STEMscopes Georgia Science Student Notebook Physics by acceleratelearning

Physics STEMscopes Georgia Student Notebook

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a part of STEMscopes NGSS

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Physics

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developed by Accelerate Learning, Inc. & Rice University

Notebook

(800) 531-0864

6/23/17 12:06 PM

GEORGIA Student Notebook – Physics ISBN: 978-1-946725-82-0

Published by Accelerate Learning Inc., 5177 Richmond Ave, Suite 800, Houston, TX 77056. Copyright © 2017, by Accelerate Learning Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written consent of Accelerate Learning Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. To learn more, visit us at www.acceleratelearning.com

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GEORGIA

This Student Notebook is designed to be used as a companion piece to our online curriculum. The pages of this book are organized and follow the 5E model.

Student Handout

ENGAGE

A short activity to grab students’ interest

Student Journal

EXPLORE

A hands-on activity in which students get expereince with the concept being taught

STEMscopedia

EXPLAIN

A reference material that includes parent connections, technology, and science news

Reading Science A reading passage about the concept that includes comprehension questions

ELABORATE Math Connection

A set of grade-level appropriate math problems that address the concept

Writing Science

EVALUATE

A writing prompt based on the concept studied in which the students can demonstrate what they have learned

Only student pages are included in this book and directions on how to use these pages are found in our online curriculum. Use the URL address and password provided to you by your district to access our full curriculum.

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Physics Student Notebook Table of Contents

Lesson P1ABC

P1D

P2AB

P2C

P2D

107

P2E

127

P3A

151

One-Dimensional Motion Two-Dimensional Motion Newton’s Laws of Motion Calculating Components of Forces Circular Motion Newton’s Universal Law of Gravitation Open and Closed Systems P3BC

Conservation of Energy and the Work-Kinetic Energy Theorem

171

P3D

197

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Page

iii

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Physics Student Notebook Table of Contents

Lesson

Page

P4ACD

223

P4BG

253

P4EF

279

P5A

311

P5B

333

P5C

355

P5D

377

P5E

403

P6ABC

421

Mechanical and Electromagnetic Waves Interference and Diffraction of Waves Light and Lenses Electrical and Gravitational Forces Charge Transfer Behavior of Charges Direct Current Circuits Electric Currents and Magnetic Fields Nuclear Processes

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Physics Student Notebook Table of Contents

Lesson

Page Appendix

Glossary

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447

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High School Physics

P1ABC

One-Dimensional Motion

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P1ABC One-Dimensional Motion

Student Handout Name:

Date:

First, measure out 3 m of tape using the meter stick or tape measure provided. Carefully place this on the floor as straight as possible. At one end, place a small piece of tape and label it “Start.” Measure 1 m away on the long piece of tape, and place a second piece labeled “1 m.” Repeat this at 2 m and 3 m. Two lab partners will time how long it takes the ball to roll. One will time from start to 1 m, and the other from start to 3 m. Have one lab partner roll the ball slowly along the tape. Try to roll the ball as straight as possible. Record the time in the table below in seconds. You are welcome to roll the ball several times to get good data! Roll #

Time: 1 min

Time: 3 min

Your team is going to calculate the average velocity of the ball. Velocity is the distance divided by the time, as shown below:

v = Roll #

t Velocity: 1 min

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Veolcity: 3 min

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P1ABC One-Dimensional Motion

Student Handout

Was the velocity over 1 m the same as the velocity over 3 m?

What could cause a difference in the velocity as distance increases?

Make a prediction about the velocity if you timed the ball over 9 m.

An instantaneous velocity is the velocity at one specific instant in an object’s motion, while an average velocity is the total distance traveled over total time taken. Is the 3-m velocity better described as an average velocity or an instantaneous velocity?

Is the 1-m velocity better described as an average velocity or an instantaneous velocity?

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P1ABC One-Dimensional Motion

Student Journal Date:

Name:

Group:

Background 1. Jane walks once around her desk and ends up at the same place. What is her displacement?

2. What tools would you use to measure displacement? What tools would you use to measure velocity?

3. What is the relationship between velocity and acceleration?

Trucker’s Journal 1. Fill in the table below using Jack’s journal. Find the displacement, total distance traveled, and driving time for each phase of the trip. Segment

Displacement (km)

Distance (km)

Time (h)

Chattanooga–Yummy’s Lunch at Yummy’s Yummy’s–B’s in Toledo Overnight in Toledo

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P1ABC One-Dimensional Motion

Student Journal Part I: Trucker’s Journal, Continued Segment

Displacement (km)

Distance (km)

Time (h)

B’s–Toledo (north side) Toledo (north side)–state trooper stop During state trooper stop State trooper stop–Flint 2. Calculate Jack’s average velocity for each segment.

3. What did the state trooper measure?

4. If it took Jack 300 m to come to a stop for the state trooper, what was Jack’s acceleration?

5. After the state trooper stop, it took Jack 30 s to reach 100 km/h. What was his acceleration?

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P1ABC One-Dimensional Motion

Student Journal Part I: Trucker’s Journal, Continued 6. How far had Jack traveled from the stop when he reached his final velocity of 100 km/h?

7. On previous trips, Jack had to slow down for road construction at the Ohio-Michigan border. If the road construction stretched for 25 km, and Jack could only drive 50 km/h through the construction site, how long would it take him to get through the site?

8. Using graph paper or graphing technology, create a distance vs. time graph for Jack’s trip. Be sure to use the total time and distance for Jack’s trip (including stops).

Reflections and Conclusions

1. What quantities did Jack record in his journal?

2. What was the easiest quantity to calculate?

3. What was the hardest quantity to calculate?

4. Explain how you used systematic approaches to answer the scientific investigative questions.

5. What were some of the limitations you encountered in completing these scientific processes?

6. Using all of the following terms, develop a graphic organizer on a separate sheet of paper. Terms: distance, displacement, speed, velocity, acceleration, average velocity, scalar quantity, vector quantity © Accelerate Learning Inc. - All Rights Reserved

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P1ABC One-Dimensional Motion

Student Journal Additional Practice The Pythagorean theorem determines the length of each side of a right triangle. The formula is a2 + b2 = c2, in which a and b are the lengths of the shorter sides and c is the length of the hypotenuse. 1. Jose ran 3 km north, made a right turn, and ran 4 km east. What was the magnitude of his displacement?

2. Mary ran 6 km south, turned west, and continued running. She did not keep track of how far she ran west, but she stopped when she arrived at a shop she knows is exactly 10 km from her starting point. How many total kilometers did Mary run?

3. A runner accelerated uniformly from rest to 5 m/s in 2 seconds. a. What was his average acceleration? b. How far did this runner travel in these 2 seconds?

4. A car accelerates from rest to 40 m/s over a distance of 100m. How long did this take?

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STEMscopedia: ONE-DIMENSIONAL MOTION P1ABC Reflect Have you ever gotten lost? You think you know where you’re going, so you’re moving quickly, but then you take a wrong turn or two and you slow down. Your speed changes as you become more or less confident of where you are headed. Sure, you finally get to your destination, but you travelled MUCH farther than you needed to. In general, motion refers to the change in position of an object. Distance, speed, and direction are some of the terms that can be used to describe motion. How do all of these terms relate to one another? How exactly do they allow us to describe motion?

Position, Scalars, and Vectors Before we really get into motion, we need to examine the difference between scalars vectors, and position. A vector has a magnitude (amount) and direction (for example, 30 meters north). A scalar has simply a magnitude (for example, 30 meters). We commonly use an arrow to indicate a vector. The longer or thicker the arrow is, the greater the magnitude of the vector. A vector with a magnitude of eight meters would be twice as long as a vector with a magnitude of four meters. A negative sign is indicative of “opposite direction.” For example, if “4 meters” indicates east, you may see “-4 meters” to indicate west. The position of an object is always defined relative to a reference point. The reference point is typically the origin of a coordinate system. To define the position of an object, we can draw a vector from the origin of a coordinate system to the location of the object. If the position of an object is changing with respect to a fixed reference point, an object is said to be in motion.

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STEMscopedia: ONE-DIMENSIONAL MOTION Look Out Vector quantities are typically written in bold with an arrow above the letter. Scalar quantities usually are written in some kind of italicized font. It’s important to understand the difference between the two. Distance vs. Displacement Think again of the scenario above in which you got lost. Maybe it’s only two kilometers from your house to your destination (displacement), but because you took several wrong turns, you travelled four kilometers (distance). In physics, the straight-line distance between the initial and final positions of an object is called displacement. Displacement is a vector. It is always a straight line, regardless of the actual path taken between two locations. To draw a displacement vector, simply draw an arrow from the initial position of an object to the final position. In contrast, the total distance walked through the maze from start to finish is called distance. Distance is a measure of the length of the path taken between two positions. It is a scalar quantity, meaning it does not have a direction like displacement. In some cases, the magnitude of an object’s displacement will be the same as the distance traveled. Can you think of a case where this might happen? (This will happen when an object travels in a straight line.) Finding distance is easy. Simply add up all the legs of your journey. The sum total is the distance. For displacement, we need to find the difference only between the starting and ending positions. Examine the image below.

Distance is just adding up A and B for a total of seven kilometers. In this instance, we use the Pythagorean theorem from algebra to find the total displacement of five kilometers. Because displacement is a vector, we would say five kilometers northeast.

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STEMscopedia: ONE-DIMENSIONAL MOTION What Do You Think? The image below illustrates the paths of two different students on their way to school. The dotted line shows the distance between each house and the school. The arrows show the path that each student walks. Which student walks the greater distance to school? Which student has the smaller displacement?

Average Velocity, Instantaneous Velocity, and Motion Graphs Think back again to being lost on your journey. Sometimes you were moving faster; other times you were moving slower. How would you figure out your average velocity over the entire journey? To do so, we would have to find our total displacement and divide it by our total time. If we moved a great distance in a short amount of time, our velocity is high. If we move a great distance over a great deal of time, our velocity is low. Consider a jogger running north in a straight line for 25 meters. We can plot the motion of the runner on a motion graph, which shows a property of an object’s motion over time. This motion graph is called a “distance-versus-time” graph (or simply a distance-time graph) because it shows how the distance of the jogger changes over a period of time. (Note that because the jogger runs in a straight line, the magnitude of the displacement will be the same as the distance traveled.) If we wanted to determine the jogger’s average velocity over the entire trip, we could divide the change in distance by the change in time. For example, if the jogger runs from zero meters to 25 meters in five seconds, what is her average velocity? Her final position is 25 meters, her initial position is zero meters, and the time interval is five seconds.

Notice that the average velocity is the slope of the line from t = 0 to t = 5 on the distance-time graph! This shows that the velocity of the jogger is constant over the entire period of the run. In fact, whenever the plot of a distance-time graph is a straight line, you can conclude that the velocity of the object is constant, and the magnitude of the velocity is the slope of the line.

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STEMscopedia: ONE-DIMENSIONAL MOTION Another way of describing velocity is by describing the instantaneous velocity of an object. This is the velocity of an object at an exact moment in time, not over a period of time. You can think of the calculation of instantaneous velocity as a calculation of average velocity over an extremely small time period. When the velocity of an object is constant, the average velocity is the same as the instantaneous velocity at all moments. However, in the following distance-versus-time graph, velocity is not constant.

In this case, the instantaneous velocity of the object at a particular time is equal to the slope of a tangent line at that particular time. (A tangent line touches a curve at only one point.) For example, the instantaneous velocity of the object at t = 5 s can be determined by drawing a tangent line to the curve at this point. The instantaneous velocity is the slope of this line.

Look Out Many people use the terms speed and velocity interchangeably in everyday language. However, the terms are slightly different in physics. Speed is a scalar quantity, while velocity is a vector. In other words, when describing velocity, we must always include the direction of motion. In contrast, when describing speed, we do not include direction. A car with a velocity of 35 kilometers per hour north is traveling at a speed of 35 kilometers per hour. Acceleration Acceleration is defined as any change in velocity. Since we know that velocity has two components, magnitude (which we often refer to as “speed”) and direction, then we know that whenever either of these things are changing, then an object is undergoing acceleration. Let’s restate that. Whenever an object’s speed, direction, or BOTH is changing, the object is accelerating. These cars may be going the same speed, but because they are changing direction as they round the curve, they are accelerating.

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STEMscopedia: ONE-DIMENSIONAL MOTION When you press down the accelerator pedal on a car, you cause the car to increase in speed. In this case, the acceleration vector points in the same direction that the car is moving. However, if you want to come to a stop, you press the decelerator pedal (or brake), causing the car’s speed to decrease. This is also a form of acceleration, though it is sometimes called deceleration. It means that the acceleration vector points in the direction opposite to the car’s motion. If you turn the steering wheel of a car, the car will accelerate in a different direction. In this case, the acceleration vector points in a different direction than the car is moving, causing the direction of the car to change. In either case, it is important to note that whenever an object accelerates, its velocity or direction (or both) changes. To calculate the magnitude of acceleration:

Kinematic Equations We use position, velocity, time, and acceleration to describe the motion of objects, and to calculate these, we use what are known as the kinematic equations. These equations are only used when the acceleration is constant. This table illustrates which value each variable stands for: Term Initial position xi Final position xf Initial velocity vi Final velocity vf Acceleration a Time interval t

Corresponding Variable

The kinematic equations relating these variables are shown below: To calculate the final position of an object: To calculate the final velocity of an object: To calculate the final or initial velocity of an object or the time interval: The kinematic equations apply only when the acceleration of the object is constant.

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STEMscopedia: ONE-DIMENSIONAL MOTION Look Out If you ever see the term “at rest,” this means the magnitude is ZERO. For instance, if an object starts at rest, its initial velocity is zero. If it “comes to a stop” or “ends at rest,” its final velocity is zero.

What Do You Know? Examine the graph below: Use the graph to answer these questions:

1. What is the displacement of the ladybug at t = 10 seconds? 2. During which time interval is the velocity of the ladybug –1 centimeters per second? (Include the entire time interval in your answer.)

3. A ladybug is moving at a speed of one centimeter per second. She begins to decelerate at a rate of –0.25 centimeters per second squared until she comes to rest. How much distance does the ladybug cover from the moment she begins to decelerate until the moment she comes to rest? (HINT: This is a two-part problem. First, use an equation to determine the time. Then plug this value into another equation to determine distance.) 14

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STEMscopedia: ONE-DIMENSIONAL MOTION Connecting With Your Child Connecting Distance, Time, and Average Speed To help students apply the concepts of distance, time, and average speed, challenge students to design their own investigation to measure the average speed of various toy cars. To set each car in motion, students can construct a ramp using books and a wooden board or cardboard. They can place each toy car at the top of the ramp and release it from rest. (If the cars are wind-up cars, this step is unnecessary.) Students will need to define the distance over which they will observe a car’s motion. For example, they may observe the distance the car travels from the bottom of the ramp to a marked area on the floor. Students should also determine how they will measure this distance (e.g., a meter stick or tape measure). Additionally, students must determine how they will measure the time interval of each car (e.g., a stopwatch or a timer app on a mobile phone). Students should construct a table in which they will record data. After data have been collected for each car, students should calculate and compare the average speed of each car.

