Consider a planet orbiting a star outside our solar system (such a planet is called an exoplanet). Both objects will

actually be orbiting a common center of mass. This means the star "wobbles" or moves in an extremely small ellipse. As it moves away from us, its light is stretched into the red end of the spectrum. As the star moves back towards us, its light is compressed into the blue end of the spectrum (diagram below). The diagram is not to scale because the common center of mass is usually very close to the star (or even within it) unless the planet is very massive. Center of mass

Planet

Long wavelength (red)

Short wavelength (blue)

NASA

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Star

Kepler 186f is the most Earth-sized planet found in a star's habitable zone. It is 500 light years from Earth.

Earth

9. How can the Doppler effect be used to find exoplanets orbiting other stars?

EXPLORE: Doppler effect and absorption lines

Hydrogen

`` Recall that absorption lines appear in a continuous

spectrum after it has passed through a gaseous element.

Helium

`` These lines occur at specific wavelengths (as for hydrogen and helium right). The Doppler effect applies to these lines. When a star's light is shifted into the blue end of the spectrum (as above) the absorption lines are also shifted – they have been blueshifted.

Vega

Infrared spectrum of Sun and Arcturus

`` Redshifting occurs when the star's light is stretched

1.1

`` The graph on the right shows a small part of the

0.9

infrared spectrum of the Sun and the star Arcturus. Although the Sun is not entirely stationary compared to the Earth, it is so close there is little effect on the absorption lines of its spectrum. The graph shows that the spectrum of Arcturus, however, is shifted towards the red end of the spectrum.

`` Doppler shifts in absorption lines can also be applied

to the motion of galaxies. Because galaxies rotate, the Doppler shifts are different for each end of the galaxy.

`` The absorption lines of each end of the galaxy and

Normalized flux

into the red end of the spectrum.

0.7

0.5

0.3

Sun Arcturus

0.1

those from the middle can be compared to determine the rotational velocity of the galaxy and the galaxy's velocity relative to Earth.

882

883 884 Wavelength (nm)

885

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10. Is the star Arcturus moving towards or away from Earth? Explain:

CL

11. Radio astronomers measured the Doppler shifts in the wavelength emitted by the neutral hydrogen of a nearby galaxy and compared them to the wavelength obtained in the lab (21.106 cm). They found that the eastern edge of the galaxy emitted a wavelength of 21.159 cm, the center emitted a wavelength of 21.154 cm, and the western edge emitted a wavelength of 21.149 cm. Describe the rotation of the galaxy and determine if it is moving towards or away from Earth:

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EXPLORE: The motion of galaxies

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`` We have seen that shifts in absorption lines can be used to determine the movement of stars and galaxies relative to

the Earth. The spectra below show simplified absorption lines for four galaxies. Below the reference spectrum there is a spectrum for four different galaxies and each one shows the absorption for hydrogen (4 lines) plus one line each for sodium (Na) and magnesium (Mg). You can explore many more of these using the Sloan Digital Sky Survey- Plate Browser, an online resource with data from hundreds of galaxies. Follow the link at the BIOZONE Resource Hub. Reference spectrum Hb Mg

Na

Ha (656.4 nm)

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Hd Hg

500

400

SDSS J095423 Hb Mg

Hd Hg

400

500

600

Na

600 Wavelength (λ) (nm)

700

800

500

400

600

SDSS J095519

400

Hd Hg

Hb Mg

Na

500

600

700

Ha (776.0)

800

400

used to calculate a z value. The greater the z value the greater the distance the object or galaxy is from Earth. z values can also be used to calculate the recessional velocity of the object (the rate at which it is moving away). z is dimensionless, so it has no units. It can be calculated by:

Dl

z

lr

`` The table on the right shows some examples of recession

velocities for a selection of z values. The third column expresses these velocities as a percentage of the speed of light. The fourth column gives the distance to the source of redshifted light at the time the light is received.

12. (a) Study the spectra of the galaxies above. What can be said about the position of the absorption lines in all the spectra compared to the reference spectrum?

Ha Na (847.8 nm)

500

z

0.001

600

v (x105 km/s)

0.003

Ha (689.1 nm)

700

% of c

0.10

800

d (x 109 ly)

0.02

0.01

0.030

1.00

0.11

0.05

0.146

4.88

0.64

0.15

0.416

13.89

2.22

0.20

0.541

18.03

2.96

0.30

0.769

25.65

4.24

0.50

1.153

38.46

6.64

1.00

1.799

60.00

12.04

2.00

2.398

80.00

18.89

4.00

2.767

92.31

28.03

6.00

2.878

96.00

32.48

8.00

2.925

97.56

33.96

Note:

v = recession velocity c = speed of light d = distance to the source of redshifted light

(b) What does this mean about the movement of these galaxies?

(c) Use the Ha values to calculate the z value for all four galaxies. Which has the greatest redshift?

(d) Use the table to give an approximate value for each galaxy's recession velocity: i SDSS J095423:

ii SDSS J095449:

iii SDSS J095519:

iv SDSS J095417:

CL

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800

700

SDSS J095417 MgHb Na

Hd Hg

`` The shift in wavelength (λ) caused by the Doppler effect can be

z = (λ observed - λ rest) λ rest

SDSS J095449 Hg Hb Mg

Hd

Ha (747.8 nm)

700

800


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relationship between the redshift of distant galaxies (from which recession velocity can be calculated) and their distance.

`` The data he and his colleagues gathered can be plotted on

a graph (right). It was the first observational evidence of what has become known as Hubble's law.

`` Hubble's law can be expressed mathematically as v =

1000

500

0 0

1 Distance (Mpc)

2

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Hd, where v is velocity, d is distance, and H is the Hubble constant. Since 1929, astronomers have used different methods to try to measure the Hubble Constant more accurately. The most recent techniques put its value of the around 70 km/s/Mpc plus or minus a few percent.

Recession velocity (km/s)

Hubbleâ&#x20AC;&#x2122;s original data (1929)

`` In 1929, Edwin Hubble published a paper examining the

13. Describe the relationship between recession velocity of a galaxy and its distance from an observer:

`` The data produced an interesting problem. If the relationship shown by the graph held true all the way to the

furthest galaxies, then those galaxies must be travelling away from us faster than the speed of light. This is clearly not possible since no object can move faster than the speed of light.

`` Hubble's data led to the idea that it is not the galaxies that are moving. It is in fact the space between them that is expanding. The galaxies are moving away from us, not because they are moving through space, but because the space between them and us is expanding.

EXPLAIN: The expanding universe

`` When we look out into space in any direction we see distant galaxies are moving away from us. The expansion of space appears to be centered on us. How is that possible? Is the Earth the center of the universe?

`` Not quite. The diagrams below show two sets of dots representing galaxies in an expanding universe. Set 2 on the right is expanded 20% compared to set 1 on the left.

`` Observe what happens below when different equivalent galaxies (marked A, B, and C) are matched up:

A

A

Set 1

Set 2

B

B

C

A

B

B

C

A

B

C

14. What appears to happen when A coincides, B coincides or C coincides?

C

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A

C

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15. What does this tell us about the expanding universe and our apparent position in it?

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`` A simple investigation can illustrate the motion of the galaxies relative to the Earth (or any other observer).

INVESTIGATION 6.2: Modeling expansion

See appendix for equipment list.

1. Set up a thick rubber band held by a pin on top of a sheet of paper, as shown in the drawing below.

2. Draw 4 marks on the band. Hold the rubber band tight (but not stretched) and record the positions of your marks, the end, and the pin's position on the paper. These are the start (original) positions. 3. Stretch the rubber band to double its length.

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4. Use a different colored pen to record the 5 new positions of the marks on the paper. Measure the distances from the pin to the marks and record them in the first two columns of the table below. Mark

Pin

Original marks

Rubber band

Original distance to pin (cm)

Stretched distance to pin (cm)

Speed (cm/s)

Pin 1 2

Paper behind

Marks after stretching

3 4

Stretch

End

16. (a) If the end of the band moves 3 cm, how far does the middle of the band move?

(b) Assume the movement of the band took one second. Using speed = distance á time, calculate the speed the mark on the rubber band was moving while the rubber band was being stretched. Record this in the table above:

17. (a) Which point was moving fastest relative to the pin (the observer)?

(b) On the grid below, plot the speed of each mark on the rubber band against the original distance from the pin. Draw a line of best fit through the points.

(c) Calculate the slope (gradient) of the line (include units). This produces the constant for the expansion of the rubber band universe - the "Rubble" constant.

(d) If the original rubber band was 200 cm long how fast would the end be moving assuming the Rubble constant you calculated holds true to that distance in the rubber band universe.

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See activity 58


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to observe galaxies that were relatively close to Earth due to the limits of technology at the time. The furthest galaxies he observed were about 2 x 106 parsecs or 8.3 million light years away. Subsequent observations have refined the original data and confirmed the Hubble law.

`` However in 1998, observations of more distant galaxies using the most advanced telescopes showed a deviation in the Hubble diagram. Distant galaxies were redshifted more than predicted. That is they were further away than expected.

Deviations from the predictions of the Hubble diagram 0.2 Error bars 0.0

-0.2

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`` This led to the conclusion that the expansion of the universe

Deviation in apparent brightness

Expansion is not uniform

`` When Edwin Hubble made his observations he was only able

was accelerating.

0.01

0.03

`` The graph on the right shows the measured "apparent

brightness" of eight averaged groups of galaxies versus z values. The dashed red line shows the expected "apparent brightness". The blue dots and blue curve (fitted within the error bars) represent the measured apparent brightness.

0.1 0.3 z value

1.0

Expected apparent brightness (Hubble) Measured apparent brightness (with error bars)

18. (a) Beyond which z value does Hubble's law no longer strictly apply?

(b) Using the table on page 255, how far away does this acceleration become apparent?

19. What does the discovery of the accelerating expansion of the universe by powerful telescopes tell us about the data and knowledge we have at any one time?

EXPLAIN: The beginning

`` Scientists realized that if the expansion of the universe was extrapolated backwards in time, then everything must have expanded from a single, immensely hot point.

`` This led to the theory of what is now commonly called the Big Bang, the moment when the universe (including time and space) suddenly began.

`` Many lines of evidence have added weight to this theory. In fact the expansion of the universe was already predicted before Hubble's work in 1929.

`` When Albert Einstein (right) published his equations for the General Theory of Relativity in 1915, they incorporated the possibility of a few different models of the universe. In 1924, Alexander Friedmann solved the equations to show that the universe could be expanding (it also could be contracting or static). Hubble's work was the first practical evidence of this expansion.

Cosmic microwave background

`` More evidence for the Big Bang was soon to come. It was realized in the late 1940s that any heat and energy left over from the Big Bang should still be present and able to be detected. Astrophysicists Ralph Alpher and Robert Herman reasoned that the expansion of the universe should have stretched the wavelength of the high energy radiation produced during the Big Bang to somewhere in the microwave region of the electromagnetic spectrum. They calculated this microwave background had a temperature of about 5 K.

`` Since the Big Bang occurred 13.7 billion years ago,

the CMB temperature should be spread very evenly by now. However, there are slight fluctuations. These are believed to be the "imprint" (on the initial radiation from the Big Bang) of variations in the density of matter present in the early universe.

The image is a satellite recorded "microwave temperature map" of the sky. The average CMB temperature is around 2.725 K. Fluctuations in this temperature are very small with the dark blue areas corresponding to 2.721 K while the red areas indicate a temperature of 2.729 K.

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Wilson at Bell Telephone Laboratories found that the communications equipment they were working with produced a steady background radio noise no matter how much they adjusted it or what direction they pointed it in. Inspection of this noise showed it to have a "noise temperature" of 4.2 K. The wavelength of this radio noise was measured at 7.35 cm, within the microwave region of the spectrum. They had accidentally found the cosmic microwave background (CMB).

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`` About 15 years later Arno Penzias and Robert

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NASA

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Composition of early galaxies and stars `` Big Bang theory states that during the few seconds after the Big Bang, some of the protons and neutrons present fused to produce helium and a trace amount of lithium. Heavy elements were not formed because the conditions for the formation of heavier elements require much more time (tens of thousands of years) than the Big Bang lasted for. Therefore, when we measure the elements in distant young galaxies we should expect to see large amounts of hydrogen (about 75% of all elements), smaller amounts of helium (about 24%), and trace amounts of lithium and other elements.

`` Measurements of these elements in young galaxies and stars Young distant galaxies comprise 75% hydrogen and 25% helium by mass, exactly what would be expected if hydrogen and helium were formed during the Big Bang.

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match these predictions precisely.

A thought experiment (Olbers' paradox, 1823) `` Consider this. If the universe was infinite, not expanding, and had been here forever, why is the night sky dark? If stars and galaxies were placed randomly around us throughout this universe then we should be able to look in any direction and see a star or point of light no matter how far away it is. If the universe is not expanding and has been here forever then a photon of light, no matter how far it has to travel, should have reached us by now from anywhere in the universe. Thus the night sky should be ablaze with light. This not what we see. It follows the universe is not infinite and has not been here forever. It must have had a start. Although there are many explanations for this paradox it is an interesting way of predicting a universe with a finite beginning.

Observer.

In an infinite universe, any line of sight is likely to intercept a distant point of light.

20. (a) What is the cosmic microwave background?

(b) Explain how the discovery of the CMB provided evidence for the Big Bang:

21. Why did only hydrogen and helium form during the Big Bang?

22. If the Big Bang happened as predicted, what composition of elements would we expect to see in distant galaxies?

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23. Study the pieces of evidence for the Big Bang presented in the 'EXPLAIN' part of this activity carefully. What is common to all these pieces of observable evidence and why does this make them much more powerful than if they did not have this common feature?


262

ELABORATE: The Big Bang

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`` We have looked at many pieces of information that point to the universe literally starting with a "big bang". It would be useful now to study the currently accepted time line of the history of the universe from the Big Bang to present day.

`` It is not known exactly what triggered the expansion of the universe, but current theory proposes that 13.7 billion

years ago an infinitely dense, infinitely hot, and infinitely small point of matter and energy called a singularity, suddenly expanded to form the universe we know today.

`` A common misconception about the Big Bang is that it was an immense explosion moving outwards into a void

of empty space. In fact, before the Big Bang there was no space. As far as we can tell there was no anything. Not even a void into which the universe expanded. Everything was contained within the soon-to-expand singularity.

`` When the Big Bang occurred, the infinitesimal point expanded and, importantly, space expanded with it (i.e. space

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went from infinitely small to billions of light years across). Think of a deflated balloon. As it is blown up it expands and the space inside it grows. The outer surface also grows, by expansion, not because more material is being added to the balloon.

Time

10-43 seconds

Photon - particles of light

The very early universe was filled with simple elementary particles and antiparticles including high energy photons (gamma rays), electrons, and positrons.

Electron - negatively charged particle. For an unknown reason, more electrons than positrons were produced in the Big Bang.

Between 10-38 and 10-35 seconds a process called inflation occurs. The universe grows by 1062 times. Inflation stops when the energy causing it is transformed into the matter and energy known today. The temperature drops to 1029 K. Gravity separates from the other three fundamental forces.

10-38 seconds

Graviton - theoretical particles that transfer gravity between objects.

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0

10-43 seconds after the Big Bang (that's a decimal point followed by 42 zeros then a 1) the temperature of the universe was 1032  K. At this temperature, there is only one unified force. It is too hot for even elementary particles to form.

Positron - electron equivalent but with positive charge.

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The universe begins at time 0. Everything that currently exists in the universe was compressed to an infinitely small point called a singularity.

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An overview of the Big Bang and the evolution of the universe

13.7 billion years after the Big Bang the universe is still expanding.

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The Big Bang. The universe expands from an extremely hot and dense state (see below).

Inflation. Following the Big bang the universe rapidly expands. Matter forms (see below).

380,000 years ago the universe becomes transparent (see over page).

Galaxies and stars form (see over page).

Dark energy appears to be accelerating the expansion of the universe, although there is no clear explanation why.

The universe continues to expand (but more slowly). The temperature drops to 5 billion K. All positrons have been annihilated in collisions with electrons.

The temperature of the universe drops to 1 trillion K. Quarks combine to form protons and neutrons.

10-12 seconds 10-4 seconds

Gluons are particles that hold quarks together.

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5 seconds

3 minutes

Proton

Proton

There are six different types of quarks. The combinations of three specific quarks produces protons and neutrons.

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Quarks are elementary particles and fundamental components of matter. There are six different types of quarks.

The universe's temperature reaches 1 billion  K, cool enough for protons and neutrons to join to together to form helium nuclei. Photons of light are still too energetic to let electrons join nuclei to form atoms.

Neutron

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The temperature of the universe drops to 1015  K. The four fundamental forces of the universe separate and particles such as gluons, and quarks form.


264 From opaque to transparent

NASA

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hot soup of atomic nuclei (hydrogen nuclei (protons) and helium nuclei) and free electrons along with very high energy photons of light called gamma rays. The energy of the photons prevented the atomic nuclei from capturing the electrons. These free electrons would have scattered the photons much like visible light is scattered by water droplets in a fog. The universe would have been opaque. After 380,000 years the photons had lost most of their energy and electrons were able to be captured by atomic nuclei. Photons were no longer scattered and the universe became transparent. The photons of light from this time make up what is now called the cosmic microwave background (CMB). It is the oldest light that we can detect.

The CMB can be detected throughout the sky in every direction.

Looking back in time `` Light travels at about 300,000 km s-1. But even at this almost unimaginable speed, light still takes time to travel the vast distances of space. The Sun is 150 million km away from Earth. Thus light from the Sun takes 150 million ÷ 300,000 = 500 seconds (about eight minutes) to reach Earth. This means we see the Sun as it was eight minutes ago. Similarly, the further out into space we look, the further back in time we see. The light from the most distant objects has taken around 13 billion years to reach us, thus we see them as they were 13 billion years ago. The image to the right shows the Hubble Ultra-Deep Field. It covers an angle of the sky of about one tenth that of the full moon. Every point of light is a galaxy. The white square contains the galaxy UDFy-38135539 – possibly the oldest object observed so far. It formed just a few hundred million years after the Big Bang.

The temperature of the universe reaches about 3000 K. Photon energies are low enough for electrons to join atomic nuclei and form atoms. Photons are no longer scattered by these electrons and the universe becomes transparent.

380,000 years

NASA

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`` Seconds after the Big Bang, the universe was a very

Gravity has had long enough to pull clumps of matter together into huge structures called filaments. Galaxies will form along these filaments along with the first generation of stars. The explosion of first generation stars produces the elements heavier than carbon.

300-500 million years

The majority of the hydrogen and helium present in the universe today was formed during the early stages of the universe.

Carbon

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Helium

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Hydrogen

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24. How long ago did the Big Bang occur? 25. How long after the Big Bang did the following form:

(a) Quarks:

(b) Protons:

(c) Atomic nuclei:

(d) Atoms:

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(e) Galaxies:

26. Explain why the universe was opaque until around 380,000 years after the Big Bang:

27. What does the cosmic microwave background represent?

28. Read the following statement: "The universe was formed when a dense ball of material exploded into space, forming the universe we see today". Identify and comment on any errors in this statement:

The Sun forms as a second generation star. The heavy elements formed by the explosions of first generation stars form the planets orbiting it. The temperature of the universe is now 15 K (-258°C). The Earth forms about 500,000 years after the Sun.

Presently the temperature of the universe is 2.73 K (-270.27°C), just a few degrees above absolute zero. The universe is still expanding and evidence suggests the expansion is accelerating.

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At the largest scale, the galaxies are collected together along huge filaments. It is suggested these filaments formed as a result of ordinary matter interacting with dark matter.

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NASA

The planets of our solar system formed from the dust around the proto-Sun.

Andrew Pontzen and Fabio Governato

13.7 billion years

9 billion years


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49 Hidden in Plain Sight Revisited

`` At the beginning of this chapter you were shown the Crab Nebula, the object at the center of it, and given some

history of its recorded observations. You should now be able to explain what caused the nebula and describe the object in the middle of it.

Both images: NASA

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The Crab Nebula

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1. Describe the event that produced the Crab Nebula and the formation of the object at its center. Explain why it could be seen clearly in the night sky in 1054 but can now only be seen with a telescope. Include an explanation of why the object in the center can only be seen clearly with x-ray telescopes

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50 Summative Assessment

1. (a) Using the list below, reproduce the model of a star's life cycle that you developed earlier. Make sure that you include a brief description of each stage. Identify the pathway that represents our Sun.

(b) The Big Bang occurred 13.7 billion years ago, forming hydrogen and some helium (about 75% and 25% of all matter respectively). Extend your model to communicate ideas about how stars, over their life cycle, produce elements. Include carbon, oxygen, and iron as well as elements heavier than iron such as uranium and gold.

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protostar, small-medium star, large-star, white dwarf, black hole, neutron star, supernova, red giant, red super-giant, planetary nebula, nebula.

EM

SPQ

ESS1.A

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268 Questions 2-4 require you to use the online resource Star in a Box. Follow the link at the BIOZONE Resource Hub or go to starinabox.lco.global.

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2. On the home screen click Open the lid. You will see a Hertzsprung-Russell diagram showing the main sequence band of stars. The program shows a default star of 1 solar mass. You will see a dotted pathway going from the star around the HR diagram. This is the path a 1 solar mass star will take around the HR diagram as it progresses through its life cycle. Click the play button in the bottom right-hand corner to see the star move along the pathway and the time it takes to do so (timer at the bottom of the screen). You can control the speed in the drop down box next to the play button. (a) According to the timer how long does a 1 solar mass star spend in the main sequence?

(b) What is the lowest surface temperature this star will reach?

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(c) When will this happen according to the timer?

(d) What will the luminosity (brightness) be compared to the Sun?

(e) On the Hertzsprung-Russell diagram below draw the star and the pathway it will take around the HR diagram.

3. Set the star's mass to six solar masses and click play.

(a) How long does this star stay on the main sequence?

(b) What is the maximum luminosity this star reaches?

(c) On the Hertzsprung-Russell diagram below draw the star and the pathway it will take around the HR diagram.

4. Set the star's mass to 20 solar masses.

(a) How long does this size star live before it ends in a supernova?

(b) On the Hertzsprung-Russell diagram below draw the star and the pathway it will take around the HR diagram.

5. You will have noticed that on some of the pathways you drew, the star loops back on itself while in the red giant stage. What might be causing these loops in its pathway?