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Here are some questions to discuss with your child: • How will you define the distance the cars travel? how can you measure it? • What is the time interval over which the cars move? How can you measure it? • How can you calculate average speed using distance and time? • What factors must be held constant in this investigation? • Which car had the greatest velocity? • Why do you think this was the case?

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P1ABC One Dimensional Motion

Reading Science Name:

Date:

Group:

Physics of Car Crashes 1

What do a car crash, a typhoon, and a new medicine have in common? Computer simulation can be used to analyze each of these. Cars are required to undergo safety testing before being sold. Many manufacturers stress the crashworthiness of their vehicles in consumer advertisements. Automotive engineers are involved in every aspect of car design. They have to design cars that are economical, attractive, convenient, and safe. Many colleges have automotive engineering programs. Often these programs are part of or associated with the mechanical engineering program. Graduates of these programs have to understand many aspects of automobile design and function. For example, they have to understand the manufacturing process and the characteristics of different materials, as well as consumer preferences. When working to design for safety, they also have to understand basic physics.

The simplest collision to analyze is a head-on collision between a car with a driver and a stationary concrete wall. The characteristics of the driver include instantaneous velocity and mass. If the driver is wearing a rigid seatbelt, the distance in which the driver stops depends on deformation of the car’s hood and the passenger compartment. A common distance is 1 m. An equation relates the average force on the driver (Favg ) to the stopping distance (d), mass (m), and instantaneous velocity (v):

Favg*d = -0.5*m*v2 3

Stopping distance is the distance the driver travels before coming to rest. Force is inversely related to stopping distance. If stopping distance is increased, the force experienced by the driver will decrease. Engineers cannot control the instantaneous velocity or the mass of the driver, only the stopping distance.

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P1ABC One Dimensional Motion

Reading Science 4

Stiffness is used to quantify the resistance of a structure to deformation. Deformation of the hood in front of the passenger compartment absorbs some of the energy of the impact. This decreases the velocity of the driver. Deformation also lengthens the stopping distance a driver travels before hitting the wall. Both decrease the force on the driver. Crumpling of the hood is therefore desirable. Deformation of the passenger compartment also absorbs energy, but too much deformation can injure the driver. If the dashboard ends up embedded in the front seat, there’s no room left for the driver! The proper amount of stiffness of both the hood and passenger compartment improves a driver’s chances of surviving an accident.

Computer simulations allow engineers to test the crash performance of cars without using actual cars. The inputs to the model include the structural geometry of the parts and the basic material properties. For example, windshield glass has different material properties than automotive steel and plastic. Mathematical techniques divide the car into more than one million small units. Each unit is connected to its neighbors through nodes. Forces are then applied. The spatial position of each unit is analyzed as a function of time. The most important output of a simulation is the forces experienced by the occupants of the car. Based on human biology, survivable limits for force have been established. For example, the force to a person’s chest cannot exceed a certain value; otherwise, the person’s rib cage will collapse, and the person is likely to die.

One way to simulate this modeling process is to take a sheet of graph paper and use it to wrap a small box. Use glue to attach the paper tightly to the box. Each square of the graph paper would be one unit, while the line intersections on the paper are the nodes. Use your hand to partly crush the box without tearing the paper. Notice how the relative position of the squares has changed where the box is crushed. Your simulation provides the time points at the beginning and the end. A computer simulation is analyzed with many steps to account for the motion of car parts and occupants during the crash.

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P1ABC One Dimensional Motion

Reading Science 1.

Automotive engineering programs at college ______________.

are frequently associated with mechanical engineering programs

don't require an understanding of math and physics

interact only with the business school

are only available in Michigan

Pam is driving a car, and Dave is riding in the front passenger seat. Both are wearing seatbelts. Pam crashes head-on into a concrete barrier driving 50 kph. Assuming that Dave’s mass is 1.5 times that of Pam’s, which statement below describes the force experienced by Dave?

Dave experiences 3 times the force that Pam experiences.

Dave experiences 1.5 times the force that Pam experiences.

Dave experiences the same amount of force as Pam.

Dave experiences half the force that Pam experiences.

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P1ABC One Dimensional Motion

Reading Science 3.

Bill is driving a very old car with a hood designed to be rigid in a crash. Linda is driving a new car with a hood designed to crumple in a crash. Both have the same mass, and both are wearing seatbelts. In a head-on collision at the same speed with a stationary wall, which driver will experience greater force?

Both will experience the same force.

Linda will experience the greater force.

Bill will experience the greater force.

It cannot be determined from the information provided.

Deformation of the hood in a head-on collision ______________. A.

increases the mass of the car and the force on the occupants

decreases the mass of the car and decreases the force on the occupants

decreases the stopping distance and increases the force on the occupants

increases the stopping distance and decreases the force on the occupants

Using a box covered with graph paper allows a student to simulate which aspect of a car crash?

The impact on occupants

The stiffness of car materials

The computer modeling

The kinematic equations

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P1ABC One Dimensional Motion

Math Connections Name:

Date:

Group:

One-dimensional motion happens along only one axis, either vertical or horizontal. It can be described using both scalar and vector quantities. Scalar quantities are described by a magnitude alone, such as speed (calculated by dividing distance traveled by time). Vector quantities require both a magnitude and a direction. Match the terms below with the graphs that follow. Beside each graph, describe a real-world situation that exemplifies that graph’s behavior. 1. Deceleration 2. Acceleration 3. Constant velocity Real world example:

Real world example:

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P1ABC One Dimensional Motion

Math Connections 4. Find the average speed of a horse that ran 140 meters in 20 seconds. (Use the formula v = d / t, where v is the velocity, d is the distance, and t is the time.)

5. A runner sprints for 20 minutes at an average pace of 7 mph. What is the distance traveled? (Use the formula v = d / t, where v is the velocity, d is the distance, and t is the time.)

6. What is the acceleration of a speedboat that goes from idle (rest) to 10 m/s in 9 seconds? (Use the formula a = V / t, where a is the acceleration, V is the change in velocity, and t is the time.)

7. Mrs. Garcia is conducting an egg-dropping experiment with her physics class from the second story of the high school. She wants to know the speed of each egg in free-fall before it hits the ground. The acceleration due to gravity is 9.8 m/s 2.

a. Chris drops his egg, and it hits the ground in 3.5 seconds. What is the egg’s speed before it hits the ground? (Use the formula Vf = Vi + at, where Vi is the initial velocity, a is the acceleration, and t is the time.) b. From how high up did Chris drop his egg? (Use the formula d = ½ gt 2, where d is the distance in meters, g is the surface gravity, and t is the time in seconds.)

8. Dale Earnhart Jr., a famous race-car driver, drives at a speed of 20 m/s on the racetrack for 3 hours. How far did he travel?

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P1ABC One Dimensional Motion

Math Connections 9. Chrissy was twirling her pencil and accidently dropped it from a height of 0.8 m. a. How much time is Chrissy allotted to grab her pencil before it hits the tile floor? (Use the formula d = ½ gt 2, where d is the distance in meters, g is the surface gravity, and t is the time in seconds, and solve for t. The acceleration due to gravity, g, is 9.8 m/s2.) b. How fast is the pencil traveling before it hits the floor? (Use the formula Vf = Vi + at, where Vi is the initial velocity, a is the acceleration, and t is the time. Round your answer to the nearest tenth.) 10. Rickie is traveling down the road at 65 mph (28.9 m/s) and comes to a complete stop in 5 seconds. a. What is the deceleration of the car? (Use the formula a = V / t, where a is the acceleration, V is the change in velocity, and t is the time.) b. How far did Rickie go after hitting the break? (Use the formula d = ½ at 2, where d is distance in meters, a is acceleration, and t is time in seconds.)

c. Graph the problem.

d. What is the slope of the graph? e. What is the y-intercept of the graph? f. Write the equation of the graph. g. What is the domain (x-values) and the range (y-values) of the graph?

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P1ABC One-Dimensional Motion

WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK Motion can be described using graphs. Graphs and charts are common scientific tools. To interpret a graph, read the axis labels and the numbers on the axis. The title should suggest the purpose of the graph. Next, examine and describe the content on the graph, such as the quantities on the x-axis and y-axis and any changes that seem to be occurring (an increase, decrease, etc.). For example, the graph above could be described as follows: As time increases from 0 to 8 seconds, the velocity of Billy increases linearly from 0 to about 14 m/s. The one-dimensional motion of a car trip can be described using several different graphs. A velocity-time graph can indicate both acceleration and displacement. Acceleration is shown by the slope of the graph, displacement by the area. In the example above, Billy and Crystal both took a short car trip along a road heading straight west from their house. They recorded their velocity every second. After they got home, each of them added their data to the graph above. WRITE Compare and constrast Billy’s and Crystals trip using physics vocabulary. Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar. © Accelerate Learning Inc. - All Rights Reserved

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P1ABC One-Dimensional Motion

WRITING SCIENCE

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High School Physics

P1D

Two-Dimensional Motion

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P1D Two-Dimensional Motion

Student Handout Name:

Date:

Directions: Conduct the Engage activity; then discuss and answer the questions below. 1.

Identify the two objects involved in this activity.

Are the motions of these objects the same? If not, how are the motions different? Comment on both the speed and direction of the motions.

If you combined the two motions observed in this activity into the motion of a single object, how would you describe the motion of that object?

What safety measures did you take while conducting the activity?

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P1D Two-Dimensional Motion

Student Journal Name:

Date:

Group:

Background 1.

How does two-dimensional motion differ from one-dimensional motion?

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P1D Two-Dimensional Motion

Student Journal Part I 1.

My question of inquiry:

_______________________________________________________________________________ _______________________________________________________________________________ 2.

Develop a hypothesis on what you will discover during this investigation.

Make a prediction about the outcome of your experiment.

Tools and equipment:

Safety precautions:

Independent variable (variable you will manipulate):

Dependent variable (variable you won’t manipulate):

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Student Journal

P1D Two-Dimensional Motion

Part I, continued 8.

Is there a control for this investigation? If so, what is it?

Procedure: List the steps of your procedure. Use additional paper if needed.

_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________.

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P1D Two-Dimensional Motion

Student Journal Part II Data Collection and Results 1.

On a separate sheet of paper, create a data table to collect your results for multiple trials.

What purpose does starting the marble at different heights serve?

_______________________________________________________________________________ _______________________________________________________________________________ 3.

Which starting height produced the largest range?

_______________________________________________________________________________ _______________________________________________________________________________ 4.

What is the maximum distance you can get from your package?

_______________________________________________________________________________ 5.

How long did it take for the marble to get to the ground?

_______________________________________________________________________________ 6.

Was the time different for each height?

How would changing the mass of the marble affect the total distance travelled?

What is the horizontal velocity of the flying mass?

_______________________________________________________________________________ 9.

What is the vertical acceleration of the flying mass?

_______________________________________________________________________________

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Student Journal

P1D Two-Dimensional Motion

Analysis 1.

Graph your data, and then describe the motion of your pendulum mass. Use additional paper, if needed.

If you know the height from which the marble is dropped, then you can calculate the time it should take for it to hit the floor. Measure the height from the floor to the place the marble starts moving, and calculate the time it should take to get to the ground.

How does that calculated time compare to the time you measured? Would the time change for each trial? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 3.

Explain why the trajectory motion of the projectile can be broken into two components.

Is projectile motion predictable or not predictable? Explain.

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P1D Two-Dimensional Motion

Student Journal Reflections and Conclusions 1.

Did your data support your hypothesis? Explain.

_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 2. Was your prediction correct? Explain. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 3. How did the results reveal a relationship between the independent and dependent variables? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 4. Where could you have made errors while collecting or organizing data? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 5. What do you conclude about this investigation? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 6. What would you do differently if you were to conduct this experiment again? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 36

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Student Journal

P1D Two-Dimensional Motion

Reflection and Conclusions, continued 7.

Using all of the following terms, develop a graphic organizer.

Terms: acceleration, average velocity, displacement, instantaneous velocity, projectile motion, gravity, horizontal component, vertical component

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STEMscopedia: TWO-DIMENSIONAL MOTION P1D Reflect Think about the different ways that a soccer ball might move in a game. When the ball is on the ground, a player kicks it in a straight-line path to another player. As you have already learned, this is an example of one-dimensional motion because the ball moves only in a straight line in the horizontal direction. However, sometimes a player will punt the ball or throw it into the air. When this happens, the ball will follow a curved path through the air as it rises up and then falls back to the ground. This is an example of two-dimensional motion because the ball moves in both horizontal and vertical directions. What are some other examples of two-dimensional motion? How can we describe and analyze two-dimensional motion? Everyday Life: Gravity and Free-Fall An important aspect of two-dimensional motion is the vertical motion Force: a push or a pull on of objects through the air. All vertical motion is subject to the force of an object gravity. On Earth, gravity is a force that pulls all objects toward the center of the Earth. The effects of gravity can be seen in nearly every aspect of the world around us. Gravity causes us to fall back to Earth when we jump. (If there were no gravity, we would ﬂy off into space!) In fact, gravity causes every object to accelerate down toward Earth whenever it is thrown upward or released into the air. Whenever an object travels through the air and experiences only the force of gravity, the object is said to be in free-fall. Objects moving straight down experience one dimensional, vertical, motion. An apple falling from a tree and the teacup and saucer in this photograph are examples of objects in one dimensional free-fall. (As objects fall through the air, they encounter resistance from the particles that make up Earth’s atmosphere. In these cases, however, we neglect the force of air resistance that might act on falling objects.) The acceleration of an object due to gravity, represented by g, is approximately constant throughout all regions on Earth. The value of g is approximately equal to 9.8 m/s2. The force of gravity, and thus the acceleration due to gravity, always acts downward in the vertical direction; it never acts in the horizontal direction. Projectile Motion If an object experiences free-fall in the vertical direction and it also moves in the horizontal direction, it is exhibiting projectile motion. That is, projectile motion is the motion of an object in two dimensions that occurs when gravity is the only force on the object. Any object that travels in the vertical and horizontal direction through the air (and experiences only the force of gravity)

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STEMscopedia: TWO-DIMENSIONAL MOTION undergoes projectile motion. An object undergoing projectile motion is called a projectile, and its path takes the shape of a parabola, as shown in the diagram at right. This path is called the trajectory. The motion of the soccer ball described earlier is an example of projectile motion. Other examples of projectile motion include water shooting in a curved path from a fountain, a rock thrown off a cliff into a canyon, and a pole-vaulter leaping over a bar. The vertical displacement of a projectile is called the maximum height of the projectile. The maximum horizontal displacement of the projectile is called the range. During projectile motion, we say that the object experiences accelerated motion in the vertical direction. It slows while moving upward and is in free fall as it comes down. However, it experiences unaccelerated motion in the horizontal direction. That is, it travels at constant speed in the horizontal direction.