HR diagram

106 105 104

102

Ma

in

10 1

se

qu

en

ce

10-2 10-3 10-4 10-5

O

B 30,000

A 10,000 Surface temperature (K)

F

G 6000

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10-1

K

M

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Luminosity (sun = 1)

103

3000

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6. Briefly describe three pieces of evidence for the Big Bang: (a)

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(b)

(c)

7. The redshift of a galaxy can be calculated by: z = (λobserved - λrest)/λrest. Study the data below:

Element

Absorption λ observed in lab

Absorption λ observed in galaxy 1

Absorption λ observed in galaxy 2

Ha

656.4 nm

740.9 nm

764.0 nm

Hb

486.1 nm

534.6 nm

569.1 nm

Mg

517.6 nm

581.9 nm

676.8 nm

Na

589.5 nm

661.4 nm

680.0 nm

(a) Calculate the redshift value z for each galaxy:

Galaxy 1: Galaxy 2:

(b) Which of these galaxies is the furthest away from Earth? Explain your answer:

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8. Describe how energy is produced in the Sun and how that energy is able to reach the Earth. Diagrams may help you:


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9. Select and read biographical material about or by an influential astronomer or cosmologist. Citing evidence from what you have read, write a letter to the scientist asking a relevant question about their work. Include a critical idea or discovery by the scientist and identify key ideas, words, and phrases relevant to the topic. Go to BIOZONE's Resource Hub for material to start you off. Your teacher may want to suggest specific scientists known for their work about the stars, Sun, planets, or universe (e.g. Stephen Hawking). Write your letter in the space below:

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Basic Skills for Physics Students

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SEP support

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Activity number

Science and engineering practices Background in activities as noted. Covered in earlier chapters in context.

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Asking questions and defining problems

c

1

Demonstrate an understanding of science as inquiry. Appreciate that unexpected results may lead to new questions and to new discoveries.

c

2

Ask and evaluate questions that you are able to investigate with the resources you have available. Ask questions that arise from observation or examining models or theories, or to find out more information, determine relationships, or refine a model.

51 51 53

Developing and using models

Develop and use models to describe systems or their components and how they work, to explain or make predictions about phenomena, or to generate data to support explanations or solve problems.

52

Develop a model that allows you to manipulate and test a system or process.

52

c

3

c

4

c

5

Plan and carry out investigations to provide data to test a hypothesis, support an explanation, or test a solution to a problem. Identify and evaluate the importance of any assumptions in the design of your investigation.

c

6

Use appropriate tools to collect, record, analyze, and evaluate data.

c

7

Make and test hypotheses about the effect on a dependent variable when an independent variable is manipulated. Understand and use controls and trial (test) runs appropriately.

56

c

8

Consider and evaluate the accuracy and precision of the data that you collect.

56

c

9

c

10

c

11

Demonstrate an ability to use mathematics and computational tools to analyze, represent, and model data. Recognize and use appropriate units in calculations and demonstrate an ability to apply unit conversions.

c

12

Create and use simple computational simulations based on mathematical models.

c

13

Apply techniques of algebra and functions to represent and solve scientific and engineering problems. Understand the use of logarithms, e.g. as in decay rates.

c

14

Apply ratios, percentages, and unit conversions in the case of complex measurement problems involving quantities with derived or compound units, e.g. kg/m3.

Planning and carrying out investigations

52

54 56 - 59

Analyzing and interpreting data

Analyze data in order to make valid and reliable scientific claims. Consider limitations of data analysis (e.g. measurement error, bias) when analyzing and interpreting data. Apply concepts of statistics and probability to answer questions and solve problems.

56 58 59

Use mathematics and computational thinking

54 - 59

52 57 58 59 54

Construct explanations and design solutions 15

Apply scientific evidence, ideas, and principles to explain phenomena and solve problems.

Engage in argument from evidence

51

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c

c

16

Use evidence to defend and evaluate claims and explanations about science.

51

c

17

Provide and/or receive critiques on scientific arguments by using scientific methodology.

51

Obtain, evaluate, and communicate information 18

c

19

Evaluate the validity and reliability of designs, methods, claims, and/or evidence. Communicate scientific and/or technical information in multiple formats. Demonstrate an ability to read critically and compare, integrate, and evaluate sources of information in different media and formats.

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c

55 58 51


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51 The Nature of Science

`` Science is a way of understanding the universe we live in: where it came from, the rules it obeys, and how it

changes over time. Science distinguishes itself from other ways of understanding the universe by using empirical standards, logical arguments, and skeptical review. What we understand about the universe changes over time as more information is gathered.

`` Science is a human endeavor and requires creativity and imagination. New research and ways of thinking can be

based on the well argued idea of a single person. It could be said that the scientific method is 'the art of embracing failure', because apparent failures can lead to new discoveries and ways of thinking.

`` Science influences and is influenced by society and technology, both of which are constantly changing. Scientists

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build on the ideas and work of their contemporaries and those that went before them. "If I have seen further it is by standing on the shoulders of Giants".....Isaac Newton

`` Science can never answer questions about the universe with absolute certainty. It can be confident of certain

outcomes, but only within the limits of the data. Science might help us predict with 99.9% certainty a system will behave a certain way, but that still means there's one chance in a thousand it won't.

1. Science is not a linear process, it is dynamic and progressive. Results may answer some questions but it may also raise new questions that require investigation. New discoveries can be made by accident or because unexpected results occur. Nor is science an isolated process. Throughout history, the work of many has been has been important to explaining or developing ideas. Collaborators bring new findings, ways of thinking, and new directions to research. Using the circles below, construct a model or mind map to show how the nature of science is dynamic and progressive.

Exploring ideas

Analysis and feedback

Investigating ideas

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Benefits and outcomes

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Gravity and orbiting objects - the nature of science

Aristotle (Greece) (384–322 BC) taught that the Earth was the center on the universe and that the Sun and planets orbited it. This seemed plainly obvious as it is what we see standing here on Earth.

Aristotle also expressed the idea that light objects, such as a feather, fall more slowly than heavy objects, such as a stone. It was accepted until at least the 15th century precisely because it appeared to match everyday observation.

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Knowledge was based on observation and experience. Ideas were not tested under controlled conditions.

Science and apparently everyday observation often come into conflict.

The testing of ideas under controlled conditions allows the underlying principles to be discovered.

As new ideas based on facts obtained by controlled experiment became more widely accepted, social and political ideas began to change.

As more information becomes available, phenomena that were once thought to be separate, e.g. falling objects and planetary orbits, can now be described under one over arching principle, e.g. gravity.

New mathematics, knowledge, and inspiration can redefine whole areas of science and society. Einstein's theory of relativity was revolutionary and has stood up to every scientific test, including gravitational waves.

In 1610, Galileo (Italy) published his observations of the moons of Jupiter, arguing that the idea that everything orbited the Earth was wrong because here were objects orbiting something else. His ideas were at odds with the Church and he spent the rest of his life under house arrest.

Around the same time, Johannes Kepler (Germany) published his laws of planetary motion around the Sun based on observational data collected by astronomer Tycho Brahe. In contrast to Galileo, his ideas were accepted relatively quickly.

In the 16th century, Galileo slowed down the motion of falling objects by using an inclined plane and balls made of different materials and masses. He used a water clock to accurately measure the time it took for the balls to roll set distances. He found that the amount of time it took for the ball to roll down the entire length of the ramp was independent of its mass. This led him to believe that all objects fall at the same rate no matter their mass.

Importantly Galileo explained his conclusion using mathematics. A physical law expressed as a mathematical equation allows for predictions that can then be tested experimentally.

In 1687 Isaac Newton (England) realized that falling bodies and orbiting planets were following the same principles, which he described in his laws of motion. Under Aristotle, different motions were explained by different causes. Under Newton, different motions were explained by the same causes. Falling objects fall because of the Earth's gravity pulling on them. Planets follow their orbital path because of the Sun's gravity pulling on them (they are continually falling towards the Sun while also moving at 90° relative to the Sun).

Observations of the orbits of planets such as Mercury didn't always match predictions based on Newton's law. In 1905 Albert Einstein (Germany) explained gravity as the curving of the fabric of space due to the mass of an object. Planets orbit a star because they are following the curve of space created by the enormous mass of the star.

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Many ideas that were at odds with social and political beliefs were oppressed, often ruthlessly.

Around 1514 Nicolaus Copernicus (Poland) proposed that the Earth and planets orbited the Sun (heliocentric model). This was at odds with the geocentric (Earth centered) model supported by the Church.

2. Work in groups to discuss how the nature of science was important in the describing gravity and orbiting objects and the eventual formulation of Einstein's theory of relativity. You should include the following in your discussion:

`` The beliefs of scientists were often different to the views held by the general population. How did these differing opinions affect the theory's progress?

`` Why was the work of earlier scientists important to those who came afterwards?

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`` Explain how the introduction of controlled experimentation and testing help sway popular thought.


52 Systems and System Models

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Systems may be open (able to exchange matter, energy and information with their surroundings), closed (exchange energy with their surroundings, but not matter) or isolated. Isolated systems exchange no energy, information or matter with their surroundings. No such systems are known to exist (except possibly the entire universe). Some natural systems approximate isolated systems, at least for certain lengths of time. The solar system is essentially isolated, as is the Milky Way galaxy if gravity from nearby stars or galaxies is ignored.

The Solar System

Modeling systems helps to understand how they work. A model is a representation of an object or system that shares important characteristics with the object or system being studied. A model does not necessarily have to incorporate all the characteristics or be fully accurate to be useful. It depends in the level of understanding required. However, in general, the model becomes more realistic as more data is added to it. Most natural systems are very complex, so it is helpful to divide it them into smaller parts to make it them easier to study. As each part of a system is modeled, we gain more information about the total system until eventually all the parts are put together (much like a jigsaw).

Modeling the evolution of stars

The laws of gravitation predict the orbital path of one body around another (e.g. the Earth around the Sun). They also allow us to predict where new bodies might lie. Scientists found irregularities in the predicted orbit of Uranus. They proposed an undiscovered planetary body was causing this. This led to the discovery of Neptune.

Models of stellar evolution are based on visual observation of numerous stars, their luminosity, measured surface color, and mass. Models of nuclear fusion are added to this data. Based on these observations, we can predict how a star of a certain mass will behave and develop over millions to billions of years.

The Sierra Nevada

Neptune

NASA

Discovering new bodies

Knowledge about forces and tectonic movement is used to model the effects of collisions on the landscape. Collisions at plate boundaries played an important role in forming the Sierra Nevada, and cause the volcanic and seismic activity California still experiences. Scientists can also develop collision models to make cars safer when they are involved in a crash.

Jeffrey Pang cc 2.0

Modeling collisions

NASA

Systems are assemblages of interrelated components working together by way of a driving force. A simple example of a system is our eight-planet Solar System. Each of the planet's orbits represents a single component of the system. The driving force of the system is gravity from the Sun.

NASA

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1. In pairs or groups, discuss the advantages and disadvantages of using models to explain a system. Why is it easier to use a series of small models to explain a complex system than one complex model? Summarize your results here:

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53 Observations and Assumptions

Assumptions and the wider universe Any investigation requires you to make assumptions about the system you are working with. Assumptions are features of the system you are studying that you are assuming to be true but that you do not (or cannot) test.