Velocity: The speed of an object in some direction. Acceleration: The change in either the speed or direction of an object.

Analyzing Projectile Motion in Two Dimensions When analyzing projectile motion in two dimensions, we can separate the motion of the projectile into two components: the vertical component of motion and the the horizontal component of motion. For example, if a projectile has a velocity v at any moment as it moves through the air, it can be thought of as having a velocity vx that points in the horizontal direction and a velocity vy that points in the vertical direction.

At left: A projectile traveling through the air has velocity v. The horizontal component of this velocity is vx, and the vertical component of this velocity is vy. At right: An airplane drops a piece of cargo as it travels to the right across the sky. The horizontal and vertical components of its velocity are shown as the cargo falls.

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STEMscopedia: TWO-DIMENSIONAL MOTION The vertical and horizontal components of the projectile’s motion are independent of each other. So when we describe and analyze projectile motion, we can analyze the horizontal and vertical components separately and apply the kinematic equations just as we did when analyzing onedimensional motion. To illustrate this concept, consider a cannon that shoots a cannonball horizontally off the edge of a cliff, as shown below. As it travels along a parabolic trajectory, the cannonball exhibits projectile motion because the only force acting on it is gravity. Now we can analyze the motion of the projectile in terms of its horizontal motion and vertical motion. A cannonball is shot horizontally from a cliff. Its motion can be separated into horizontal and vertical components. In the horizontal direction, the cannonball travels as though it were traveling in a straight line to the right at constant speed. In the vertical direction, the cannonball travels as though it were dropped straight down from rest. Because gravity accelerates the cannonball, its speed increases in the vertical direction.

In the horizontal direction, the cannonball is thrown with an initial speed vx. Because it experiences no acceleration in this direction, the cannonball travels at constant speed vx for the entire journey in the horizontal direction. In this direction, the cannonball moves as if it were traveling at a constant speed in a straight line to the right. In the diagram, the horizontal velocity arrows are the same length for the entire journey. In the vertical direction, the cannonball has no initial speed because it was thrown in the horizontal direction. However, because gravity accelerates the cannonball downward, the speed of the cannonball in the vertical direction, vy, increases as it falls. In this direction, the cannonball moves as if it had been dropped from rest at the top of the cliff. In the diagram, the vertical velocity arrows increase as the cannonball drops.

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STEMscopedia: TWO-DIMENSIONAL MOTION Solving Projectile Motion Problems In general, you can solve for any quantity of projectile motion by separating the motion into vertical and horizontal components and then applying the kinematic equations in that direction. Remember: • There is zero acceleration in the horizontal direction. • Acceleration due to gravity (g) equals 9.8 m/s2 and acts in the vertical direction. The following diagram reviews the components you will need to solve each kinematic equation. A cannonball is shot horizontally from a cliff. What are the vertical and horizontal components of the cannonball’s motion? (In the following, x refers to horizontal motion and y refers to vertical motion.) • xi , yi : the cannonball’s initial position • xf , yf : the cannonball’s final position • vix , viy : the cannonball’s initial velocity • vf x , vf y : the cannonball’s final velocity Note the vertical component of the cannonball’s initial velocity (vi y) equals 0. Horizontal Kinematic Equations To calculate the final position (xf) of a projectile x, you need to know the projectile’s initial position (xi) and its constant velocity (vx), and the time of motion (t ): xf = xi + vx t Remember that initial velocity in the horizontal direction equals final velocity! Vertical Kinematic Equations To calculate the final position (yf) of a projectile y, you need to know the projectile’s initial position (yi) and initial velocity (vi y), and the time of motion (t ): yf = yi + viy t − 1 gt 2 2

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STEMscopedia: TWO-DIMENSIONAL MOTION To calculate the ﬁnal velocity (vfy) of a projectile y, you can use either of these equations, depending on the information you know: v 2f y = v 2iy – 2g(yf – yi ) vf y + vi y – gt To calculate the ﬁnal or initial velocity of a projectile over a time interval, use this equation: yf – yi =

(v +2 v )t fy

Combining Components To determine the magnitude of the displacement (s) or velocity (v) of a projectile at any point in its motion, you can recombine the components using the Pythagorean Theorem, as shown in these equations: S = √x 2 + y 2

Displacement: the straight-line distance between an object’s initial and final positions

√

2 2 V = vx + vy

Look Out Two pencils are held at the same height above the ground. Pencil A is dropped from rest. Pencil B is thrown horizontally with an initial speed vx. If both pencils are released at the same time, which pencil will strike the ground ﬁrst? Circular Motion Another form of two-dimensional motion is circular motion, which occurs when an object travels around a circular path. A special case of circular motion is uniform circular motion. An object moving with uniform circular motion travels around a circular path at a constant speed. A Ferris wheel, a merry-go- round, and the rotating hands on an analog watch are examples of circular motion. Some objects exhibit uniform circular motion even if they do not travel in a full circle. For example, when a car enters a curved exit ramp, it may travel around a portion of a circular path, but it still undergoes circular motion during that time.

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STEMscopedia: TWO-DIMENSIONAL MOTION We can calculate the average speed, v, of an object traveling in uniform circular motion around a circle of radius r. To do this, recall that the average speed of an object in one- dimensional motion is equal to the total distance traveled divided by the total time of the journey: v = distance time When an object travels around a circular path, the total distance that it travels in one complete loop is equal to the circumference of the circle. The equation for the circumference, C, of a circle of radius r is as follows: C = 2πr = distance We can deﬁne the time it takes for an object to complete one full loop around the circle as T, which is also called the period of the motion. We can plug these variables into the equation for average speed to determine the equation for average speed in uniform circular motion: v = distance = 2πr time T Although the object moves with constant speed, its direction is constantly changing. Thus, the object is accelerating. The acceleration of an object in uniform circular motion is called centripetal acceleration. This vector points inward, toward the center of the circle. The magnitude of centripetal acceleration, ac, can be calculated using the following equation: 2 ac = v r

The velocity vector of an object exhibiting uniform circular motion always points tangent to the path of the motion. The centripetal acceleration vector always points inward, toward the center of the circle, as shown in this diagram:

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STEMscopedia: TWO-DIMENSIONAL MOTION Look Out cceleration in two-dimensional motion has the same meaning as in one-dimensional motion. If A an object is accelerating in two dimensions, we can conclude that its velocity is changing, either in magnitude, direction, or both. However, the acceleration of objects undergoing projectile motion or uniform circular motion can be described with some general rules. • In projectile motion, an object always accelerates in the vertical direction, but it never accelerates in the horizontal direction. • In uniform circular motion, an object constantly experiences centripetal acceleration that keeps the object moving in a circle. In other words, the direction of the object is constantly changing as it moves. Be careful! While the speed of an object in uniform circular motion is constant, its velocity is constantly changing because it is always changing direction. What Do You Know? Write your answers in the spaces next to each question. 1.

A ball rolls off of a tall shelf with a horizontal speed of 2 m/s. The shelf is 4.9 m high. How long will it take for the ball to strike the ground?

A yo-yo hangs from a string of length 0.25 m. A person holds the free end of the string and swings the yo-yo around in a circle. It makes one rotation every 0.50 s. What is the average speed of the yo-yo?

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STEMscopedia: TWO-DIMENSIONAL MOTION Connecting With Your Child Modeling Centripetal Acceleration Many children have trouble understanding the concept of centripetal acceleration in circular motion. In particular, they have trouble understanding that centripetal acceleration points inward, toward the center of the circle around which the object is moving. Your child can observe a real-world demonstration of centripetal acceleration by constructing a simple accelerometer. An accelerometer is a device that indicates the direction in which an object is accelerating. To construct an accelerometer, your child will need an empty plastic bottle, string, a cork, a thumbtack, and water. (A wide bottle, such as a 2-liter bottle, is ideal.) Your child will attach one end of the string to the cork using the thumbtack. He or she will then fill the bottle with water and lower the string and cork assembly into the bottle. The cork should hang down freely, not touching the bottom of the bottle. To secure the string assembly, have your child tighten the lid of the bottle over the string so that the free end of the string is “fastened” tightly to the lid of the bottle. To model centripetal acceleration, have your child invert the bottle so that the cork floats vertically. Then your child can hold the bottle tightly in one hand and extend his or her arm. He or she should then begin to spin in a circle and observe what happens to the cork in the bottle. (If it is too difficult for your child to observe this while spinning, you can spin with the bottle and have your child observe the cork.) The

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cork should lean inward, toward the center of the circle, while you spin. This demonstrates that the cork experiences an inwardly pointing acceleration. Allow your child to observe how the cork changes as you spin the bottle more quickly or slowly. Allow your child to observe how the cork changes when you move the bottle inward, toward your body, as you spin. Here are some questions to discuss with your child: • What happens to the cork as the bottle moves in a circle? Why do you think this happens? • Which equation describes centripetal acceleration? What is the radius of the circular motion in this model? • How might the tilt of the cork change if you were to spin more quickly? How would it change if you spun more slowly? • How might the tilt of the cork change if you were to pull the bottle inward, toward your body, as you spin? • Based on this investigation, do you think a race car driver experiences a greater acceleration when he or she travels around a tight turn (with a small radius) or a wide turn (with a large radius)?

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P1D Two Dimensional Motion

Math Connections Name:

Date:

Group:

Two-dimensional motion can be described using two separate components. The two separate motions are in horizontal and vertical directions, respectively. Projectile motion is two-dimensional because it has a horizontal component and a vertical component. The following terms and equations will be used to answer questions throughout this worksheet: Variables r = length of vector a = acceleration F = force m = mass Vx − dir = horizontal direction Vy − dir = vertical direction Vi = initial velocity g = −9.8 m/s2

Formulas Vx − dir = r (cos θ) Vy − dir = r (sin θ) F = ma Dx = Vxt y = Vy i t + (½)gt2 y = ½ gt2, when Vy i = 0

1. Velocities moving against each other cancel each other out. What is the velocity of an airplane that flies at 500 mph and then encounters a 50 mph headwind (wind going against the direction of the plane)?

2. Velocities moving in the same direction are summative. Using the scenario above, calculate the plane’s speed with a 50 mph tailwind (wind going with the direction of the plane).

3. A right triangle has sides measuring 5 and 12 inches. If the two vectors have a magnitude of 5 and 12 and are at right angles to each other, then what is their resultant? Use the Pythagorean theorem to calculate the resultant.

4. Given that a 17-unit vector makes a 38° angle, find the magnitude of the horizontal and vertical components. Round to three decimal places. (Hint: use Vx − dir and Vy − dir formulas.)

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P1D Two Dimensional Motion

Math Connections 5. Given the data below, what would be the centripetal acceleration of the object, given a centripetal force of 12 N? (Hint: look for a constant mass, and use F = ma.) Force (N)

Acceleration (m/s2)

0.13

0.26

0.52

0.78

6. An astronaut on the Moon jumps 12 feet vertically off the ground. Acceleration due to gravity on the moon is 5.25 ft/s2. How long is the astronaut off the ground? Use the formula y = ½ gt2. Draw a diagram to represent the problem. Round your answer to the nearest hundredth.

7. In the scenario above, the astronaut is now traveling horizontally on a skateboard. Would the hang time be more, less, or the same as if the astronaut just jumped in the air?

8. A ball is rolled off a table that measures 1 meter in height. The ball travels at an initial velocity of 2.25 m/s. With these measurements, determine the range of the ball. Round your answer to the nearest hundredth. (Hint: solve for t in y = ½ gt2, then use dx = Vxt.)

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P1D Two Dimensional Motion

Math Connections 9. A cannonball is shot out of a cannon that is at a 50° angle off the ground. The ball travels at a velocity of 100 m/s. Find the following: a. Vx − dir (round to the nearest ten-thousandth) b. Vy − dir (round to the nearest ten-thousandth) c. Write an equation to find the height of the cannonball at any time during its flight. (Hint: you are looking for y, the vertical component.)

d. Draw a graphical representation of this scenario. What type of graph does this represent? Label the graph as you answer the following questions.

e. In how much time does the cannonball rise to its maximum height? Round your answer to the nearest tenth. (Hint: V = Vyi + gt, where V = ?.) f. What is the maximum height to which the cannonball rises? Round your answer to the nearest tenth. (Hint: y = Vyit + ½ gt 2, and plug in the above answer for t.) g. How high is the cannonball in the air at t = 5.2 seconds? Round your answer to the nearest tenth.

h. Determine the domain and range of the graphical representation. Why is there a restriction? Solve algebraically, and use the graphing calculator to check your answer. (Hint: To determine the range, factor the original equation and solve for t.)

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P1D Two-Dimensional Motion

WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK In projectile motion, the only force acting upon the object is gravity. Many real-world situations can be described using projectile motion. One such situation is air drops. Air drops are often used in extreme circumstances. For example, during the winter months, landing airplanes at McMurdo Research Station in Antarctica is impossible. The extremely low temperatures turn normally liquid hydraulic fluids into sludge. This impairs aircraft-handling. Fierce winds are another concern on many winter days. Because of these conditions, when McMurdo has to be resupplied, air drops may be used. For the prompt below, assume there is no wind and the air resistance of the box is negligible. WRITE Describe how to determine where the box will land. Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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P1D Two-Dimensional Motion

WRITING SCIENCE

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High School Physics

P2AB

Newton’s Laws of Motion

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P2AB Newton’s Laws of Motion

Student Handout Name:

Date:

Physics Magic Draw a diagram of the setup of the cup, playing card, and coin.

Describe what happened to the coin when you flicked the card.

Explain why this happened.

A magician can pull the tablecloth out from under a fully set table without disturbing any of the dishes or silverware. How does this connect with the coin?

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P2AB Newton’s Laws of Motion

Student Journal Name:

Date:

Group:

Part I: Understanding Forces and Motion 1.

Draw your first free-body diagram below.

Are the forces balanced or unbalanced as shown on the free-body diagram?

Describe what happened in this experiment.

Explain what happened using the terms balanced force and unbalanced force.

Draw your second free-body diagram below.

Are the forces balanced or unbalanced as shown in the free-body diagram?

Describe what happened in this experiment.

Explain what happened using the terms balanced force and unbalanced force.

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P2AB Newton’s Laws of Motion

Student Journal Part II: Understanding Forces and Motion 1.

Draw your third free-body diagram below.

Are the forces balanced or unbalanced as shown on the free-body diagram?

Describe what happened in this experiment.

Explain what happened using the terms balanced force and unbalanced force.

Draw your fourth and fifth free-body diagrams below.

What changed experimentally from the first and second experiments?

What effect did this have on the behavior of the sliding block?

Explain what happened using the terms balanced force, unbalanced force, and inertia.

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P2AB Newton’s Laws of Motion

Student Journal Reflection Questions 1.

What were the most important things to remember when drawing the free-body force diagrams?

How do you determine whether an object will accelerate (remember that beginning motion is a type of acceleration)?