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For our universe to make sense, and for us to make sense of the universe, we have to assume certain ideas hold true everywhere in the universe and, if they don't, we have to be able to explain why not. There are essentially two rules that are assumed to be true in science.

This means the laws have been, and always will be the same. There can't be one set of laws that apply in our universe today and a different set of laws that applied yesterday. The laws are the same throughout the universe no matter where you are.

2 These laws can be determined by observation of the universe around us.

What if the laws that govern the universe were not able to be understood? What if the number of laws was essentially infinite? No matter how carefully you observed something or how general your equations, you would never be able to write down a law that could be applied reliably to more than one situation.

NASA

1 The universe is governed by rules (laws) that are the same everywhere, and those rules cannot be broken.

Applying assumptions

It has been observed that at the center of our galaxy about a dozen stars are orbiting a common point that appears empty. Some of the stars are moving through space at speeds of over 5000 km/s (the Sun moves at about 220 km/s). Assuming that the laws of gravity apply in the center of the galaxy the same as they apply here on Earth then it can be calculated that there must be an unseen object (called Sagittarius A*) with a mass of 4 million times the Sun holding the stars in their orbits.

The least complicated explanation is most often correct

`` There are many explanations to account for phenomena we see, but some explanations are very complicated and require many assumptions for the phenomenon to have occurred. For example, you put a candy bar aside to take to school the next day. In the morning it was gone. You come up with two explanations. The first is that someone else ate it (or moved it) after you went to bed. The second is that during the night you sleep-walked to the kitchen, found the candy bar, ate it, put the wrapper in the trash and went back to bed without anyone seeing you. solution. Occam's razor helps rule out hypotheses or explanations that contain too many assumptions. The one with the least number of assumptions should be used.

`` For example there are two possible models for the organization of the

solar system. The geocentric model states that the Sun and planets orbit the Earth. The heliocentric model states that all the planets, including Earth, orbit the Sun. Both can be used to calculate the position of the planets as we see them in the sky but the geocentric model makes many more assumptions. Therefore, it makes sense to accept the heliocentric model because it makes far fewer assumptions.

NASA

`` We apply a principle called Occam's razor to choose the most likely

Copernicusâ&#x20AC;&#x2122; heliocentric model has just seven assumptions. The geocentric model makes many more assumptions, including that the laws of gravity don't apply to the Earth and Sun, and that the planets all have secondary "epicycles" along their orbits.

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1. Why do we sometimes need to make assumptions in science?

(b) Why did you choose that explanation?

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2. (a) Think about the candy bar example. Which explanation is most likely if you apply Occam's razor?


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54 Measurement and Units

Measurement and units

You will take many measurements during your study of physics. One of the most important things to remember is to always record and report the units of measurement. Without units, the measurements are meaningless (below).

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16

A student measured the length of wood (above) and recorded the length as 16. 16 what? Without the units we know nothing about the physical quantity. We have no idea of the missing unit. As soon as you add the unit (e.g. 16 cm) we can immediately quantify the measurement. A few measures (e.g. temperature in Kelvin) have no units because they are already calibrated against another scale (°C).

Non-metric units can be confusing! A US ton is 2000 lb and different to the British ton (2240 lb). A metric ton or tonne (1000 kg) is ~2204 lb. With a metric ton, there is no confusion.

SI units

Different units are used to measure quantities in different countries. For example, in the US, miles are commonly used to measure distance but most other countries use kilometers. To standardize measurement, scientists use SI units (International System of Units) to remove these differences. Base units Base units are the building blocks of the SI system. These are units that can be used on their own. For example: Kilogram (kg) is a base unit because it is independently expressed (other units are not required for it to make sense). The seven base units are:

Derived units Derived units are expressed using combinations of base units. They are formed by powers, products or quotients of the base units and cannot be expressed in the absence of basic units. In SI units, inverse notation is used as a rule, although we have replaced it here with the solidus (/). Some commonly used derived units in physics are:

Quantity name

Unit name

Unit symbol

Quantity name

Unit name

length

meter

m

speed, velocity

meter per second m/s

v

mass

kilogram

kg

time

second

s

acceleration

meter per second m/s2 squared

a

electric current

ampere

A

force, weight

newton

kg.m/s2

N

Pa

thermodynamic temperature

kelvin

Expression

Unit symbol

K

pressure, stress

pascal

N/m2

joule

Nm

J

amount of substance

mole

mol

energy, work, heat

luminous intensity

candela

cd

power

watt

J/s

W

electrical charge or quantity of electricity

coulomb

A.s

C

frequency

hertz

s-1 (per second)

Hz

(a) speed, velocity (v):

(b) force, weight (N):

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2. Name the basic SI units in the following derived SI units:

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1. Explain why using standardized units is important in science:

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Distance

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The units used to measure distance depend greatly on the distance being measured. Distances in the classroom may be measured in meters. On Earth, distance is commonly measured in kilometers. Distances in space, however, are too large for kilometers to be a useful expression of distance so other units are used (below). A parsec is the distance to a point that produces a parallax angle of one arcsecond (one 3600th of a degree) when using one AU as the base line. It is equal to 3.26 light years.

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One astronomical unit (AU) is defined as the distance from the Earth to the Sun (150 million km). AUs are useful for measuring distance within the solar system.

At the scale of planets, kilometers is a useful unit of distance.

A light year (LY) is the distance light travels in one year. Light years are the most common unit of measure when comparing interstellar distances.

Force

A force is a push or a pull, and the push or pull needs to be exerted on an object. The unit of force is called a newton and is represented by the symbol N.

Force can be measured by force meters (sometimes called force gauges). They can be very simple and consist of a spring in a marked cylinder (right) or they can be more complicated digital devices. As force is applied, the spring is stretched and the force is read off the scale. A spring-based force meter is a reliable measure of force because the extension or compression of a spring is proportional to the applied force.

A force diagram can be drawn to show all the forces acting on an object, and indicate the force's direction and magnitude. It is usually shown with the object represented by a dot, and the vectors are labeled by the type of force, the object exerting the force, and the object receiving that force. In a force diagram, the longer the arrow, the bigger the force. Several types of force are typically used:

`` Gravity: Fgrav, direction downward.

`` Applied: Fapp, applied to an object.

`` Support (normal): Fnorm, perpendicular to surface. `` Tension: Ftens, along a string/rope/chain.

`` Friction: Ffric, direction opposing relative motion.

3. Why can't we use kilometers to measure distance in space?

4. Light travels at 299,792.458 kilometers per second. How far in kilometers is one light year? 5. What is an astronomical unit?

6. Abseilers descend down a vertical face using ropes. Use arrows to name the forces acting on the abseiler on the diagram (right):

3N

20 N

6N

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6N

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7. A very simplified force diagram is shown below. Describe what it shows:


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Recording your results accurately is very important in any type of scientific investigation. If you have recorded your results accurately and in an organized way, it makes analyzing and understanding your data easier. Log books and dataloggers are two methods by which data can be recorded.

Log books

Tables

`` A log book records your ideas and

A table (below) is a good way to record and present results. Patterns, trends, or anomalies can be easier to see. You may want to change your experimental conditions as a result of emerging trends. For example, increase the frequency of data collection if changes are occurring quickly.

results throughout your scientific investigation. It also provides proof that you have carried out the work.

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`` A lined exercise book is a good

choice for a log book. Write ideas, record results and paste in photos or extra material (such as printouts).

09 / 21 / 2019

Saturation density of water vapor in the air

`` Each entry must have the date recorded.

`` Your log book is a full record of your work. Include

any mishaps, failed experiments, or changes in methodology in your logbook. Where possible, explain the reasons for the failure or change. Sometimes failed experiments can be just as valuable as successful experiments in understanding a result.

`` Make sure that you can read what you write at a later

date. A log book entry is meaningless if it is incomplete or cannot be read.

Dataloggers

Graphtecinst CC4.0

Dataloggers (right) are electronic device that automatically records data over time. In physical sciences, they can be used to measure motion, pressure, heat, sound, light, or radioactivity among others. Some advantages of a datalogger are:

`` Recordings have a high degree of precision and accuracy (which is known and factory-set).

`` Can be left without needing to be monitored.

`` Can be set to take readings over a long period of time

(e.g. hourly readings every day) or many readings in a short period of time.

`` Can be used when there is a safety risk involved (e.g. radiation exposure or extreme heat).

`` Data collected can be downloaded to a computer so that the data can be accessed and analyzed.

Temperature (°C) 0 5 10 15 20 25 30 35

Saturation density (kg/m3) 0.0049 0.0068 0.0094 0.00128 0.0173 0.0228 0.0304 0.0396

`` Title, row and column headings must state clearly and accurately what the table is about.

`` Tables allow you to systematically

record and condense a large amount of information. They provide an accurate record of your data.

`` Columns can be added for calculated

values such as density, rate, and summary statistics (e.g. mean).

`` Summary statistics make it easier to

identify trends and compare treatments. Rates are useful in comparing multiple data sets, e.g. if recordings were made over different time periods.

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8. Why is it important to keep a detailed logbook during a scientific investigation?

9. (a) Describe some advantages of using a datalogger over a person manually recording the data:

(b) What do you think might affect the accuracy of readings made with a datalogger?

CL

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55 Useful Concepts in Physics

Energy

Stored mechanical

`` Energy is the ability of a system to do work. It may

Chemical

be transferred between systems and transformed into different forms but it can not be created or destroyed. The amount of energy in a closed system is the same before and after a transformation. Energy is measured in joules (J).

Nuclear

Gravitational

Potential

`` Energy can be classified as potential (stored) or

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kinetic (movement) (right).

Energy

`` Energy can be transformed. For example, a ball at the top of a hill has gravitational potential energy. As it rolls down the hill the ball loses gravitational potential energy and gains kinetic energy. Some of the energy is also lost as heat and sound as it rolls down the hill.

Kinetic

Light

Radiant

`` Visible light is part of the spectrum of electromagnetic radiation. Visible light is defined as the part of the electromagnetic spectrum with a wavelength between 400 and 700 nanometers. Light waves near 400 nm appear blue, while light at 700 nm appears red. Light travels in a vacuum at around 299,792,458 m/s.

Electrical

Sound

Motion

Long = red

Short = blue

`` The speed of light is sometimes called the universal

speed limit. Nothing can travel at or above the speed of light (nothing that we know of). This speed limit stops logical paradoxes occurring, e.g. arriving somewhere before your image.

400 nm

700 nm

1. What is energy?

2. What are the two main types of energy? Give examples of each: (a) (b)

3. Energy can not be created or destroyed but only transformed. Explain this statement:

4. What kind of energy is light?

(b) What is the wavelength of red light?

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5. (a) What is the wavelength of blue light?

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6. Why is the universal speed limit of the speed of light important in our understanding of the universe?


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Inverse square law

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The inverse square law describes how the intensity of an effect varies with distance. Specifically, the intensity of an effect (e.g. light) changes in inverse proportion to the square of the distance from the source. To put it simply, the further the distance between two objects, the less intense the effect (see diagram below). A number of physical properties reduce in magnitude as they become more distant in a way that can be represented by an inverse square law. These include:

The inverse-square law can be written as: Intensity is proportional to:

1

distance squared (d2)

If the intensity at one distance is known the intensity at a second distance can be calculated using the following equation: intensity1 x distance12 = intensity2 x distance22

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`` Gravity

`` Electric field

Where:

`` Light intensity `` Radiation

`` Sound intensity

I1 =

Intensity 1 at D1

I2 =

Intensity 2 at D2

D1 =

Distance 1 from source

D2 =

Distance 2 from source

Distance = 3 Brightness = 1/32

Distance = 2 Brightness = 1/22

Distance = 1

= 1/9

= 1/4

=1

Brightness = 1/12

7. If a flashlight has a light intensity of 15.0 candela (cd) at a distance of 1 m from the lens what is the intensity of the light at 100 m from the lens? Show your working in the space below.