How can force diagrams be used to determine motion? Explain.

What are the characteristics of a system with an unbalanced force?

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P2AB Newton’s Laws of Motion

Student Journal Part III: Calculating Force 1. A 0.55 kg block is being pulled by a 2.5 N force east across a horizontal frictionless surface. What is the acceleration of the block? Free-body diagram:

List of variables:

Show your work:

2. A 3.2 kg pail of water is being lifted in a well with a constant force of 45 N. What is the acceleration of the pail? Free-body diagram:

List of variables:

Show your work:

3. A 55 kg box is pushed from opposite sides on a frictionless surface. A 320 N force is applied from the right and a 180 N force from the left side. What is the acceleration of the box? Free-body diagram:

List of variables:

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Show your work:

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P2AB Newton’s Laws of Motion

Student Journal Practice Force Calculations 1.

A 1500 kg car is moving 18 m/s. How much force is required to bring the car to a stop in 12 seconds?

A mover is pushing on a very large box with a force of 850 N, but he can’t get it to move. What force is the box exerting on the mover?

A 60 kg teenager is standing on a skateboard. What force does the skateboard exert on the teenager?

A 3.5 kg mass has an initial velocity of 4.0 m/s. How much force is required to increase the velocity of the mass to 8.0 m/s in 3.0 seconds?

Reflection Questions 1.

What is the difference between Newton’s first, second, and third laws?

When a force is applied to a 10-kg block compared to a 100-kg block, would the two blocks experience the same acceleration? Why or why not?

Why does an object experience acceleration when there is an unbalanced force but not when the forces are balanced?

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STEMscopedia: NEWTON’S LAWS OF MOTION P2AB Reflect Have you ever helped someone move furniture and noticed that some pieces are harder to push across the floor than others? Did you notice that it seemed to take a lot of force to start the piece of furniture moving from a rest position, but that once it began moving, it took less force? Inertia Inertia is a property of all matter. When an object is resting, it seems to want to continue resting, or not moving, so when you want to make it move, you must apply a force that is strong enough to overcome the object’s inertia. Think of moving a heavy piece of furniture. You push, but it won’t budge. You keep pushing harder until it begins to slide. Once it begins moving, you don’t have to push quite as hard to keep it moving across the floor. What happened to the resistance you first experienced? This example of inertia can be explained by Newton’s first law of motion, often called the law of inertia. It states that an object at rest tends to stay at rest, and an object moving in a straight line at a constant speed will continue to do so, unless acted on by an outside force. In the case of the furniture, you applied the external force to it until it began to move. In other words, you overcame its inertia, which was keeping it from moving. Now that it is moving, its inertia keeps it moving at a constant speed in a straight path until other external forces act on it. Newton’s Second Law If you want to change the direction it is moving, you will have to add an external force toward the direction you want it to move. When you apply a force to the object and it changes direction or speed, you have caused it to accelerate. The relationship between force, mass, and acceleration is known as Newton’s second law of motion. It is represented by the equation F= ma, where F is force, m is mass, and a is acceleration. Think again of the example of moving a piece of furniture. If you need to turn it through a doorway, you will have to apply a force that will cause it to change direction, which is a form of acceleration. Likewise, if you apply more force by pushing harder, it might move faster, which is another way it can accelerate. Recall that acceleration is a change in velocity. The acceleration can be calculated if you know the amount of force acting on an object, as well as the object’s mass. You can manipulate the equation, F=ma, to solve for acceleration, a=F/m.

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The mass of the soccer ball will remain constant, so when the girl kicks the ball, it will accelerate. The harder the ball is kicked, the faster it will move.

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STEMscopedia: NEWTON’S LAWS OF MOTION Practice Problems: 1.

A soccer player kicked a 0.43 kilogram stationary soccer ball with enough force to cause it to accelerate at 10 m/s2. What force was applied to the ball?

Given: m= 0.43kg a= 10 m/s2 F=? 2.

Two volleyball players hit the ball at the same time as it comes over the net. One player hits the ball with 10 newtons of force, and the other player hits the ball in the same direction with 12 newtons of force. The mass of the volleyball is 0.5 kilograms. What is the acceleration of the ball?

Given: m= 0.5 kg F= 10N + 12N = 22N a=? 3.

You are pushing a door with 22 newtons of force. Your friend is on the other side of the door, pushing with the same force in the opposite direction. The door has a mass of 50 kilograms. What will be the acceleration of the door, and in what direction will it move?

Given: m= 50 kg F= 22N - 22N= 0 N a=? There would be no acceleration; therefore, the door will not change speed or direction.

Look Out There are many types of forces that can act on objects, and most objects have many forces acting on them at the same time. The sum of all the forces acting on an object is the net force. When you do calculations with forces, you should consider all the forces acting on an object. In Practice Problem #2, you had two forces acting on the volleyball in the same direction. You had to add them to get the net force. If forces are acting in opposite directions, as in Practice Problem #3, subtract them to get the net force.

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STEMscopedia: NEWTON’S LAWS OF MOTION Table 1 shows some of the forces that can act on objects. Type of Symbol Description Force Force caused by an object or person Applied Fapp pushing or pulling another object or Force person. Force caused by the attraction of obGravity Fgrav jects with mass; pulls objects toward (Weight) the center of the masses. Force caused by surfaces rubbing or Friction Ffrict sliding across one another. Force perpendicular to a surface on Normal Fnorm which another object is pushing. Force Force in a string, rope, or wire when it Tension Ftens is pulled at both ends. Force applied by a stretched or comSpring Fspring pressed spring to an object to which it is attached. Force applied to any object moving Air ResisFair through air. tance

Needs to Contact Object to Apply Force Yes

Yes Yes Yes Yes

Yes

Free Body Diagrams In physics it is often helpful to sketch a diagram showing all the forces acting on an object. A free body diagram, or FBD, shows the relative magnitudes and directions of all the forces acting on an object. FBDs can also be referred to as force diagrams. A free body diagram shows all the forces acting on an object in a given situation, represented by arrows indicating their magnitudes and directions. The size of the arrow represents the magnitude of the force acting on the object and the direction of the arrow represents the direction of the applied force.

N E

W S This free body diagram has four forces acting on it. Which way is it accelerating?

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STEMscopedia: NEWTON’S LAWS OF MOTION A free body diagram whose forces are balanced does not accelerate. It is in equilibrium. Recall that acceleration occurs when an object changes its speed or direction. Think about a book sitting on a table. If its forces are all balanced, it is not accelerating. What do you think a free body diagram representing this book would look like?

Fnorm The free body diagram on the right represents the picture on the left.

Fgrav What Do You Know? Try these problems using F=ma: 1. A golfer hits a 0.046 kilogram golf ball with a force of 47 newtons. What will its acceleration be? 2. A 17 kilogram toddler tries to run from his mother with a force of 80 newtons. She is pulling the toddler back toward her with a force of 90 newtons. How much will the toddler accelerate, and will he move toward or away from his mother? 3. A 0.43 kilogram football was punted so that its acceleration was 12.9 m/s2. What force did the kicker apply to the ball? 4. A watermelon rolls off the picnic table and hits the ground with a force of 147 newtons. It accelerates at a rate of 9.8 m/s2. What is the mass of the watermelon? Newton’s Third Law Have you ever been in a boat and tried to step out of the boat onto a pier? Did the boat move away from the pier when your foot pushed down? If so, it’s because of Newton’s third law: For every action (force), there is an equal and opposite reaction (force). When your foot pushed on the pier you were applying a force (your weight), to the pier. The pier pushed back on your foot with an equal and opposite force, causing the boat to move backward due to the lack of friction between the boat and the water. Most of the time you don’t notice the reaction forces like you do in the boat because of the friction between your feet and the ground. For example, if you pushed on a tree trunk, the tree would push back on you with an equal and opposite force. It’s likely neither of you would move because the tree is anchored by its roots and there is friction between your shoes and the ground. 70

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STEMscopedia: NEWTON’S LAWS OF MOTION Look Out Newton’s third law applies to pairs of objects acting on each other. See Table 2 below: Action Force Reaction Force Object Pair Your hand lifts an apple The apple pushes down Hand and apple (up). on your hand. The rocket pushes gases. The gases push back on Rocket and gases the rocket. A book pushes down on a The table pushes up on Book and table table. the book.

The dog is pulling on the leash, and the human is pulling back on the leash. Is this an example of Newton’s third law? Why or why not?

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STEMscopedia: NEWTON’S LAWS OF MOTION Connecting With Your Child Help your child find an example of each of Newton’s three laws of motion in your home or neighborhood. For each example: write a brief description of the example and how it fits the law; draw a free body diagram and label all the forces; and classify the net force on each example as in equilibrium (balanced) or in non-equilibrium (unbalanced). Newton’s First Law Example

Description

Free Body Diagram

Forces in equilibrium or non-equilibrium

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STEMscopedia: NEWTON’S LAWS OF MOTION Newton’s Second Law Example

Description

Free Body Diagram

Forces in equilibrium or non-equilibrium Newton’s Third Law Example

Description

Free Body Diagram

Forces in equilibrium or non-equilibrium

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P2AB Newton's Laws of Motion

Reading Science Name:

Date:

Group:

The History of the Law of Inertia 1

Newton’s first law—the law of inertia—states that objects do not change their motion unless acted uponby a net force. An object at rest will remain at rest. A moving object will remain in motion with constant motion unless acted upon by a net force. The concept of “net force” is crucial. Both a book lying on a table and a bowling ball rolling along an ideal surface in a vacuum have forces acting upon them. However, the net force acting upon the book is 0, so it remains at rest. The net force acting upon the bowling ball is also 0, so it remains in motion. Any acceleration, or change in motion, means that a net force is acting on the object. These aspects of motion were not always appreciated.

Aristotle was the first person in recorded history who addressed objects in motion. Born in 384 BC, he wrote extensively on subjects such as politics, metaphysics, ethics, logic, and science. One of his ideas was that constant force had to be applied to keep an object moving. As soon as the force was removed, the object would slow down and come to rest. Although he proposed using detailed observation to arrive at scientific conclusions, his observations in physics were much less thorough than those in biology. Nonetheless, Aristotle's idea of motion was accepted and largely unchallenged for more than 1,000 years: until Galileo.

Galileo Galilei was an Italian scientist, mathematician, and philosopher living from 1564 to 1642. He is most famous for his discoveries in astronomy, such as building telescopes and discovering the moons of Jupiter. However, he also contributed to the laws of motion. Galileo introduced the idea of a frictional force, a force that affects objects in motion and slows them down. This contradicts Aristotle’s idea that an object remains in motion only as long as a force is applied. Galileo died the year Isaac Newton was born.

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P2AB Newton's Laws of Motion

Reading Science 4

Isaac Newton was born in England in 1642. His childhood was affected by the death of his father and the remarriage of his mother when he was three. His mother’s new husband had no interest in young Isaac, and so he was left to the care of his grandmother. After her second husband’s death, Isaac’s mother was reunited with her son, but his feelings of abandonment may have contributed to his anger throughout his life. Isaac lived to work and never married. Some scholars have suggested that he had Asperger’s syndrome, others that he was simply a brilliant, socially awkward man.

In 1686–1687, Isaac Newton published his Mathematical Principles of Natural Philosophy. He answered the questions surrounding moving objects using three laws. The law of inertia was the first law he proposed. His second law states that acceleration depends on two things: the object’s mass and the force acting upon it. The third law states that for every action there is an equal and opposite reaction. Newton formalized the description of motion and recognized that these three laws together are sufficient to explain and predict the motion of objects.

Newtonian mechanics apply to objects in our everyday experience: from cars to planets. However, different laws govern objects that are either very small or moving very fast. The motions of atoms and subatomic particles cannot be explained using Newton’s laws. Quantum mechanics can be used to more accurately predict their behavior. Objects moving near the speed of light require special relativity to describe their motion.

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P2AB Newton's Laws of Motion

Reading Science 1.

Newton’s first law states that objects do not change their motion unless acted upon by a net force. What does the word “net” mean in this context? A.

A woven net, such as a fishing net or basketball net

To catch or ensnare

Remaining or left over after everything has been accounted for

To cover, such as with mosquito netting

In Aristotle’s time, many people used ox-drawn carts. When the ox stops moving, the cart also stops moving. According to Aristotle, what caused the ox cart to stop moving? A.

The friction of the ground acting on the ox cart

The lack of force applied to the ox cart

The gravitational attraction between the ox cart and Earth

The force of the ox cart on the ox

What was Galileo’s contribution to the laws of motion? A.

He introduced the concept of frictional force.

He built telescopes that could detect motion.

He taught Newton at the university.

He lived in the same country as Newton.

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P2AB Newton's Laws of Motion

Reading Science 4.

Isaac Newton grew up – A.

in a happy household with brothers and sisters.

cared for by his grandmother after his mother’s remarriage.

mostly in the Italian countryside.

surrounded by many friends and acquaintances.

How can Newton’s laws be used when addressing the motion of objects? A.

Only to explain

Only to predict

Both to explain and predict

Both to observe and predict

Newton’s laws do not predict the motion of all objects. The motion of which of the objects below does not obey Newton’s laws? A.

A car sliding on ice

Jupiter’s moons

A pendulum swinging

The electrons in a hydrogen atom

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P2AB Newton's Laws of Motion

Math Connections Name:

Date:

Group:

When forces act on an object, a free-body diagram can be used to show the magnitude of those forces and the direction in which they are going. In drawing a free-body diagram, each force is labeled, and the length of the arrow indicates the magnitude of the force. Given the following scenarios, draw a free-body diagram of each scenario, labeling the forces and their directions. 1.

A bowling ball being dropped off the Empire State Building:

A person jumping out of a plane:

A leftward force is used to push a pencil across a desk with leftward acceleration. Friction acts on the pencil, but air resistance does not.

A baby is hanging in a swing suspended from a door frame. The swing is not moving. Draw the forces acting on the baby and the door frame.

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P2AB Newton's Laws of Motion

Math Connections Use the following information to answer questions 5–8. Newton’s second law of motion states that when a force acts on an object, it will cause the object to accelerate. The larger the mass of the object, the greater the force will need to be to cause that object to accelerate. Newton’s second law of motion can be calculated using this formula: Force (F) = Mass (m) × Acceleration (a) Acceleration due to gravity (g) = 9.8 m/s2 5.

If mass is calculated in kg and acceleration is calculated in m/s2, what would the units for force be measured in? This unit is also known as a Newton (N).

Jack uses a pick-up truck to drive to work. He was in a hurry this morning, forgot to fill up the tank, and ran out of gas. If the truck weighs 1,632 kg, and he is able to accelerate the car to go 0.07 m/s2 by pushing it, how much net force is he exerting on the car?

If a tenpin bowling ball weighing 3,630 g is accelerating down the bowling lane at a rate of 4 m/s2, what is the net force applied to the bowling ball?

In Alamogordo, New Mexico, falling rock is a hazard along US Highway 82. If a rock falls from a cliff with 157 N of force, what is the mass of the rock?

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P2AB Newton's Laws of Motion

Math Connections Use the following data to answer questions 9–11. The Guidry Motor Company is testing the effects of an increased payload on acceleration of its newest model truck. The company loaded the truck with increasing amounts of mass and tested the amount of force it takes to achieve an acceleration of 6.10 m/s2. The results are below. 9.

Calculate the amount of force exerted on the truck as the mass increases. Input your calculations into the table below. Mass (kg) 2,800 2,850 2,900 2,950 3,000

Acceleration (m/s2) 6.10 6.10 6.10 6.10 6.10

Force (N)

10. Create a graph below, charting the mass vs. net force exerted on the truck to achieve an acceleration of 6.10 m/s2.

11. What is the relationship of the mass on the net force?

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P2AB Newton’s Laws of Motion

WRITING SCIENCE Name:

Date:

Group:

LOOK

Image courtesy of NASA

THINK Gravity is a non-contact force acting over great distances. The International Space Station (ISS) continues to orbit Earth. Astronauts live on the ISS for months at a time. A feature of living inside the ISS is the experience of weightlessness. On Earth, amusement rides can provide brief periods of weightlessness. Many amusement parks have a free-fall tower attraction. Riders are strapped in place and ride to the top of a tall, vertical tower. They then drop for a distance. During the drop, the only force acting on them is gravity. Astronauts experience weightlessness their entire time aboard the ISS. Working, eating, sleeping, and using the bathroom all become challenging for them. NASA has designed many tools to make astronauts’ everyday tasks easier. WRITE Using a description of the free-body diagram for an astronaut aboard the ISS, explain why astronauts experience weightlessness. Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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P2AB Newton’s Laws of Motion

WRITING SCIENCE

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High School Physics

P2C

Calculating Components of Forces

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P2C Calculating Components of Forces

Student Handout Name:

Date:

Attach the spring scale to the block. Drag the block across the desk a distance of 0.5 m. Write down the largest reading once the block starts moving on the spring scale below.

Attach the spring scale to the block. Set the block at one end of the ramp. Drag the block up the ramp a distance of 0.5 m. Write down the largest reading once the block starts moving on the spring scale below.

Attach the spring scale to the block. Pick the block up until it is 0.5 m above the ground. Write down the reading on the spring scale below.

Which situation (horizontal, inclined, or vertical) took the most force to move the block?

Create an explanation for the results of your experimentation.

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P2C Calculating Components of Forces

Student Journal Name:

Date:

Group:

If a person weighs 95 kg sitting in a chair, what are the gravitational force and the normal force acting on the person?

If the chair has a coefficient of static friction of 0.35, what is the friction force present between the person and the chair?

Your teacher will give you a block with a hook in it and a spring scale. Using the balance, determine the mass of the block. Calculate the gravitational force and the normal force for the block as it rests on the table.

Hook the spring scale onto the block of wood and rest the assembling on the board when the board is flat. Slowly pull on the spring scale horizontally until the block just begins to slide. Record the force measured on the spring scale below. This is your friction force. Using your answer from question 3, determine the coefficient of static friction.

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P2C Calculating Components of Forces

Student Journal 5.

Take the string and tie it to the hook on the block. Grasping the string firmly, lift the block about 0.5 m above the surface. Being careful to not move the block once it is in the air, estimate the acceleration on the block.

Using your answers from questions 3 and 5, calculate the tension in the string.

Untie the string and reattach the spring scale. Without lifting or applying any force to the scale, note the location of the indicator on the scale. Lift the block until it just begins to no longer touch the table or desk. Measure how much the scale’s indicator has moved from its resting state with the metric ruler. Write the distance below in meters.

Assuming that the spring force is equal but opposite to the block’s gravitational force, calculate the spring constant for the spring inside the spring scale. Use your answers from questions 3 and 7 in your calculation.

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STEMscopedia: CALCULATING COMPNENTS OF FORCE P2C

Reflect What forces are acting on you at this moment? This is not a question we often ask ourselves. Perhaps this is because only a few types of forces exist in nature, and we have become so familiar with their effects that we rarely think about them. For example, a force that is always acting on you is gravity. This attractive force—which exists between all things with mass in the universe—is what pulls you toward Earth’s surface and keeps you from floating off into space. As we will see, gravity is usually accompanied by an equal and opposite force. The force of gravity also pulls Earth and the Sun toward each other, as well as Earth and the Moon, Mars, and all the other planets in the solar system. (Each of these bodies also has its own momentum, which balances the force of gravity. If it were not for momentum, gravity would cause these bodies to crash into each other, and if it were not for gravity, momentum would cause these bodies to fly apart. Instead, Earth and the planets orbit the Sun, and the Sun revolves around the center of the Milky Way galaxy.) Although you don’t feel it, gravity even attracts you to your computer, your chair, the people in the room around you, and everything else that has mass. Why don’t you feel these other gravitational forces? The force of gravity on you from Earth has a much greater strength, so you do not notice the other pulls.

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STEMscopedia: CALCULATING COMPNENTS OF FORCE

Two objects with mass exert a gravitational pull on each other. The force on one of the objects in the pair has the same magnitude, or strength, as the force on the other object, but it points in the opposite direction. The force on the first object points toward the second object. The force on the second object points toward the first object. Both objects feel the same magnitude of force. This fact means that Earth feels the same magnitude of gravitational force toward you as you do toward Earth! The equation for gravitational force is: F = Gm1m2 r2 In this equation, the gravitational force (F) is equal to the product of the two masses (m1 and m2). It is inversely proportional to the square of the distance (r) between the objects. Gravitational force is measured in units called newtons (N). A newton equals 1 kg∙m/s2. For example, suppose a system contains two 50 gram masses (m1 and m2) separated by a distance (r) of 5 meters. We can plug these numbers into Newton’s equation to determine the gravitational force (F) on the system. (For the moment, we can ignore G.) F = G(50g)(50g) = G(2500g) = G(100g/m2) (5m)2 25m2 Now, suppose you doubled one mass (m1 = 100 g). What is the new gravitational force on the system? F = G(100g)(50g) = G(5000g) = G(200g/m2) (5m)2 25m2 Therefore, doubling m1 doubles F. Mass and gravitational force are directly proportional. What happens if you double the distance in the original system (r = 10 m)? F = G(50g)(50g) = G(2500g) = G(25g/m2) 100m2 (10m)2 Therefore, F is four times smaller when r is two times larger. Distance and gravitational force are inversely proportional. Gravitational Constant What is G? G is a universal constant called the gravitational constant. It is approximately equal to 6.67 × 10–11 m3∙kg–1∙s–2. The force of gravity between any two objects in the universe depends on the same G.

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STEMscopedia: CALCULATING COMPNENTS OF FORCE

We can calculate the force of gravity between two objects if we know their masses and the distance between them. For instance, Earth has a mass of about 6.0 × 1024 kilograms, and the Moon has a mass of about 7.3 × 1022 kilograms. The distance between the centers of Earth and the Moon is about 3.8 × 108 meters. These numbers give a force of gravity between Earth and the Moon equal to about 2.0 × 1020 newtons.

Look Out Other common forces are friction, tension, spring force, and mechanical force. How could you draw a diagram showing the effects of all the forces acting on an object such as this penny? Take a moment to try, then read on.

Because forces are vectors, they can be represented by arrows. A scalar quantity, such as speed, has only magnitude. A vector quantity has both magnitude and direction. We can use vector quantities to describe properties such as velocity, acceleration, and force. A force vector is represented by an arrow that points in the direction in which the force is acting. The length of the arrow is proportional to the magnitude of the force. In other words, a longer arrow represents a stronger force, and a shorter arrow represents a weaker force. If two arrows are of equal length, they represent forces of equal magnitude. When describing objects on Earth, the vector arrow for gravity always points toward the planet’s center (down in most diagrams) because that is the direction in which gravity acts. The magnitude of the vector representing gravity is equal to the object’s weight.

This force-body diagram shows four equal forces acting on the box. (Because the forces are equal, the arrows are the same length.) Notice that the force of gravity (Fgravity) is countered by an equal and opposite force (Fnormal); you will learn about this force in the next section.

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STEMscopedia: CALCULATING COMPNENTS OF FORCE

Friction is a force that always acts in the opposite direction of movement. Friction occurs when two surfaces are in contact, such as the bottom of a person’s shoes walking on the ground. The amount of friction between two surfaces depends on the material of the surfaces and the amount of force pressing them together. Smooth surfaces, such as an ice rink or wood floors, have less friction than rough surfaces, such as sandpaper or cement. Also, surfaces that have less force pressing them together have less friction; surfaces that have more force pressing them together have more friction. The diagram above shows a man pushing a box at a constant velocity across a flat surface. You can represent the force of the man’s push (in this case, 50 newtons) with a horizontal vector arrow pointing in the direction of the push. The force of friction resisting the man’s push is represented by a vector of equal length pointing in the opposite direction (in this case, –50 newtons). Things can get more complicated for forces acting at angles and in different directions. Techniques of vector addition must be applied to find the net, or overall, force. Force vectors can be combined to determine the net force. Forces acting along the same straight line—that is, in one dimension—can be added and subtracted arithmetically. For the diagram on the previous page, the forces pushing and pulling on the box are equal and of opposite sign, so the net force is zero: 50 N + (–50 N) = 0 N. The term for such a diagram is free body diagram. A free body diagram shows objects in equilibrium, or a steady state. In contrast, this diagram shows a car accelerating as it leaves a stop sign.

The five arrows represent five forces acting on the car. The downward-pointing arrow is the force of gravity, and the upward-pointing arrow is the normal force the highway exerts on the car. (The normal force is equivalent to the force of gravity.) The two arrows pointing to the left represent friction and air resistance. The arrow pointing to the right is the forward force the tires exert on the pavement. Note the forward-pointing arrow is longer than the friction and air resistance arrows combined. This means there is a net forward force pushing the car away from the stop sign. (This makes sense because the car is accelerating.) Subtracting the total backward force from the forward force gives a net forward force that can be represented by a forward-pointing arrow equal to the difference, as shown in the box above the car.

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STEMscopedia: CALCULATING COMPNENTS OF FORCE

If the forces are not at right angles, finding the net force is more complicated. The child on the swing in this photograph is acted on by two forces: the tension on the ropes (FT) and the force of gravity (FG). The swing is an example of pendulum motion. It moves back and forth around an equilibrium point at the bottom of its path. When the swing is not at equilibrium, a force is acting to restore it to equilibrium. This is the net force, also called the resultant force (FR). The diagram at right shows all three forces.

You can calculate FR by adding FT and FG. To do this, you must rearrange the vector arrows to form a triangle, as shown in the diagram at right. If we know the values of FT and FG, we can find FR by using trigonometric functions. Another type of force is spring force. To describe the potential energy of a mass on a spring, note that a spring will remain at rest in an equilibrium state unless it is stretched or compressed by another force. The amount of force required to stretch or compress the mass on the spring is related to the stiffness of the spring. This is described by a variable called the spring constant, k. If a spring is very difficult to stretch or compress, k is high. Conversely, if a spring is easy to stretch or compress, k is low. The spring constant is a measured property of a spring. Whenever you stretch or compress a spring away from the equilibrium position, the spring gains some elastic potential energy. A spring scale is an example of a system consisting of a mass on a spring. Without the mass, the spring will hang at an equilibrium position. When the mass is attached, the force of gravity stretches the spring, giving the system elastic potential energy. The equation for force on a spring is: F = -kx, where k is again the spring constant (depending on the spring) and x is the distance the spring has stretched from its original position.

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STEMscopedia: CALCULATING COMPNENTS OF FORCE

Look Out The force of gravity reaches everywhere, even space. You may have seen videos of astronauts floating in the International Space Station. Do these videos show the lack of gravity? No. In fact, the force of gravity keeps the astronauts in orbit around Earth. Without gravity, the space station would fly off into the universe. The astronauts appear to float because they are actually falling toward Earth’s surface, due to gravity. The space station is falling at the same rate, though, so the astronauts appear to float above the floor. If the space station is falling toward Earth, why doesn’t it crash on the planet’s surface? As gravity pulls the space station toward Earth, the space station is also moving in a circle around Earth. This forward momentum around Earth keeps the space station from colliding with Earth, while gravity keeps the space station from flying off into space. Both forces work together to keep the space station in continual orbit around our planet.

What Do You Think? In this equation, F is force, m is mass, and a is acceleration. (The equation is often written F = ma.) Consider again the car and the girl on the swing, and use the formula to determine what would happen if the forces were unchanged but the masses were changed. If the car were more massive, it would accelerate at a slower rate. If the girl were a more massive adult, you would have to redraw the vector diagram because the force of gravity would be greater. Consider again the car and the girl on the swing in the previous diagrams. What would happen if you replaced the car with a more massive car or the girl with a larger adult? Assuming force remains constant, how would these changes in mass affect acceleration? You can check your answer below.

What Do You Know? Remember, the force formula states that acceleration and mass are inversely proportional. Therefore, when mass increases, acceleration decreases if force remains constant. A more massive car or a larger adult would accelerate at a slower rate, assuming the same amount of force is applied to them. Now let’s look at gravitational force. Earlier, the gravitational force constant was ignored. Let’s now calculate an equation with the gravitational constant. A system consists of two masses, m1 and m2, separated by a distance r: • m1 = 4.00 kilograms • m2 = 3.00 kilograms • r = 2.00 meters

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STEMscopedia: CALCULATING COMPNENTS OF FORCE

What is the gravitational force, in newtons, between these masses? (Remember: G is approximately equal to 6.67 × 10–11 m3 • kg–1•s–2.)

What happens when parts of this system change as described in the following table? Predict how each system change described below will affect the gravitational force between m1 and m2. (Will F increase, decrease, or remain constant?) Then plug the new values into Newton’s equation and check your predictions. It may help to sketch the initial system before making your calculations.

How does the system change?

How does the force of gravity (F) change (increases, decreases, or remains constant)?

m1 is halved m2 doubles r triples r is halved

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STEMscopedia: CALCULATING COMPNENTS OF FORCE

Connecting With Your Child Studying the Effects of Force and Mass on Acceleration This will be a qualitative study of motion, as represented by the equation: F = ma. (Remember, F is force, m is mass, and a is acceleration.) For this experiment, you will need two meter sticks or yardsticks and several objects of various masses in the range of 20 to 200 grams. Stones and pebbles will work. Rest one of the meter sticks at its exact center on an object about three or four centimeters high. Place one of the stones on one end of the meter stick and drop another stone on the other end, which will catapult the first stone into the air. Each time you do this, drop the stone from the same height and measure how high the other stone rises. Try catapulting stones of different masses with the same dropped stone, and try catapulting the same stone with dropped stones of different masses. Make sure nobody is standing in front of the catapult before dropping a stone. To explain your results, rearrange the equation to this form: a = F/m Acceleration (a) is the acceleration of the catapulted stone, which accelerates from the time the dropped stone hit the meter stick until it became airborne. The greater the catapulted stone’s acceleration, the greater its initial velocity and the greater the height it will reach. Therefore, you can compare acceleration under different conditions by comparing height. The mass of the dropped stone determines the force (F). Dropping more massive stones should send the catapulted stone higher. Mass (m) is the mass of the catapulted stone. Less massive stones should rise higher when catapulted (per Newton’s second law). Here are some questions to discuss with your child: 1.