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8. The intensity of an iridium 192 source was 62 milliroentgen/hour at 100 m. What is the intensity at 1 m? Show your working in the space below.

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56 Accuracy and Precision

`` Accuracy refers to how close a measured or derived value is to its

true value. Simply put, it is the correctness of the measurement. The accuracy of a measurement can be increased by increasing the number of measurements taken. For example, the accuracy of determining how long a ball takes to roll down a ramp can be increased by increasing the number of times the experiment is carried out.

`` Precision refers to how close repeated measurements are to each other, i.e. the ability to be exact.

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A balance with a fault in it could give very precise (repeatable) but inaccurate (untrue) results. Data can only be reported as accurately as the measurement of the apparatus allows. It is often expressed as significant figures (the digits in a number which express meaning to a degree of accuracy).

Visualizing accuracy and precision

The analogy of golfers trying to get their golf balls in the cup is a good one for explaining accuracy and precision. Imagine four golfers each hit five golf balls. The results from each golfer are shown below.

The balls are all far apart and not close to the cup.

Reducing error

Sometimes reducing error requires taking more measurements over a longer period of time. For example, waves breaking on a shore do so with a relatively regular frequency, e.g. 1 per 5 s. Recording the time between one wave breaking and the next (the period) may be difficult to determine precisely for an individual wave and the waves may be breaking too quickly to enable accurate recordings.

The balls are all close to the cup and also clustered close together.

Student B

Time for swing (s)

Set

Time for 10 swings (s)

1

2.7

1

20.3

2

2.1

2

20.1

3

2.5

3

19.8

Mean (1 swing)

Mean (10 swings) 1 swing

(a) Calculate the mean for each student's results and the time for one swing for student B.

(b) Why are student B's results more accurate than student A's:

If the time recorded for 10 waves to break was 51.1 s, then the time for one wave to break is 5.1 s. The error is spread over the whole 51.1 s (0.3 ÷ 51.1) and thus is much smaller at just 0.6% of the wave period.

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The balls are all clustered close together but not close to the cup.

Student A

Example: Actual wave period: 5.0 seconds. Accuracy of timer (i.e. reaction speed) 0.3 seconds

In each measurement above, the error is about 0.3 s producing an error of up to 6.7% (0.3 ÷ 4.5 x 100) of the recorded value of a wave period.

Golfer 4: accurate and precise

1. The period of a pendulum is based on the length of the pendulum and the mass at its end. Two students measure the time it takes for a pendulum to swing back and forth (its period). Student A measures three individual swings and calculates a mean (average) value. Student B measures three sets of ten swings and calculates a mean. Each student measures the accuracy of the timer as 0.2 seconds. The results are shown below:

To increase the accuracy of measuring the period between each wave, it is best to record the time for a larger number of waves to break (e.g. 10) and divide by that number to obtain the period between each wave. This allows for slight variations in the period and reduces the total error in the measurement.

Measurements of individual periods (in seconds): 5.4, 5.7, 5.7, 5.8, 4.5, 4.6, 5.7, 5.8, 5.1, 5.3 Mean: 5.4

Golfer 3: precise but inaccurate

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The ball are all close to the cup but quite spread apart.

Golfer 2: inaccurate and imprecise

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Golfer 1: accurate but imprecise


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57 Working With Numbers

`` Using correct mathematical notation and being able to carry out simple calculations and conversions are fundamental

skills in science. Mathematics is used to analyze, interpret, and compare data. It is important that you are familiar with mathematical notation (the language of mathematics) and can confidently apply some basic mathematical principles and calculations to your data.

`` Much of our understanding of the physical sciences is based on our ability to use mathematics to interpret the patterns seen in data and express laws of the universe in simple notation.

Length

In mathematics, universal symbols are used to represent mathematical concepts. They save time and space when writing. Some commonly used symbols are shown below.

Kilometer (km)

1000 m

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Commonly used mathematical symbols

= Equal to

Meter (m)

1000 mm

Volume Liter (L)

1000 mL

> The value on the left is greater than the value on the right

Milliliter (mL)

= 1 mm3

< The value on the left is less than the value on the right

∝ Proportional to. A ∝ B means that A = a constant X B

Area

~ Approximately equal to

Square kilometer

∞ Infinity

Hectare

√b The square root of b

Square meter

b2 b

squared (b x b)

1,000,000 m2 10,000 m2

1,000,000 mm2

Temperature

bn b to the power of n ( b x b... n times)

0°C = freezing point of pure water

∆ The change in. For example ∆T /∆d = the change in T ÷ the change in d (see rates below right).

100°C = boiling point of pure water

Kelvin scale (K) and °C have the same magnitude. Kelvin scale starts at absolute zero (−273.15 °C).

Decimal and standard form

Rates

Decimal form (also called ordinary form) is the longhand way of writing a number (e.g. 15,000,000). Very large or very small numbers can take up too much space if written in decimal form and are often expressed in a condensed standard form. For example, 15,000,000 is written as 1.5 x 107 in standard form.

Rates are expressed as a measure per unit of time and show how a variable changes over time. Rates are used to provide meaningful comparisons of data that may have been recorded over different time periods.

In standard form a number is always written as A x 10n, where A is a number between 1 and 10, and n (the exponent) indicates how many places to move the decimal point. n can be positive or negative.

Often rates are expressed as a mean rate over the duration of the measurement period, but it is also useful to calculate the rate at various times to understand how rate changes over time. The table below shows the distance traveled by a rolling ball. A worked example for the rate at 2 seconds is provided below.

For the example above, A = 1.5 and n = 7 because the decimal point moved seven places (see below).

1 5 0 0 0 0 0 0 = 1.5 x 107

Time (s)

Distance traveled (m)

Rate of movement (speed) (m/s)

0

0

0

Small numbers can also be written in standard form. The exponent (n) will be negative. For example, 0.00101 is written as 1.01 x 10-3.

2

34

17*

4

42

?

6

48

3

0. 0 0 1 0 1 = 1.01 x 10-3

8

50

1

10

50

0

Adding numbers in standard form

Numbers in standard form can be added together so long as they are both raised to the same power of ten. E.g: 1 x 104 + 2 x 103 = 1 x 104 + 0.2 x 104 = 1.2 x 104

* meters moved between 0- 2 seconds: 34 m _ 0 m = 34 m

Rate of movement (speed) between 0- 2 seconds 34 m÷ 2 seconds = 17 m/s

(a) √ 9:

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1. Use the information above to complete the following calculations: (e) Convert 10 cm to millimeters:

(b) 43:

(f) Convert 4 liters to milliliters:

(c) Write 6,340,000 in standard form:

(g) Write 7.82 x 107 as a number:

(d) Write 0.00103 in standard form:

(h) 4.5 x 104 + 6.45 x 105:

CL

2. Using the rate table (above right) calculate the speed of the ball between 2 and 4 seconds:

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Dealing with large numbers

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Earth and space sciences often deal with very large numbers or scales. Numerical data indicating scale can often increase or decrease exponentially. Large scale changes in numerical data can be made more manageable by transforming the data using logarithms.

Exponential function Exponential growth or decay occurs at an increasingly ``

rapid rate in proportion to the increasing or decreasing total number or size.

`` In an exponential function, the base number is fixed (constant) and the exponent is variable.

work with.

`` The log of a number is the exponent to which a fixed value

(the base) is raised to get that number. So log10 (1000) = 3 because 103 = 1000.

`` Both log10 and loge (natural logs or ln) are commonly used.

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`` The equation for an exponential function is y = cx.

Log transformations A log transformation can make very large numbers easier to ``

`` An example of exponential decay is radioactive decay.

Any radioactive element has a half-life, the amount of time required for its radioactivity to fall to half its original value.

`` Log transformations are useful for data where there is an exponential increase or decrease in numbers. In this case, the transformation will produce a straight line plot.

`` To find the log10 of a number, e.g. 32, using a calculator, key

1.0

in log 32 = . The answer should be 1.51.

Radioactivity

`` An example of a log scale is the Moment Magnitude scale

used to measure the energy released during earthquakes. Each step of the scale is approximately 101.5 times greater than the step below it. Calculating the difference in energy released between earthquakes can be done by finding the inverse log10 of the difference in magnitude (10 (1.5 x (m1-m2)).

0.5

`` Also the number of earthquakes around the world at each magnitude follows a negative logarithmic spread (below).

0.125 0.0

0

5730

11,460

17,190

Time (years)

Example above: Carbon-14 (14C) has a half life of 5730 years. If a sample with a mass of 10 g was left for 5730 years half the sample will have decayed, leaving 5 g of radioactive material. After another 5730 years, 2.5 g of radioactive carbon will be left.

Earthquake magnitude

0.25

8 6 4 2

0

0

2

4

6

Log10 number of earthquakes per year

3. The Moment Magnitude scale is a measure of the energy released during an earthquake.

(a) How many times more energy is released by the magnitude 6 earthquake than a magnitude 4 earthquake?

(b) How many times more energy is released by the magnitude 7.5 earthquake than a magnitude 4.3 earthquake?

4. The pH scale measures the acidity of a substance. It is a negative logarithmic scale. A pH of 3 has a hydrogen ion concentration (which is responsible for acidity) ten times greater than a pH of 4.

How many times greater is the hydrogen ion concentration of a pH 2 solution than a pH 6 solution?

CL

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5. Carbon-14 (14C) is found in living organisms. It has a half life of 5730 years. When an organism dies it stops taking in 14C and this results in a change in the ratio of 14C to 12C. Using these pieces of information explain how we can calculate how long ago an organism died:


58 Graphical Analysis

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284

`` Graphs are a good way of visually showing trends, patterns, and relationships without taking up too much space. Complex data sets tend to be presented as a graph rather than a table.

`` You should plot your data as soon as possible, even during your experiment, as this will help you to evaluate your results as you proceed and make adjustments as necessary (e.g. to the sampling interval).

`` Give your graph a title and appropriately labeled axes so the information displayed is clearly communicated.

Scatter plot

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Line graph

`` The data must be continuous for both variables

`` The data must be continuous for both variables

`` The response variable is dependent on the

`` There is no manipulated (independent) variable

`` The points are connected point to point.

`` The points on the graph should not be connected but

`` Used to illustrate the response to a manipulated

`` Used to show the relationship between two correlated

(i.e. not counts and not categories).

independent variable. The independent variable is often time or the experimental treatment.

(i.e. not counts and not categories).

but the variables are often correlated, i.e. they vary together in a predictable way.

a line of best fit can be drawn through the points. A line of best fit should follow the trend of the data with roughly half the data points above the line and half below.

variable, e.g. distance versus time.

variables, e.g. atomic number vs atomic radius.