If objects in motion at constant velocity tend to stay in motion, why do all moving objects on the surface of Earth eventually come to a stop?

If an arrow is used to represent a force, what two properties of the force does the arrow indicate?

A boy throws a 0.2 kilogram ball five meters into the air. How high could he throw a 0.4 kilogram ball if he exerted twice as much force?

A boy standing motionless on ice skates throws a large snowball, which causes him to move backward. Which law of motion explains why he moved backward?

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P2C Calculating Components of Forces

Reading Science Name:

Date:

Group:

Comparing Rocket and Airplane Vectors 1

Both rockets designed for space flight and airplanes designed for atmospheric flight respond to external forces that have magnitude and direction and are expressed as vectors. Recall that vectors are not scalar quantities because they have both magnitude and direction. Vectors involved in airplane and rocket flight are made up of component vectors in two dimensions: a horizontal component and vertical component. The combination of vectors in flight are complex. For example, look at the NASA diagram of rocket forces showing the four vector forces that affect flight: gravity (weight), thrust, lift, and drag.

Gravity (weight): Weight is the amount of gravitational force exerted by Earth’s planetary mass on objects. The magnitude of the weight vector depends on the mass of all the rocket parts. The direction of the weight vector is toward Earth’s center.

Thrust: The direction of the thrust force in a simple rocket is along the longitudinal axis of the rocket and acts through the center of gravity. More advanced rockets have a gimbal action, where their nozzles can produce a force at an angle different than their center of gravity. The magnitude of the thrust depends on the rate of flow of engine fuel and the velocity and pressure with which it leaves the nozzle.

Lift and drag: Lift is the force perpendicular to motion, and drag is caused by friction from air resistance. The magnitude of the lift and drag forces depend on rocket size, shape, and velocity in relation to the condition of the atmosphere. The direction of lift and drag are through the pressure center of the rocket, but that is not as important in boosters that only last a short time. Lift and drag only apply within the atmosphere, not in outer space.

During a flight trajectory, the vectors can change in magnitude and often change in direction. The addition of component vectors (horizontal and vertical) are complex. A simple flight of a model rocket that goes up and then comes down does not have the same complexity as the forces working on rocket that has a booster stage, goes into orbit around Earth, and then is set on a flight path to orbit the Moon or another planet.

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Reading Science 6

The same four forces that affect rocket flight work on an airplane, but there are major differences. With rockets, thrust is used to overcome weight; however, with airplanes, lift force is used to overcome the weight. Lift can be used on rockets to control flight direction. On an airplane, lift and drag are created by the wings and the tail. For a rocket, those same forces are created by the fins, nose cone, and body. Also, many airplanes have a high lift-to-drag ratio, unlike rockets, which often have greater drag than lift and therefore need a powerful propulsion system.

Additionally, the power supplies that provide the lift and thrust are different. Airplanes are powered by engines that burn fuel by combining oxygen from the atmosphere and the fuel in a combustion engine. Conversely, rockets bring tanks of oxygen aboard for combustion. This means that rockets have a self-contained combustion system of fuel and oxygen tanks. Airplanes have fuel on board, and they must take in oxygen from the atmosphere to operate their combustion engines.

For example, the famous Apollo program that sent astronauts to the Moon in the 1960s was powered by massive Saturn V rockets that had a lift-off thrust of about 8 million pounds at lift-off, with each rocket engine burning 3 tons of fuel each second. Another major difference between rocket and airplane vectors is constancy. The magnitude and direction of forces acting on an airplane are usually constant, but those same forces acting on a rocket change significantly with the flight.

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Reading Science 1.

Why are vectors not considered scalar quantities? A.

Scalar quantities have direction, while vectors have both magnitude and direction.

Scalar quantities have magnitude, while vectors just have direction.

Scalar quantities have direction and magnitude, while vectors have only magnitude.

Scalar quantities have magnitude, while vectors have both magnitude and direction.

Which vector’s magnitude is the mass of all the rocket parts and whose direction is toward Earth’s center?

Weight (gravity)

Thrust

Drag

Lift

Which two vectors’ magnitudes depend on the rocket’s size, shape, and velocity in relation to the atmosphere? A.

Weight and thrust

Weight and drag

Lift and drag

Thrust and lift

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Reading Science 4.

With rockets, unlike airplanes, which of the following forces overcomes weight? A.

Thrust

Lift

Drag

Gravity

Which of the following statements is true regarding the difference between airplane and rocket combustion that provides the power to move. A.

Rockets are self contained with oxygen and fuel aboard.

Airplanes are self contained with oxygen and fuel aboard.

Rocket only carry fuel.

None of these are correct.

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P2C Calculating Components of Forces

Math Connections Name:

Date:

Group:

Gravitational force is one of the four fundamental forces of nature. It always involves attraction between two bodies, and it acts between all particles of matter. The gravitational force of one object on a second one acts in the opposite direction and is equal to the force exerted by the second object on the first one. The gravitational force between two objects can be calculated: It is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The surface gravity, g, on a planet can be calculated using the formula: • • •

G = gravity = 6.673 x 10-11 m = mass in kg r = radius in m

N*m2 kg2

Gm , where r2

Characteristics of Solar System Objects Solar System Object

Mass (kg)

Radius (m)

Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune Pluto (dwarf planet)

3.30 x 1023 4.87 x 1024 5.97 x 1024 7.35 x 1022 6.42 x 1023 1.90 x 1027 5.69 x 1026 8.66 x 1025 1.03 x 1026 1.31 x 1022

2,440,000 6,051,000 1,738,000 3,397,000 71,492,000 25,559,000 24,764,000 1,160,000

Surface Gravity (m/s2) 3.70 9.79 1.62

10.45 8.84 0.65

Use the table above to answer the following problems. Insert your answers into the spaces in the table. 1.

Calculate the surface gravity on the following planets: a. Venus

b. Jupiter

c. Neptune

d. Mars

Calculate the radius of the following planets: a. Earth

b. Saturn

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Math Connections 3.

Use the table on page 1 to answer the following problems: a. Calculate your mass on Earth using the formula W = mg, where m is your mass in kg, and g is the surface gravity on Earth. (1 pound = 2.2 kg). b. Calculate your weight and mass on Mercury (the unit for weight is Newtons). c. Calculate your weight and mass on the Moon. d. Calculate your weight and mass on Uranus.

Calculate the surface gravity at a height of 2 Earth radii above Earth’s surface. (Note: The distance of 2 Earth radii is measured as 3 Earth radii from Earth’s center.) Gm g= r2

Review of one- and two-dimensional motion: a. How much time would it take for a brick to free-fall 50 m on Mercury? Since velocity = 0, use the following equation: d = 1/2gt2, where d is distance in meters, g is surface gravity, and t is time in seconds. 6. You can throw a baseball straight up with a velocity of 25 m/s. a. Find the baseball’s maximum height on Earth. (Hint: max height is when v0 = 0; use g = 10 m/s2.) b. Find the baseball’s maximum height on Mars. c. On which planet would the brick in question 5 travel highest? d. On which planet would that brick spend the least amount of time in the air?

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WRITING SCIENCE Name:

Date:

Group:

Look

THINK When operating a sailboat, some people have the misconception that they cannot sail upwind. If this were the case, and the direction of the wind did not change, it would be impossible to return the sailboat back to shore. However, sailors use a technique called tacking in which they angle the ship back and forth, not directly into the wind, to maneuver the boat against the wind. Suppose the water is exerting a force of 180 N eastward and the wind is exerting a force of 390 N north. The boat and the passengers have a total mass of 270 kg. WRITE Describe the forces at work, and calculate the magnitude of acceleration of the sailboat in the example provided. Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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WRITING SCIENCE

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High School Physics

P2D

Circular Motion

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P2D Circular Motion

Student Handout Name:

Date:

Circular Motion Angular Speed (rotations or degrees per time)

Object

Time

# of Revolutions

Angular Speed

Linear Speed (distance per time) 1.

A horse on a carousel is 2 m from the axis of rotation. The carousel rotates 5 times per minute. What is the linear speed in meters per second?

The outer edge of a large industrial fan blade is 1 m. The fan blades rotate 80 times per minute. What is the linear speed in meters per second?

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P2D Circular Motion

Student Journal Name:

Date:

Group:

1. 2. 3. 4. 5.

Mass of the stopper __________g ______________kg Distance from hand to stopper on string ____________ m Number of rotations in 5 s ________________ Rotations per second ___________________ Using the equation provided in your Student Guide, convert the rotations per second (rotational velocity) into meters per second (linear velocity). Show your work below.

Calculate the centripetal acceleration acting on the stopper.

Using F = ma, calculate the centripetal force acting on the stopper.

What happened to the stopper when the string was let go?

Did the stopper move in a straight line or in an arc after being let go?

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Student Journal Student Journal, continued For spinning the stopper in a vertical direction. 10. Distance from hand to stopper on string ____________ m 11. Number of rotations in 5 s ________________ 12. Rotations per second ___________________ 13. Using the equation provided in your Student Guide, convert the rotations per second (rotational velocity) into meters per second (linear velocity). Show your work below.

14. Calculate the centripetal acceleration acting on the stopper.

15. Using F = ma, calculate the centripetal force acting on the stopper.

Analysis 1.

Is the force acting on the stopper a pushing force or a pulling force?

Why did the stopper move in the direction it did on steps 8-9?

Which of Newton’s laws is at work here on steps 8-9?

Explain why centripetal motion is not a violation of Newton’s first law.

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STEMscopedia: CIRCULAR MOTION P2D

Reflect Close your eyes and imagine you are at an amusement park. Look around you at the rides. Can you see of some objects that move in circular motion? Make a mental list of them. What do they have in common? What might be different about them? Do you notice anything about the force that causes them to move in a circle?

Look Out Some objects exhibit uniform circular motion even if they do not travel in a full circle. For example, when a car enters a curved exit ramp, it may travel around a portion of a circular path, but it still undergoes circular motion during that time. Circular motion is a form of two-dimensional motion that occurs when an object travels around a circular path. A weed eater, an electron, and the rotating hands on an analog watch are examples of circular motion.

circular motion: when an object travels or rotates around the circumference of a circle

A special kind of circular motion is called uniform circular motion. An object moving with uniform circular motion travels around a circular path at a constant speed, like a ceiling fan set on high.

uniform circular motion: when an object travels or rotates around the circumference of a circle at a constant speed

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STEMscopedia: CIRCULAR MOTION What causes circular motion? Centripetal force causes circular motion. Any force can be a centripetal force if it results in an object traveling along a path that follows the circumference of a circle. For example, the force of friction can become a centripetal force if it allows a car tire to grip the surface of the road and make a circular motion. Gravity can also be a centripetal force. The Sun’s gravity keeps Earth and the other planets orbiting the Sun. gravitational force: the attractive force between any two objects with mass, which is the force that keeps celestial bodies in orbit around more massive bodies

centripetal force: a force that causes an object to travel in a circular path

A challenging concept of acceleration is understanding that acceleration occurs not only when there is a change in speed but also when there is change in direction. When an object is experiencing circular motion, it is always changing direction. Because it is constantly changing direction, that means a force must be acting on it to cause this acceleration, called centripetal acceleration. The force that is acting on the object is centripetal force. According to Isaac Newton and his laws of motion, without the presence of centripetal force, objects travel in straight lines rather than circles. How does centripetal force work? The effect a force has depends on the direction of the force compared to the object upon which it is acting. Speed can be increased or decreased depending upon the direction of the force and the original movement of the object. If an object is traveling in one direction and a force is applied in the SAME direction the object is traveling, the object’s speed will increase. If an object is moving in a specific direction and a force is applied in the OPPOSITE direction as the object is traveling, the object’s speed will decrease. How does force cause an alteration in the direction an object is moving? In the case of circular motion, when a force perpendicular to the motion of the object is applied, it results in the object altering its course from a line to a circle. However, this force needs to constantly adapt to remain perpendicular to the changing motion of the object. Centripetal force always points toward the center point of the circle. In uniform circular motion, an object constantly experiences centripetal acceleration that keeps the object moving in a circle. In other words, the direction of the object is constantly changing as it moves. Be careful! While the speed of an object in uniform circular motion is constant, its velocity is constantly changing because it is always changing direction.

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STEMscopedia: CIRCULAR MOTION If for some reason, centripetal force ceases, what happens to the object upon which the centripetal force was acting? The object stops traveling in a circle and moves off in a straight line. If the Sun suddenly disappeared, what would happen to Earth? Gravity, which in this case is acting as the centripetal force on Earth, would cease to exist. Eight minutes later (since the force of gravity travels at the speed of light), Earth would experience darkness and would move out into deep space in a straight line along the exact pathway it was traveling when centripetal force stopped acting upon it. Have you ever ridden in the passenger seat of a car, and when the car makes a left turn, you slide to the right against the door? Centripetal force is working on the vehicle by pushing it toward the center, but there seems to be a different force working on you, pushing you in the opposite direction. This force is called centrifugal force. However, it is not really a force at all. What is really happening is inertia. Inertia means that you keep moving in the same direction in a straight line, but when the car turns, it feels like you are pushed in an outward direction. Although centrifugal force is not real (because it is inertia), the effect is measurable. It feels like centrifugal force.

centrifugal force: the effect of inertia on an object that is following a circular path (an imaginary force) normal force: a perpendicular force that is exerted by one object on another object where their surfaces meet

What Do You Think? Formulas: Circumference: C = 2πr • When an object travels around a circular path, the total distance that it travels in one complete loop is equal to the circumference of the circle. The equation for the circumference, C, of a circle of radius r is equal to twice the radius multiplied by pi. It is the distance around the outside of a circle. Velocity: v = d/t • We can calculate the average speed, v, of an object traveling in uniform circular motion around a circle of radius r. Velocity is equal to the distance an object travels divided by the time it took to travel that distance. Velocity requires information of both speed and direction. Period: T = 2πr/v • We can define the time it takes for an object to complete one full loop around the circle as T, which is also called the period of the motion. Period is equal to the circumference of a circle (the product of twice the radius and pi) divided by the velocity of the moving object. Period is the amount of time required for a complete cycle to occur. In the case of circular motion, period refers to how long a revolution takes. Period is the inverse of frequency. Frequency: f = v/2πr • We can calculate how often a cycle happens in a given amount of time. In reference to circular motion, it means how many times an object rotates or revolves around another object in a certain amount of time. It is the inverse of the period, which means it is velocity divided by the circumference of the circle (the product of two radii and pi). Centripetal Acceleration: ac = v2/r

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STEMscopedia: CIRCULAR MOTION •

Centripetal acceleration is the change of speed or direction caused by centripetal force. Although an object traveling in uniform circular motion moves with constant speed, its direction is constantly changing. Thus, the object is accelerating. The acceleration of an object in uniform circular motion is called centripetal acceleration. It is measured based on the radius that is tangential (or perpendicular) to the motion. The motion is inward toward the center of the circle. The magnitude of centripetal acceleration, ac, can be calculated by finding the square of the velocity of an object divided by the radius of the circle around which it travels.