Relationship between recession velocity and distance

Distance versus time graph for a freely falling body

Recession velocity (km/s)

0

Distance (meters)

5

10 15

20

Line connecting points

25 30 35 40

1

2

3 4 5 6 Time (seconds)

Line of best fit

1000

7

500

Outlier: a data value that lies outside the main spread of data

0

0

1 Distance (Mpc)

2

`` Positive gradients (blue line): the line slopes upward to the

3

right (y is increasing as x increases).

`` Negative gradients (red line): the line slopes downward to the right (y is decreasing as x increases).

`` Zero gradients (green line): the line is horizontal (y does not change as x increases).

2 1 0 0

1

2

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5

The graph on the right illustrates three types of gradients for a line graph.

3

4

5

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Measuring gradients and intercepts

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`` Data plotted as a linear (straight) line can give us information about the system we are observing. `` A linear line can be described by the equation: y = mx + c. `` The equation can be used to calculate the gradient (slope) of a straight line and tells us about the relationship

between x and y (how fast y is changing relative to x). For a straight line, the rate of change of y relative to x is always constant. y

The equation for a straight line is written as:

6

Where :

5

The intercept (c) on a graph is where the line crosses the y-axis.

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y = mx + c

y = the y-axis value

4

m = the slope (or gradient)

3

x = the x-axis value

c = the y intercept (where the line crosses the y-axis).

5

2

1

11

Determining "m" and "c"

1

To find "c" just find where the line crosses the y-axis. To find m:

2

3

4

5

6

7

8

9

10

11

x

For the example above:

1. Choose any two points on the line.

2. Draw a right-angled triangle between the two points on the line.

3. Use the scale on each axis to find the triangle's vertical length and horizontal length. 4. Calculate the gradient of the line using the following equation: change in y (rise)

c=1

m = 0.45 (5 á11)

Once c and m have been determined you can choose any value for x and find the corresponding value for y. For example, when x = 9, the equation would be: y = 9 x 0.45 + 1 y = 5.05

change in x (run)

Distance (meters)

0

0

1

7

2

14

3

21

4

28

5

35

(a) Plot the data on the grid (right). Remember to give your plot a title and axes labels:

(b) What type of gradient does the data show?

(c) Determine c (intercept) for this graph: (d) Calculate m (slope):

(e) Determine the distance the student ran in 3.5 seconds:

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Time (seconds)

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1. A student measured the how far their classmate ran when she ran at a steady pace for five seconds. Distance was measured every second and their results are shown in the table below.


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59 Describing the Data

Most data shows variability. Descriptive statistics (e.g. mean and standard deviation) are used to summarize important features of a data set such as central tendency (the mid-point of the data's distribution) and how the data values are distributed around this value.

Mean

PR E O V N IE LY W

The mean is a single value representing the central position in a set of data with a normal distribution (see plot below). In biology, the mean is often used to describe a variable in a population (e.g. mean height). Data sets are often large. In physics, the mean is most often applied to smaller data sets (e.g. the mean lap time of a race car over 10 laps). How is the mean calculated? The sample mean (x̄ ) is calculated by summing all the data values (x) and dividing them by the total number of data points (n). Outliers (very extreme values) are usually excluded from calculations of the mean.

It is not always appropriate to calculate a mean. Do not calculate a mean if: `` The values are already means (averages) themselves.

`` The data are ratios, such as percentages.

For very skewed data sets, it is better to use the median as a measure of central tendency. This is the middle value when the data values are placed in rank order. If two values share the central position, the sum of the two values is divided by two.

`` The measurement scale is not linear (e.g. pH units).

Ball release speed (m/s)

1. Write a mathematical expression for how to calculate a mean:

2. A handball player wanted to know if she could throw the ball faster using an above-head release or a siderelease throw. She threw the ball five times using each method. The ball release speed is recorded in the table, right.

Throw number

Above-head throw

Side-release throw

1

24.3

22.6

2

23.6

23.0

3

24.8

22.2

4

23.9

21.9

5

24.5

22.4

Sum (S)

(a) Complete the table by calculating the sum and the mean for each data set:

(b) Which type of throw produced the fastest release speed?

Mean (x̄ )

3. During throw 3 of the above-head throws, the ball slipped from the player's hand and recorded a speed of 10.2 m/s. The player decided not to use this value and rethrew the ball.

(a) Recalculate the mean using 10.2 instead of 24.8 m/s:

(b) Was retesting throw 3 the correct choice? Explain your reasoning:

Standard deviation

`` The lower the standard deviation, the more closely the data values cluster around the mean.

15

68%

10 5 0

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x̄ ± s. In normally distributed data, 68% of all data values will lie within one standard deviation (1s) of the mean and 95% of all values will lie within two standard deviations (2s) of the mean (right).

Normal distribution 20

2.5%

2.5%

95%

x -2s

x -1s

x

x +1s

x +2s

Size class

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`` Sample standard deviation (s) is usually presented as

25

Frequency

While it is important to know the mean of a data set, it is also important to know how much spread there is within the data. For normally distributed data (right) this is measured using standard deviation. It provides a way to evaluate the reliability of estimates of the true mean.

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Sample standard deviation is very easily calculated using the equation on the right. It is often calculated using a spreadsheet by entering the data into columns and typing the formula using standard spreadsheet formula rules (see BIOZONE's Resource Hub). A group of students wanted to determine if the degree of incline influenced how long it took for a large marble to roll down a track measuring a total length of 120 cm.

∑(x – x̄)2 n –1

∑(x – x̄)2 = the sum of squared deviations from the mean n = sample size (number of data values). n -1 provides a unbiased s for small sample sizes (large samples can use n).

PR E O V N IE LY W

Trial 1: `` The students set up a ramp up with a 10° incline and marked 120 cm with tape. Once the ramp was set up, a student used a ruler to hold the marble at its starting position.

s=

`` When the timer was ready, the ruler was quickly removed and the marble began rolling.

`` Another student used a stopwatch to measure the time taken for the marble to reach the end point. They repeated the procedure 10 times.

Trial 2:

`` In the second trial the students adjusted the incline to 15° and repeated the experiment as described above.

`` The students recorded their results in the table (below right).

4. (a) Use the calculated statistics for each data set to comment on how incline affected the time taken for the marble to roll 120 cm:

Effect of incline on the time taken for a marble to roll 120 cm Time (s)

(b) The data for the 15° incline has a lower standard deviation than the date for the 10° incline. What does this tell us about the reliability of the data?

5. Calculating a 95% confidence interval (95% CI) provides a good estimate of how close the sample mean is to the true mean. The mean ± the 95% CI gives the 95% confidence limits. On average, 95 times out of 100, the true population mean will lie within the confidence limits. The ± 95% CI can be added to points on a plot of data to determine significance. If the confidence intervals overlap, there is no significant difference between the data at P= 0.05.

10° incline

15° incline

1

1.73

1.20

2

2.26

1.15

3

1.73

1.11

4

1.89

0.98

5

1.96

1.14

6

2.11

0.99

7

2.29

1.05

8

2.04

1.08

9

1.76

1.21

10

1.93

1.18

Sum (S)

19.7

11.09

Mean (x̄ )

1.97

1.11

Standard deviation

0.21

0.08

2.5

(a) Plot the mean time and 95% CI for both sets of data on the grid (right). Plot as a column graph with error bars.

1.5

(b) Is the difference significant at P = 0.05? Why or why not?

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2.0

Time (s)

The 95% CI for the 10° incline data is 0.15 and for the 15° incline data is 0.06 at P = 0.05.

1.0

0.5

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0


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Relative atomic mass

Name

Chemical symbol

Atomic number * = unknown

Electronegativity

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60 The Periodic Table

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Appendix: Equipment list

The equipment list provides the material and equipment needed per student, pair, or group.

IS 1: Forces and Motion

INVESTIGATION 2.8: Polarity Per student/pair 50 mL burette Clamp Distilled water Cyclohexane 100 mL beaker Glass rod Silk or polyester fabric or towel

PR E O V N IE LY W

INVESTIGATION 1.1: Distance, displacement, and velocity Per class Measuring tape (at least 10 m) Flag or bright fabric as starter signal 12 stop watches (watches/cell phones)

1 small garbage or plastic bag 10 paper clips String 20 plastic or paper straws Equipment can be modified with equivalent replacements

INVESTIGATION 1.4: Shape and compressive strength Per student/pair/group Thin card or cartridge paper, roughly 200-300 gsm Thick card as support for masses Scissors Ruler Tape Masses (range 10-200 g)

INVESTIGATION 1.5: Building bridges Per student/pair/group 18 plastic drinking straws or 36 dry spaghetti straws 1 g Blu Tack or similar adhesive putty 30 cm string 4 x 1- g masses 1/2 sheet US letter or A4 copy paper Computer/device and access to internet INVESTIGATION 1.6: Investigating momentum Per student/pair/group Marble and ball bearing of similar size but different mass Ramp Tape measure Carpeted area for run INVESTIGATION 1.7: Building a lander Per student/pair/group 1 egg 1 plastic egg (for testing) Tape 5 medium sized rubber bands

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INVESTIGATION 2.1: Cavendish's experiment Per student/pair/group 2 x 1 m rulers or 1 x 2m ruler or thin wooden rail Tape or rubber bands Nylon fishing line or similar 2 x large masses (5-10 kg) 2 x small masses (1 kg) Video recorder or cell phone camera INVESTIGATION 2.2: Parallax Per group of four Protractor (a 180° is easiest to use) Corkboard or thick card Tape Push pins Plastic straw Measuring tape INVESTIGATION 2.3: Orbits Per student/pair String (15 cm) Two thumbtacks Pencil Corkboard or card

INVESTIGATION 2.4: Computational models of orbits Per student/pair Computer Spreadsheet application such as Microsoft Excel INVESTIGATION 2.5: Balloon electrostatics Per student/pair Two balloons Fabric (wool or synthetic) Nylon thread or fishing line

INVESTIGATION 2.6: Threading the needle Per student Sewing needle Nylon thread and cotton thread of same gauge INVESTIGATION 2.7: Observing the inverse square law Per student/pair Black marker pen Balloon (not black)

INVESTIGATION 2.9: What is affected by magnets? Per pair/group (modify list as required) Magnet Aluminum foil Pure iron Pure copper Paper clips Copper penny Nickel or dime Stainless steel Brass Minerals (e.g. quartz, hematite, calcite, pyrite) PVC plastic Styrofoam Wood Paper INVESTIGATION 2.10: Charges and magnets Per student/pair Magnet 2 x plastic rulers Wool Small bottle lid

INVESTIGATION 2.11: Magnetic fields Per student/pair Two bar magnets Zip lock sandwich bag Iron filings (or powder) Index card (or ruled card)

INVESTIGATION 2.12: Strength of a magnetic field Per student/pair Sheets of copy paper Magnet Metal paper clip

INVESTIGATION 2.13: Making a magnet Per student/pair Bar magnet Iron object, e.g. nail or needle Pen to mark nail center Compass or iron objects to test

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INVESTIGATION 1.3: Investigating compressive strength Per student/pair/group Cardboard tube (e.g. toilet tissue roll) Empty aluminum can Paper cup Styrofoam cup Empty "tin" food can, 300-400 mL Thick card or very thin board Masses (range 200 g to 1 kg)

IS 2: Forces at a Distance

INVESTIGATION 2.14: Patterns in materials Per student/pair Magnifying glass or dissecting microscope Conductivity meter or simple circuit Materials to test: metal paper clip, plastic paper clip,

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INVESTIGATION 1.2: Investigating pressure Per student/pair/group High heel/stiletto shoes Flat boots or shoes Area of sand, mud, uncompacted soil, or lawn


290 bigger than the tube but smaller than the spring) may be needed.