Using the above formulas, work the following problems. 1. A merry-go-round with a radius of two meters spins with a speed of three kilometer per hour. What is the period of the merry-go-round?

A yo-yo hangs from a string of length 0.25 meters. A person holds the free end of the string and swings the yo-yo around in a circle. It makes one rotation every 0.50 seconds. What is the average speed of the yo-yo?

A second hand on a clock has a radius of 10 centimeters. What is the circumference of the circle around which the second hand travels?

Pretend that Earth travels around the Sun in a perfect circle. Earth is 150,000,000 kilometers from the Sun and travels at a uniform speed of 30 kilometers per second. What is the centripetal acceleration of Earth?

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STEMscopedia: CIRCULAR MOTION What Do You Know? Another kind of circular motion is vertical circular motion. In vertical circular motion, gravity plays a big role in constantly altering the speed of an object. When an object rises, the force of gravity works against it and slows it down. Conversely, when an object falls, gravity speeds it up. Therefore, an object is at its slowest speed at the uppermost point of the circle and at its fastest speed at the bottom of the vertical circle. The force of gravity always acts in the same direction on the circle, but the force of tension differs. Have you ever tried swinging a bucket of water in a vertical circle to see if you could prevent the water from falling on you? If you swing the bucket quickly, you will probably remain dry. If you swing the bucket slowly, you might get wet. What is happening? When the bucket of water is at the bottom of the vertical circle, there is no chance of the water spilling out on you. Why? Although centripetal force is applying an upward force on the water toward the center of the circle at that point, gravity is applying a strong downward force on the water, holding it in place. When the bucket is at the top of the circle, there is a chance of the water spilling out on you. Why? Gravity and centripetal force are both acting to pull the water down out of the bucket and onto you. Since two forces are acting to pull the water out of the bucket and onto your head, what prevents it from happening? The water in the bucket is falling, but the bucket is also falling due to the centripetal force that is causing the bucket to travel in a circle. Therefore, the bucket seems to be causing centrifugal force that pushes the water back against the bottom of the bucket. In reality, it is inertia, and the centripetal force from that doesn’t allow the water to spill. Questions: • Can you think of a scenario in which the water would still spill on your head? Hint: Think about the period of vertical revolution of the bucket. • What shape will the water be at the bottom of the bucket as it is experiencing constant speed and vertical circular motion? What would happen if the speed decreased? What would happen if the speed increased? • Can you think of some other examples of vertical circular motion?

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STEMscopedia: CIRCULAR MOTION Connecting With Your Child Modeling Centripetal Acceleration Many students have trouble understanding the concept of centripetal acceleration in circular motion. In particular, they have trouble understanding that centripetal acceleration points inward, toward the center of the circle around which the object is moving. Your child can observe a real-world demonstration of centripetal acceleration by constructing a simple accelerometer. An accelerometer is a device that indicates the direction in which an object is accelerating. Materials: • Empty plastic bottle (A wide bottle, such as a two-liter bottle, is ideal.) • String • Cork • Thumbtack • Water Procedures: • Your child will attach one end of the string to the cork using the thumbtack. • Your child will then fill the bottle with water, then lower the string and cork assembly into the bottle. The cork should hang down freely, not touching the bottom of the bottle. • To secure the string assembly, have your child tighten the lid of the bottle over the string so that the free end of the string is “fastened” tightly to the lid of the bottle. • To model centripetal acceleration, have your child invert the bottle so the cork floats vertically. • Then your child can hold the bottle tightly in one hand and extend his or her arm. • He or she should then begin to spin in a circle and observe what happens to the cork in the bottle. (If it is too difficult or your child to observe this while spinning, you can spin with the bottle and have your child observe the cork.) The cork should lean inward, toward the center of the circle, while you spin. This demonstrates that the cork experiences an inwardly pointing acceleration. • Allow your child to observe how the cork changes as you spin the bottle more quickly or slowly. • Permit your child to observe how the cork changes when you move the bottle inward, toward your body, as you spin. Questions: Here are some questions to discuss with your child: • What happens to the cork as the bottle moves in a circle? Why do you think this happens? • Which equation describes centripetal acceleration? What is the radius of the circular motion in this model? • How might the tilt of the cork change if you were to spin more quickly? How would it change if you spun more slowly? • How might the tilt of the cork change if you were to pull the bottle inward, toward your body, as you spin? • Based on this investigation, do you think a race car driver experiences a greater acceleration when he or she travels around a tight turn (with a small radius) or a wide turn (with a large radius)?

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P2D CircularMotion

Reading Science Name:

Date:

Group:

Space Junk and Circular Orbits 1

When scientists at NASA plan for a spacecraft mission that involves orbiting another body, such as a satellite revolving around Earth, a moon, or another planet, they need to understand two concepts: circular motion and gravity. When you hold an object on a string and swing it around you, it stays in a circle due to centripetal force (string tension). For a satellite in orbit around Earth, that centripetal force comes from Earth’s gravity.

NASA scientists use the following formula: GMm/R2 = mv2/R R = total distance between Earth and the satellite G = gravitational constant M = mass of Earth m = mass of satellite v = speed of satellite

The scientists also use the following formula on the acceleration due to gravity or gravitational field strength (or the force per unit mass) because in orbit, gravity accelerates satellites:

F = GMm/R2 = mg’ where g’ is the gravitational field strength (orbit height)

The gravitational field strength is inversely proportional to the distance. This means there is much less gravitational field strength, as the object is farther away from the center of Earth.

For example, for a geostationary satellite: g’ = GM/R2 g’ = 0.2m -2 or (0.2Nkg-1) 5

As a satellite’s orbit increases, the acceleration due to gravity decreases. That is another reason the satellite can go a bit slower without concern for falling back to Earth.

Remember, the center of an orbit of a satellite is the center of whatever it is orbiting, such as Earth. This is also the direction of the force exerted by the larger object it orbits. According to Newton’s second law of motion, an accelerating object must experience a net force when the direction of the net force is in the same direction as the acceleration. Therefore, for an object moving in a circle, an inward force acts upon it to cause inward acceleration. This is centripetal force.

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Reading Science 7

There are close to 13,000 pieces of near-Earth orbiting objects, including existing space stations, current satellites, old satellites, pieces of debris, etc. The U.S. Space Surveillance Network tracks most of these objects but cannot track all of the smaller pieces. Because orbits of these objects have different directions, orbital planes, and speeds, collisions are highly probable. As their orbits decay, pieces of debris are overcome by centripetal force and fall to Earth. NASA is investigating methods for dealing with this orbiting debris and the risk of future impacts on Earth.

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P2D CircularMotion

Reading Science 1.

Compare centripetal force A holding an object circling around you on a string with centripetal force B keeping the Moon in orbit. A.

A is the string tension, and B is the Moon.

A is the object, and B is the Moon.

A is string tension, and B is Earth’s gravity.

A is the object, and B is Earth’s gravity.

Gravitational field strength is inversely proportional to distance between the object and the center of the body it is orbiting, which means ____________. A.

as distance increases, gravity decreases

as distance decreases, gravity decreases

as distance increases, gravity increases

as distance increases, gravity stays the same

Where does the direction of the centripetal force come from for a satellite revolving around Earth? A.

Half-way between the object and Earth

Center of Earth

Surface of Earth

Center of the Sun

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Reading Science 4.

What direction is acceleration in circular motion? A.

Outward

Inward

Linear

North

What is the problem with orbiting space junk? A.

Orbital decay and too many small ones to track

Solar radiation

Interference with airplane routes

Interference with space launches

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P2D Circular Motion

Math Connections Name:

Date:

Group:

Circular Motion Uniform circular motion describes the motion of an object traveling in a circular path at a constant speed. We can use mathematics to calculate the velocity, acceleration, and forces being exerted on the object. Calculating Velocity When an object is traveling in a linear path, we used the following formula: Velocity = Distance / Time However, if the object is moving in a circular path, we must modify the formula by substituting the circumference and period for distance and time. 1.

What is the formula for the circumference of a circle? _____________________________

What is the definition of the period of an object traveling in a circle? What variable is used to denote the period? ____________________________________________________________

Substitute the formula for circumference for distance and period for time in the formula for velocity above. Velocity of Object in Circular Path = ___________________

An object with a mass of 10 kg is traveling in a circular path with a radius of 26 m and makes one revolution per 7.425 seconds. What is the velocity of the object? _________m/s

The Skyview Atlanta is a ferris wheel that towers 20 stories over Centennial Park. The ferris wheel has a diameter of 50.6 meters and make a full circle every 1 minute 50 seconds. What is the velocity of the Skyview Atlanta? ________ m/s

Velocity is a vector quantity described by its magnitude and direction. If an object moves in a uniform circular path, will the velocity stay constant? Prove your answer. _________________ ___________________________________________________________________________ ___________________________________________________________________________

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P2D Circular Motion

Math Connections Calculating Acceleration The speed of an object traveling with a uniform circular motion has a constant speed, but the direction of its velocity vector is constantly changing. Therefore, since the velocity is changing, the object must be accelerating. When an object is traveling in a linear path, we use the following formula to calculate acceleration: Acceleration = (distance / time)2 However, if the object is moving in a circular path, we must modify the formula by substituting the circumference and period for distance and time. 7.

Substitute the formula for circumference for distance and period for time in the formula for velocity above. Simplify the equation. Acceleration of Object in Circular Path = ___________________ We can also use the following formula: Acceleration = v2/R, where v is velocity and R is radius

An object with a mass of 15 kg is traveling in a circular path with a radius of 42 m at a velocity of 29 m/s. What is the acceleration of the object? ______________m/s2

A tether ball with a mass of 0.5 kg is orbiting around a pole on a rope 2 m long. It is traveling at a velocity of 1.5 m/s when it changes direction. Calculate the acceleration of the tetherball.

10. A postman traveling on a moped at a speed of 15 m/s takes a turn around a cul-de-sac with a radius of 22 m. Calculate the acceleration acting on the postman and his moped.

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P2D Circular Motion

WRITING SCIENCE Name:

Date:

Group:

Look

THINK Newton discovered principles regarding the behavior of objects in motion. He found that an object in motion will stay in motion unless a force acts on it. That means a force is necessary for an object to follow a circular path. A merry-go-round, or carousel, remains in circular motion due to these unbalanced forces. When riding on a carousel, the people sitting closer to the center feel less dizzy than those sitting on the outermost point. WRITE Explain the difference in the force felt by riders of a carousel based on where they sit. Then, provide an example investigation and evidence for the force required to move an object in a circular motion. Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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P2D Circular Motion

WRITING SCIENCE

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High School Physics

P2E

Newton’s Universal Law of Gravitation

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P2E Newton’s Law of Universal Gravitation

Student Handout Name:

Date:

Directions: Watch the video clip of the space jump. Then discuss and answer the questions below. 1.

What evidence is there that a force was acting on Felix?

Which force do you think is responsible for Felix’s motion?

Between which two objects do you think the force exists?

If Felix jumped from an even greater distance, do you think the force on him would be different? If so, how?

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P2E Newton’s Universal Law of Gravitation

Student Journal Date:

Name:

Group:

Procedure 1.

On your computer, smartphone, or tablet, search for “PhET Gravity Force Lab” and select the first result.

Click on the play button to start the app.

Play around with moving the two masses closer and further apart and changing the mass by moving the sliders.

Click the reset button in the lower right corner.

You start the mass of object 1 at 50 kg, and then double the mass to 100, 200, 400, and 800, recording the force each time. Do not change the mass of object 2 or the distance. Record the data in your data table.

Mass 1 (kg)

Mass 2 (kg)

Distance (m)

Force (N)

Force in Scientific Notation

200

0.000000042101

4.2101 x 10-8

100

200

400

200

800

200

Graph the data above placing mass 1 on the x-axis and the force on the y-axis.

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Student Journal 7.

For the second data collection, reset the app. Leave the mass of object 1 at 50 kg and the same distance, but change the mass of object 2 to 50 kg. Record the force, then double object 2’s mass to 100, 200, 400, and 800. Record the data in your data table. Mass 1 (kg)

Mass 2 (kg)

Distance (m)

Force (N)

Force in Scientific Notation

0.000000010628

1.0628 x 10-8

100

200

400

800

Graph the data above, placing mass 2 on the x-axis and the force on the y-axis.

For the third data collection, set the mass of both object 1 and object 2 to 200 kg and keep them constant. You start the distance at 2 m, and then increase the distance to 9 m. Record the force in your data table. Mass 1 (kg)

Mass 2 (kg)

Distance (m)

Force (N)

Force in Scientific Notation

200

0.000000662402

6.663402 x 10-7

200

10. Graph the data above placing the distance on the x-axis and the force on the y-axis. 132

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Student Journal 11. Analyze your data tables and fill in your analysis in the table below. the force As I (increases, stays the same, decreases). double mass 1,

double mass 2,

double both mass 1 and mass 2,

move the masses closer together,

12. Looking at your graphs, determine a general relationship between force, mass, and distance.

Reflections and Conclusions 13. If I increase the mass of one sphere, what happens to the gravitational force, Fg?

14. If I increase the mass of both spheres, what happens to the gravitational force, Fg?

15. If I increase the distance between the spheres, what happens to the gravitational force, Fg?

16. Using all of the following terms, develop a graphic organizer. Use additional paper, if needed. Terms: gravitational force, mass, weight, radius, distance, gravitational constant

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STEMscopedia: NEWTON’S UNIVERSAL LAW OF

GRAVITATION P2E

Reflect Have you ever thought about what would happen to Earth if the Sun disappeared? For the first eight minutes and 30 seconds, no one on Earth would even know that anything had happened. Then complete darkness would cover Earth. At the same time that darkness fell, Earth would fly out of its orbit because the Sun’s gravity would no longer exist. Light travels at approximately 300,000 kilometers per second, and scientists know of nothing that can move faster than light. A gravitational wave, however, travels at that same speed. Earth would continue to travel at its current speed, which is about 30 kilometers per second in a straight line out into deep space. The same scenario would occur with the other planets in our solar system, just on separate time tables because of being various distances from the Sun. Who Was Newton? Sir Isaac Newton (1642-1726) was born in England in 1643. He attended Cambridge University during the middle of the scientific revolution. Always a brilliant mind but not an impressive student, he became a scientist and mathematician who specialized in the field of physics. Isaac Newton was one of the most influential scientists of all time. He published his great work Principia in 1687. It thoroughly covered all aspects of physics minus the topic of energy. He invented the reflecting telescope and the concept of infinitesimal calculus, discovered principles of light and color, and pondered motion and gravity. During his life, he tried to quantify natural phenomena. He formulated numerous laws, including his three laws of motion and his law of universal gravitation. •

Newton’s First Law of Motion: An object at rest will stay at rest, and an object in motion will continue in motion with the same velocity unless acted upon by an outside force.