INVESTIGATION 2.15: What is used where No special equipment required

INVESTIGATION 4.2: Making a cloud chamber Per group/class Clear plastic cup or plastic tank Felt to cover the base of cup/tank Glue or other adhesive Plasticine (if using cup) Isopropyl alcohol (propanol) Styrofoam tray/ice box lid Dry ice to fill tray/ice box lid Metal tray Flashlight

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thin block of wood, concrete/brick, length of nylon, length of cotton, a stone, a nail, glass, natural quartz.

IS3: Energy Conversion and Renewable Energy

INVESTIGATION 5.8 Your own double slit experiment Per student/group/class 1 x microscope slide painted black 1 x craft knife 1 x ruler Plasticine or blu-tak 1 x laser pointer

PR E O V N IE LY W

INVESTIGATION 3.1 A simple power plant Per student/pair/group 2 x 1.5 volt electric motors Wires 1 x galvanometer or center zero voltmeter 1 x Low voltage light bulb Material to construct turbine blades (optional)

INVESTIGATION 5.7 Damping a building Per student/group 1 x Manila folder 1 x pair of scissors 1 x ruler Tape 1 x drawing compass or needle Thread 1 x small weight (e.g. fishing sinker) 1 x block of wood

INVESTIGATION 3.4 Electricity affects a compass part 3 Per student/pair/group 1 x 1.5 volt AA cell Insulated wire Electrical tape Cardboard 1 x compass INVESTIGATION 3.5 Electricity from magnets Per student/pair/group Insulated wire 1 x bar magnet 1 x cardboard tube 1 x galvanometer

IS4: Nuclear Processes and Earth History INVESTIGATION 4.1: Modeling the strong nuclear force Per group/class An old click pen 2 x small neodymium magnets with central holes NOTE: The diameter of the spring needs to be greater than the diameter of the hole in the magnets otherwise 2 washers (outer diameter bigger than hole in the magnets and inner diameter

IS5: Waves and Electromagnetic Radiation INVESTIGATION 5.1 Modeling the stadium wave Per class 1 x video recording device (e.g. phone) Screen to play video on INVESTIGATION 5.2 Water waves Per student/group 1 x large plastic tray Water 1 x plastic float (e.g. bottle cap) 1 x small piece of wood INVESTIGATION 5.3 Slinky springs Per pair 1 x Slinky spring

INVESTIGATION 5.9 Investigating two properties unique to waves Per pair/group 1 x square tray 1 x ruler or thin stick Blocks of wood (3 shorter, 3 longer) Water

IS6: Stars and the Origins of the Universe INVESTIGATION 6.1: Measuring the diameter of the Sun Per student/pair Aluminum foil Push pin Card (to make a frame for the foil) Ruler INVESTIGATION 6.2: Modeling expansion Per student/pair Thick rubber band Push pin Different colored pens (red/blue) Black marker

INVESTIGATION 5.4 The speed of sound in air Per group/class Set of tuning forks or frequency generator with speaker 1 x clamp stand and clamp Water 1 x large beaker 1 x PVC pipe (30-60 cm) INVESTIGATION 5.5 Amplitude Per pair 1 x rope (at least 4 m long) Masking tape 1 x Timer INVESTIGATION 5.6 Modeling an earthquake Per student/group 1 x Manila folder 1 x pair of scissors 5 x binder clips 2 x blocks of wood Rubber bands or tape

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INVESTIGATION 3.3 Electricity affects a compass part 2 Per student/pair/group 1 x 1.5 volt AA cell Insulated wire Electrical tape Cardboard 1 x compass Clear tape

INVESTIGATION 4.4: Half lives 2 Per group of two or three 30 x 6 sided dice (or up to that number as available)

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INVESTIGATION 3.2 Electricity affects a compass part 1 Per student/pair/group 1 x 1.5 volt AA cell Insulated wire Electrical tape Cardboard 1 x compass

INVESTIGATION 4.3: Half lives 1 Per student/group of two A4 or US letter sized sheet of paper Scissors Ruler

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Appendix: Units & Formulae

MULTIPLES AND CONVERSIONS

USEFUL FORMULAE IN PHYSICS

FORCES AND MOTION

PR E O V N IE LY W

MULTIPLES

MULTIPLE

PREFIX

SYMBOL

EXAMPLE

109

giga

G

gigawatt (GW)

106

mega

M

megawatt (MW)

103

kilo

k

kilogram (kg)

102

hecto

h

hectare (ha)

10-1

deci

d

decimeter (dm)

10-2

centi

c

centimeter (cm)

10-3

milli

m

milliimeter (mm)

10-6

micro

µ

microsecond (µs)

10-9

nano

n

nanometer (nm)

10-12

pico

p

picosecond (ps)

Change in distance (Dd) = velocity (v) x change in time (Dt) Acceleration (a) = change in velocity (∆v) ÷ change in time (Dt) Force (F) = mass (m) x acceleration (a) Pressure (P) = force (F) ÷ area (A)

Momentum (p) = mass (m) x velocity (v)

Weight (W) = mass (m) x strength of gravity (g) ENERGY

Work (W) = mass (m) x acceleration (a) x distance (d) Power (P) = energy (E) ÷ time (t)

CONVERSION FACTORS FOR COMMON UNITS OF MEASURE

Efficiency (%) = (useful energy out ÷ total energy in) x 100

For all conversions multiply by the factor shown

WAVES

LENGTH

Centimeters to inches:

0.393

Meters to feet:

3.280

Kilometers to miles:

0.621

Speed (v) = frequency (f) x wavelength (λ) Frequency (f) = 1 / T (period)

Wein displacement law:

Wavelength lmax (m) = 2.898 x 10-3 (b) ÷ Kelvin (T)

VOLUME

Milliliters to fluid ounces:

0.034

Liters to gallons:

0.264

Cubic meters to gallons:

264.1

Z value calculations: z = (λ observed - λ rest) ÷ λ rest ORBITS AND GRAVITY

AREA

Square meters to square feet:

10.76

Hectares to acres:

2.471

Square kilometers to square miles

0.386

Newton's law of universal gravitation:

F=G

M1M2 r2

Kepler's law:

TEMPERATURE

°C to °F: Formula °C to °F:

0°C = 32°F 100°C = 212°F

°F = °C x 1.8 + 32

T12

a13

=

T22

a23

1055.06

M=

a3 T2 q1q2

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Newton's rewriting of Kepler's law ENERGY BTU to joules

Coulomb's force: F=k

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q1q2 r2

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F=k ELECTRICITY AND MAGNETISM r2


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Image credits

PR E O V N IE LY W

We acknowledge the generosity of those who have provided photographs or diagrams for this edition including: • Felix Hicks for original drawings of the ice skaters and astronauts, and cation and anion diagrams • Scott McDougall for the image of the comet • Biomimetics and Dexterous Manipulation Lab, Stanford University for the image of the person climbing glass.

We also acknowledge the photographers that have made their images available through Pixabay (pixabay.com) or Wikimedia Commons under Creative Commons Licences 2.0, 2.5, 3.0, or 4.0: • Niel Noorhoek • Qfl247 • Luka Adikashvil • Jeffrey Pang • G310Luke • Julius Reque • Ang MoKio • Mirceas Madau • Ricardo Nunes (NASA) • Wilco Oelen • Hans-Joachim Engelhardt • Jeffrey Pang • Graphtecinst • Ravedave • USAF Staff Sgt. Jim Araos • Judy Schmidt • ALMA (ESO/NAOJ/ NRAO)/E. O’Gorman/P. Kervella • ESO • Andrew Pontzen and Fabio Governato • Conn, Kit • David Monniaux • USAF • Claude Renault • Jurii • Chocolateoak • Gregory H. Revera • Adrzej Mirecki • H. Rabb • Maximilien Brice • gamsiz • National Nuclear Security Administration • Mike Beauregard • jstuby • G310Luke • Eugen Zibiso • Gregory H. Revera • Ken Lund from Reno, Nevada, USA • PHAN J. Alan Elliott • Armand du Plessis • Brocken Inaglory • Wing-Chi Poon • Gopherboy6956 • Anton Yankovyi • Amber Stuver • • Vic Mirmow • Plantsurfer • Phrontis • Mikenorton

Contributors identified by coded credits are: ISS: International Space Station, KP: Kent Pryor, NASA: National Aeronautics and Space Administration, NASA/ESA: National Aeronautics and Space Administration / European Space Agency NASA/ JPL: NASA Jet Propulsion Laboratory, NHTSA: National Highway Traffic Safety Administration, NOAA: The National Oceanic and Atmospheric Administration, USDE: United States Department of Energy, USGS: United States Geological Survey

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Royalty free images, purchased by BIOZONE International Ltd, are used throughout this workbook and have been obtained from the following sources: • iStock images • Corel Corporation from their Professional Photos CD-ROM collection • ©Digital Vision • Gazelle Technologies Inc. • PhotoDisc®, Inc. USA, www.photodisc.com • 3D images created using Bryce, Poser, and Pymol

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Index

95% confidence interval 287

Energy and work 117-119 Energy conservation 107 Energy consumption, USA 110 Energy conversion devices - designing 136-139 Energy Island 135 Energy sources 107-116, 244 Energy, types of 279 Engineering, egg lander 39 Epicenter of earthquake 205 Erosion 171 Escape velocity 59 Event horizon 251 Expansion of universe - modeling 259 Explosions, 34 - nuclear 157 Exponential functions 283 Eyes 212

Helium - absorption spectrum 256 - formation after Big Bang 264 Helmets, tests 38 Hertzsprung-Russell diagram 239 Hot spots, Hawaii 169 Hubble Space telescope 251 Hubble's law 258 Hydroelectric power 113, 119, 134 Hydrogen absorption spectrum 256 Hydrogen bonds 82 Hydrogen formation - after Big Bang 264

PR E O V N IE LY W

A Absorption spectra 256-257 - of stars 237-238 Absorption, of light 213 AC generator 128 Acceleration 9-10 Acceleration and force 13, 20 Acceleration, investigating 16 Accretion disk 251 Accuracy of data 281 Action reaction 20 Age of the Earth 174 Alpha decay 156 Alpha particles 154-155 Amplitude modulation (AM) 221 Amplitude, of waves 200, 211 Analog information 222-223 Anions 77 Apparent magnitude of star 234 Assumptions in science 275 Astronomical unit, see AU 62 - defined 277 Atomic mass 148 Atomic structure 75 Atomic theory, history of 146 AU 62, 277

Convergent boundaries 169 Cosmic microwave background (see CMB) 260, 264 Coulomb's law 71 Covalent bonds 79-80 Crab nebula 232 Crash helmets 38 Crash test 38 Crater counting 176, 179 Craters 170 Crumple zones 37 Curie, Marie 155 Current electricity 124

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G g, see force due to gravity 12 Galaxies - calculating the motion of 257 - composition of 261 Galaxy, Milky Way 254 Gamma decay 156 Gamma radiation 211 General theory of relativity 260 Generators 128 Geostationary orbit (GEO) 64 Geothermal power 115 Gluon, elementary particle 150, 263 Gold foil experiment 147 Gradients, on graphs 284-285 Graphs, types of 284 Gravitation, Newton's law 52 Gravitational constant, G 52 Gravitational potential energy 118, 279 Gravitational theory 273 Graviton, elementary particle 262 Gravity - defined 50 - on Earth 53 - relative strength 151

IJ Igneous rocks 168 Impulse 35 Information storage, sound waves 224 Information technology, using waves 220 Infrared light 211 Intercepts, on graphs 285 Interference, waves 216-217 Intermolecular forces 82 International Space Station (ISS) 64 Intramolecular bonding 70-81 Inverse square law 71-72, 145, 280 - defined 54 - light 214 Ion, formation of 75-77 Ionic bonds 79 Ionic substances, properties of 93 Ionizing radiation, and health 219 Island arc 169 Isolated systems 274 Isotopes 148 ISS 64 K Kepler's laws 60 - Newton's derivations 62 Kinetic energy 118 - types of 279 kWh, defined 122

L Lander, design 39 Large Hadron Collider 150 Laser light 222 Law of inertia 22 Law of reciprocity 22 Law, Coulomb's 71 Laws, Kepler 60 Life cycle of stars 249-251 Lift force 18-19 Light 211, 279 - and atmospheric phenomena 209 - duality theory of 218 - effect on electrons 131 - speed of 193 Light waves, lightning 193 Light year (LY), defined 277 Lightning 86 - light waves 193 LIGO 210 Line graph 284 Line of best fit 284 Log books in science 278 Logarithms 283 Longitudinal waves 196, 202 Low Earth orbit (LEO) 64 Luminosity of star 234

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C Calculations, making 282 Car, design of 2 Carbon footprint 108 Carbon-14 166 Carbon, formation of 264 Cations 77 Cavendish, experiments 51 CD technology 222 Cells, photovoltaic 132-133 Chemical explosions 158 Chemical potential energy 279 Closed systems 274 Cloud chamber 153-154 CMB, see cosmic microwave background 260, 264 Coal formation 112 Collisions 31-33 Combined cycle power plant 121 Comets - information from 181 - orbit 59 Communication, using waves 220 Compressive strength 25 Condrites, dating 177 Confidence intervals 287 Conservation of energy 107 Conservation of momentum 31, 33 Conservation of nucleons 156 Constructive factors 171 Constructive interference waves 217 Convection zone, Sun 244

E E=mc2 159 Earth, age of 174 Earth rocks, dating 175, 177 Earth's crust 169 Earth's gravity 53 Earthquake waves 202 Earthquakes, - building safety 207-208 - information from 206 - locating 204 - modeling 207 Eccentricity 60 Efficiency - of power generation 120-122 Egg lander, design 39 Einstein, Albert 260 Electrical energy 279 Electricity and magnetism 124-127 Electricity generation, - and pollution 109 - effect on compass 125 - methods of 105-106 - simple 124 Electromagnetic forces 86 - applications of 89 Electromagnetic spectrum 211, 233, 279 Electromagnetic waves 210 Electromagnetism 86, 151 Electron-hole, photovoltaics 129 Electron, elementary particle 262 Electrons 75-77 - detecting 154 Electrostatic forces 70 Electrostatics, and bonding 79 Elementary particles, defined 150 -detecting 154 - in Big Bang 262-263 Elements, origin 152 Elliptical orbits 59

F Faults 40 Ferromagnetic materials 87 Fission, nuclear 160-161 FM 221 Fogbows 209 Force carrier 150 Force due to gravity 12 Force pairs 21 Force - and acceleration 13 - defined 11 - friction 14 - gravitational 52-53 - magnetic 83-88 - measuring 277 - normal 25 - support 25 Forces - in Earth system 41-43 - in free body diagrams 18-19 - intermolecular 82 Formula 1 car 2 Free body diagrams 18-19 Frequency modulation (FM) 221 Frequency of waves 197, 211 Friction 14 Fusion, nuclear 162

H Half lives 163-167 Halos 209 Health, and the EM spectrum 219 Heat rate 122

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B Balloon electrostatics 70 Base isolation 208 Base units 276 Becquerel, Henri 155 Beta decay 156 Beta particles 155 Big Bang 260-265 Binary code - in digital information 223 Blu-ray technology 222 Blue shift 256 Bonding, and electrostatics 79 Bonds - intermolecular 82 - intramolecular 70-81 - types of 79 Bridge design 23-27 BTU defined 122 Building, earthquake safety 207-208

D Damping, buildings 208 Data, accuracy 281 Dataloggers 278 DC generator 128 Decimal form 282 Deposition 171 Derived units 276 Descriptive statistics 286 Design, bridge 27 Destructive factors 171 Destructive interference, waves 217 Diffraction, waves 216 Digital information 222-223 Dipole-dipole forces 82 Displacement 4, 6, 10 Distance 4 - effect on gravitational force 53 - measuring 277 Distance to planets, measuring 56 Divergent boundaries 169 Doppler effect 255-256 Double slit experiment 214 Drag force 18-19 Duality theory of light 218 DVD technology 222

M Magnetic fields 85-86 Magnetism 83-88 - and current electricity 124-127


294 - travel time 204 Parallax 56 - investigation 57 Parsec, defined 277 Period of waves 201 Periodic table of elements 78, 288 - patterns in 148-149 Photoelectric effect 132-133, 217-218 Photometeors 209 Photon 218 Photosphere, Sun 244 Photosynthesis 107 Photovoltaic cell 115, 129, 132-134 Planetary motion 55-63 Polarity, molecular 81 Pollution - and electricity generation 109 Positron 154, 262 Potential energy 118 Potential energy, types of 279 Power plant - combined cycle 121 - efficiency of 120-122 - in California 123 Precision of measurements 281 Pressure 24 Pressure waves 194 Probability, in radioactive decay 164 Proton number 148 Proton 75 - in Big Bang 263

- speed of 193 - thunder 193 Sound, speed of 198 Space probes 181 Spectrum, solar radiation 212 Speed 5 Stadium wave 191 Standard deviation 286-287 Standard form 282 Star - color and temperature 235 - formation 248 - life cycle 249-251 - magnitude and luminosity 234 Stars, absorption spectra 237-238 Statistics, descriptive 286 Stellar evolution 249-251 Stellar nucleosynthesis 242, 250-251 Stellarator 246 Storage of information 224 Strong nuclear force 150-151, 159 Sun dogs 209 Sun - size of 240 - structure of 243 Sunlight energy 107 Sunspots 245 Supergiants 250-251 Supernova 250-251 Supernovae, origin of elements 152 Support force 25 Systems 274

- earthquake 202 - properties 197 Weak force 151 Weathering 171 Weight force 18-19 Weight vs mass 12 Wein's law 235 Wind power 114, 134 Work, defined 117 X X-rays 211, 219

PR E O V N IE LY W

CL N AS OT SR F OO OR M US E

Magnets, and charge 84 Major axis, defined 60 Mars landing 36 Mass damping 208 Mass vs weight 12 Mass wasting 171 Mass-energy equivalence 159 Mass, effect on acceleration 17 Materials, properties of 89-95 Mean 286 Measurement 276 Mechanical energy - interconversion of 119 Mechanical potential energy 279 Mechanical waves 194-195, 210 Medium Earth orbit (MEO) 64 Metallic bonds 79, 81 Metals, properties of 92 Metamorphic rocks 168 Meteorites, dating 175, 177 Mexico city earthquake 190 Microwaves 211 Milky Way Galaxy 254 Minor axis, defined 60 Model, atomic 75, 146 Modeling, radioactive decay 163-164 Models 274 Modulation 221 Molecular polarity 81 Molecular substances - properties of 94-95 Momentum 28-31 - conservation of 31, 33 Moon rocks, dating 176-177 Motion 3-5 - kinetic energy 279 - laws of 15 - of galaxies 257 - planetary 55-63 Motion graphs 4-8 Mountains - and forces 40 - height 49 Muons 154-155 MWh, defined 122

P P-waves 202

S S-waves 202 - travel time 204 Satellites 64 Scalar variable 4-5 Scatter plot 284 Science, nature of 272 Sea floor spreading 173 Sedimentary rocks 168 Seismic waves 202-203 - use of 204 Seismograph 202, 205 Semiconductors 130 Semimajor axis, defined 60 Semiminor axis, defined 60 SI units 276 Slinky springs, waves in 196 Slope, calculating (see gradient) 285 Smoke detector 153 Solar power 115 Solar flares 245 Solar mass, unit 62 Solar power 129 Solar radiation, spectrum 212 Solar system 254 Sound energy 279 Sound waves

U Ultraviolet light 211 Units of measurement 276, 282 Universe - expansion of 258-260 - origins of 262-265 - shape of 253 - size of 254 Uranium-238 166 V Valence shell 76 Van der Waals forces 82 Variable scalar 4 Variable, vector 5 Vector 5 Velocity 5, 10 - of waves 197, 201 Venus, orbit 59 Visible light 211, 279 Vision 212 Volcanic activity 171 Voyager 2 145

N AS OT SR F OO OR M US E

O Observations in science 275 Occam's razor 275 Oil, formation 111 Olbers' paradox 261 Open systems 274 Orbital period, T 62 Orbits 55, 58-65 - modeling 65-68 - satellites 64-65 Oxygen isotopes, and dating 178

R Radiant energy 279 Radiation zone, Sun 244 Radio waves 211, 221 Radioactive decay 155-156 - modeling 163-164 Radioactivity 153-162 Radiometric dating 166-167 - and the rock cycle 173 - Earth's history 174-180 - of seafloor 180 Rainbows 209 Rates, calculating 282 Recessional velocity of galaxies 257 Redshift, Doppler effect 256 Reflection, of light 213 Refraction, of light 213 Relativity, general theory of 260 Renewable energy 110, 112-115 - evaluating 134 Resource use, simulation 142-143 Rock cycle 172 Rocks, age of 168 Rutherford, Ernest 146-147, 155

T Tables, using 278 Technology, and EM spectrum 213 Tectonic activity 171 Thermal imaging 213 Thermal pollution 120 Thought experiment - and finite universe 261 - motion 15 Thrust force 18-19 Thunder, sound waves 193 Time, role in describing motion 4 Timeline - atomic theory 146 - Big Bang 262-265 - gravitational theory 273 Transmission, of light 213 Transverse waves 195, 202

W Water waves, investigating 195 Water wheel 119 Wave period 201 Wave properties 215-216 Wave velocity 201 Wavelength 197 - of waves 211 - shift in 257 Waves - and energy 192

CL

N Natural gas formation 111 Natural gas power plant 121 Nebula, Crab 232 Neodymium magnets 151 Network molecules 95 Neutral atom 75 Neutron, in Big Bang 263 Neutrons 75 Newton's law of gravitation 52 Newton's laws of motion 15, 22 Non-renewable energy 109-112, 116 Normal force 25 Nuclear chain reactions 156 Nuclear fission 160-161 Nuclear fusion 162, 246 Nuclear potential energy 279 Nuclear power 116 Nuclear power plant 161 Nuclear reactions 156-161 Nucleon number 148 Nucleons, conservation of 156 Nucleosynthesis 242 - stellar 250-251 Nucleus, atom 75 Nucleus, gold foil experiment 147 Nuclide notation 148

Q Quantum mechanics 146 Quark 150, 263

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