•

Newton’s Second Law of Motion: The greater the net force on an object, the greater its acceleration will be, or acceleration is force divided by mass (a=F/m).

•

Newton’s Third Law of Motion: For every action force, there is a reactioforce equal in strength and opposite in direction.

•

Newton’s Law of Universal Gravitation: Any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. G=m1m2/2

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GRAVITATION

What Is Newton’s Law of Universal Gravitation? Newton’s law of universal gravitation states that every object in the universe attracts every other object, and that the force is affected by both mass and distance. Specifically, the greater the mass of an object, the greater the gravitational attraction (effect of mass); the closer the objects are, the greater the attraction (effect of distance). Conversely, the less the mass of the object, the weaker the gravitational attraction; the farther an object is, the weaker the gravitational attraction is as well. Considering the effect of distance on gravity, what planet would you expect to have the greatest gravitational attraction to the Sun? Which would have the weakest? Since Mercury is closest to the Sun, it would experience a strong gravitational pull, while Neptune and Uranus feel weaker gravitational attractions.

As discussed earlier, Newton did not just theorize his laws. He quantified them as well. This means Newton’s law can calculate a number value for the gravitational attraction between two celestial objects.

G=m1m2/d2

• • • •

G = gravity M1 = mass of celestial object 1 M2 = mass of celestial object 2 D = distance between the two objects

What Do You Know? Practice calculating the attractive force of two celestial objects by working the problems below. 1. Saturn has a mass of 5.68 x 1026 kilograms, while Mars has a mass of 6.39 x 1023 kilograms. Saturn and Mars are 1.2 x 109 kilometers apart. In the space below, calculate the gravity between the two planets.

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STEMscopedia: NEWTON’S UNIVERSAL LAW OF

GRAVITATION

The Sun has a mass of 1.989 x 1030 kilograms, while Neptune has a mass of 1.024 x 1026 kilograms. The Sun and Neptune are 4.503 x 109 kilometers apart. In the space below, calculate the gravity between two celestial bodies.

The Sun has a mass of 1.989 x 1030 kilograms, while Mercury has a mass of 3.30 x 1023 kilograms. The Sun and Mercury are 4.70 x 107 kilometers apart. In the box below, calculate the gravity between the two celestial bodies.

Although Newton understood the effect of gravity, he was unclear on the specifics of how gravity actually worked. He realized that gravity was a force, but he did not comprehend how the force moved from one object to another. Gravity is like a magnet in that its force comes from a field. Mass creates a gravitational field, so any object that has mass has a corresponding gravitational field. However, gravity is not a very strong force, so it takes an immense mass (like a planet) to generate a relatively strong gravitational field. In order for gravity to act on another body, two steps take place (which happen at the speed of light): 1. Mass produces a gravitational field. 2. The created gravitational field applies force on other bodies. A gravitational field exerts force on objects in all locations. Field lines in a gravitational field illustrate the direction of the force acting on objects. Look at the simplified example of Earth’s gravitational field to see how the direction of gravitational force would affect a body that entered Earth’s gravitational field.

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GRAVITATION

What Do You Think? Newton’s law of universal gravitation can be manipulated to solve for force of the gravitational field of an object. The rearranged formula is g = Gm2/r2 where • • • •

g = strength of gravitational field G = 6.67 x 10-11Nm2/kg2 is the universal gravitational constant m = mass in kg of the object r = radius of the object

Calculate the strength of the gravitational field of Venus. It has a mass of 4.867 x 1024 kilograms and a radius of 6.05 x 103 kilometers.

Calculate the strength of the gravitational field of Jupiter. It has a mass of 1.898 x 1027 kilograms and a radius of 7.1492 x 104 kilometers.

Calculate the strength of the gravitational field of a golf ball. It has a mass of 45.93 grams and a radius of 21.33 millimeters.

Do you feel the pull of gravity between yourself and the golf ball? Why?

Calculate the strength of the gravitational field of Earth. It has a mass of 5.972 x 1024 kilograms and a radius of 6.3781 x 103 kilometers.

Do you feel the pull of gravity between yourself and Earth? Why?

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STEMscopedia: NEWTON’S UNIVERSAL LAW OF

GRAVITATION

Connecting With Your Child Gravitational Calculations Complete the following exercise to help your student better understand Newton’s law of universal gravitation. First, research together the masses of the other planets (and the Sun) in our solar system and the distances between each of these and Earth.

Then use the formula below to calculate the gravitational attraction between Earth and the other celestial bodies in our solar system. G = m1m2/d2 • G=gravity • m1 = mass of celestial object 1 • m2 = mass of celestial object 2 • d = distance between the two objects Here are some questions to discuss with your student: 1. Which force acts between all celestial bodies? 2. What does Newton’s law of universal gravitation state? 3. How does distance impact gravity? 4. How does mass impact gravity?

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P2E Newtons Universal Law of Gravitation

Reading Science Name:

Date:

Group:

Measuring the Universal Gravitational Constant 1

Henry Cavendish is credited with measuring the universal gravitational constant in his experiments in 1797–1798. His original purpose was to determine the mean density of Earth. The mean density of Earth was of great interest in his time. He set up a complex apparatus. Small balls were suspended at the end of a rod. The rod was hung by a wire. Each ball was also hung by a thin wire. Larger weights were moved close to the balls. The deflection of the rod was determined once the system came to rest. The deflections Cavendish measured were in the millimeter range. A detailed account of his work is available in Scientific Memoirs IX, The Laws of Gravitation, edited by J. S. Ames. To accurately determine G, measurements had to be accurate to tenths of a millimeter. Cavendish carefully addressed several sources of error. Some of these are discussed below.

Air currents were a significant source of error. Even small air currents could move the rod and affect his measurements. A difference in air temperature leads to different air density and air currents, also known as wind. To prevent errors due to wind, Cavendish enclosed his apparatus as much as possible and placed it in an enclosed room. He knew his body heat would heat the air in the room and cause air currents. Therefore, he used telescopes to observe the rod’s deflection from outside the room. He moved the larger weights remotely, using a system of pulleys.

Cavendish observed that the deflection of the rod was a function of time in some experiments. One possible reason was the behavior of the wire suspending the rod. Therefore, he tried wires of varying stiffness. Deliberately moving the rod’s position far outside the range of deflections, he observed and measured its movement over time, which also contributed to his explanation.

Another force Cavendish knew about was magnetism. If balls acquired magnetism from Earth’s magnetic field, their attraction or repulsion could affect the rod’s deflection. Cavendish performed a series of experiments in which he rotated the balls along their vertical axes, or replaced the balls with magnets. In the end, he concluded that magnetism was not a significant source of error.

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Reading Science 6

The temperature of the balls was another concern. Metal retains heat far longer than air. The experiment could be affected if the balls were at a different temperature from the surrounding air and/or change temperature during the experiment. Cavendish drilled a hole in the balls and inserted a small thermometer that he could observe with the telescopes. Heating the balls using a lamp or cooling them using ice did affect his experiment.

None of the experiments listed above contributed directly to measuring G, but each was critical for explaining Cavendish's observations and exploring the sources of error. Scientists today still consider and address sources of error in their measurements. Frequently, additional experiments are performed to determine whether a source of error exists and what the magnitude of the effect is. Just like modern scientists, Cavendish relied on a combination of careful experimental design, meticulous documentation, knowledge of the field of science, and mathematical modeling to address sources of error. Although it is possible to measure many more quantities much more accurately than in Cavendish's time, creativity and thoroughness are still important!

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Reading Science 1.

The original goal of Cavendish's experiments was to measure the _____________.

mean density of Earth

universal gravitational constant

effect of air currents on experiments

mass of small and large balls

One procedure Cavendish used to minimize the effect of air currents was _____________. A.

standing in the room with his apparatus

enclosing his apparatus as much as possible

waiting at least three hours between measurements

running ceiling fans on low

Why did Cavendish use a telescope to observe the deflection of the rod? A.

He needed a way to magnify the rod.

He needed a way to make the rod look smaller.

He needed a way to observe the rod from a distance.

He needed a way to move the rod.

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Reading Science 4.

Magnetism was another potential source of error. The source of the magnetic field Cavendish was concerned about was _____________. A.

the enclosure around his apparatus

Earth

the metal balls and rods

the air currents

What did Cavendish discover with respect to temperature of the balls in his experiment? A.

It had no effect.

It could be a source of error.

It was better to use balls at many different temperatures.

It was better to freeze balls before using them.

Experiments exploring sources of error _____________. A.

were performed only by scientists working before 2000

are performed only by contemporary scientists

are considered unimportant with modern instruments

are important for most scientific studies

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P2E Newton’s Universal Law of Gravitation

Math Connections Name:

Date:

Group:

m1m2

In the following questions, use the formula F=G r2 . In the formula, G represents the -11 gravitational constant 6.674×10 , F is the force, m1 and m2 are the masses of the two objects and r is the distance between the two objects. Calculate the force for the following scenarios. 1)

2) 3 kg

6 kg 14 kg

_____________ kg

8 kg

16 m

_____________ kg

20 kg

2.5 kg

13 m

_____________ kg

Two trains are heading toward each other. Train A weighs 852 kg and train B weighs twice as much. At the point where the trains are 164 m apart, what is the force?

As the trains head toward each other, how does the force change if the distance between them gets smaller? Give an example.

If Train B from problem 4 weighs six times what Train A weighs, how does the force change?

If Train A from problem 4 weighs six times its current weight, how does the force change?

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Math Connections 5.

In the given equation, solve for the gravitational constant. F=G

m1m2 r2

Marie is looking at the relationship between force and mass. The gravitational constant is 6.674×10-11, the mass of object 1 is 16.5 kg and the distance between the two objects is 83.5. Create a graph to show the relationship between force and the mass of object 2. Mass 2

m1m2

In the given equation, solve for the distance between the two objects. F=G

In the given equation, solve for the mass of object 1. Would the equation be different if you were solving for the mass of object 2? F=G

m1m2

Describe the relationship between the mass of an object and the force of a system.

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Math Connections 10. Donald is looking at the relationship between force and the distance between two objects. The gravitational constant is 6.674×10-11, the mass of object 1 is 16.5 kg, and the mass of object 2 is 23.2. Create a graph to show the relationship between force and distance. r

11. Describe the relationship between the distance between two objects and the force of a system.

12. Jules is looking at the relationship between mass 1 and mass 2. The gravitational constant is 6.674×10-11, the force is 78.8, and the distance between the two objects is 83.5. Create a graph to show the relationship between mass 1 and mass 2. Mass 2 Mass 1

13. Describe the relationship between the masses of objects in a system.

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P2E Newton’s Universal Law of Gravitation

WRITING SCIENCE Name:

Date:

Group:

Look

THINK Newton’s law of gravitation states that gravitational force between objects depends upon the mass of each object and the distance between their centers. Scientists apply Newton’s law of gravitation to satellites orbiting in space. If their calculations are incorrect, satellites will fall back to Earth. Based on Newton’s findings of the relationship between mass, distance, and force, in relation to the Earth’s gravitational pull, scientists are equipped to produce enough sideways energy to keep a satellite in space from falling. Think about Newton’s law of gravitation and how its components of mass, distance, and force work together mathematically. WRITE Describe a model in which mass, distance, and force demonstrate the mathematical relationship expressed by Newton’s law of gravitation. Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar. © Accelerate Learning Inc. - All Rights Reserved

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P2E Newton’s Universal Law of Gravitation

WRITING SCIENCE

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High School Physics

P3A

Open and Closed Systems

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P3A Open and Closed Systems

Student Handout Name:

Date:

Directions: Watch the video clip of the amusement park ride. Then discuss and answer the questions below. 1.

What did you watch?

Where did the energy to power the ride come from?

What happened to the speed the riders experienced on the ride from beginning to end?

At the bottom of the hill, the ride was moving at its fastest. As the ride progressed, it slowed. When did the ride have the most energy? When did the ride have the least energy?

Did the mass of the ride change?

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Student Journal Name:

P3A Open and Closed Systems

Date:

Group:

Part I: Hot vs. Cold Your teacher has set out six different kinds of containers. Examine each of them, then answer the questions below. 1.

Which container would work best for keeping very hot water hot?

Explain your reasoning for question 1.

Which container would work best for keeping very cold water cold?

Explain your reasoning for question 2.

Were your answers for 1 and 2 the same? Why or why not?

Something is hot because of the amount of thermal energy present. A good container prevents that thermal energy from doing what?

Something is cold because of the amount of thermal energy present. A good container prevents that thermal energy from doing what?

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Student Journal

P3A Open and Closed Systems

Part II: Open vs. Closed An open system is an object that allows energy to be transferred into or out of the object. A closed system is an object that prevents energy from being transferred in or out of the object. 1.

Are any of the containers closed systems? Explain your reasoning for question 1.

Are any of the containers open systems? Explain your reasoning for question 2.

If your objective was to create a container that was a closed system for thermal energy, what criteria or properties would it have?

Reflection Questions 1.

What makes something a closed system?

What distinguishes it from an open system?

Is your home an open or closed system? List the criteria or properties to justify your answer.

Is your car’s air conditioning system an open or closed system?

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STEMscopedia: OPEN AND CLOSED

SYSTEMS P3A

Reflect Physics allows us to predict the outcomes of lots of different scenarios. For example, it is possible to describe what would happen if you were to collide with a wall while walking because you were looking at your smartphone instead of where you were going. You would need to know your mass and your velocity right before impact. Then, using conservation of momentum, you could predict how much force you would suffer as you smacked into the wall. Many physics problems depend on the fact that the scenario described is a closed system. A system is an object or objects being studied or analyzed. For example, you and the wall were the system in our example. A closed system is only possible when there are no external forces that would alter the outcome. For example, as you are walking toward the wall, what if one of your friends tried to stop you? They would be exerting a force that would reduce your forward momentum, causing the force exerted on your body by the wall from the collision to be smaller. Alternatively, one of your friends could shove you forward, increasing your velocity and thus the force you would then experience. In both of those situations, we are dealing with an open system. Because there is an external input of force from your friends, you can’t easily predict the outcome of your collision. Drag and friction are both external forces that make it much harder to get results exactly as predicted by the math.

Look Out Systems are not just limited to motion. In thermodynamics, the movement of energy into or out of a system may make the experiment open or closed. For example, the human body is an open system. Heat energy, in the form of food calories, is input into the system. This is converted into mechanical energy, allowing the human to move. An example of a closed thermodynamic system would be a bomb calorimeter, a device designed to measure how much energy is in food. The food is burned inside a metal container, surrounded by water. The water is insulated from the outside, preventing any energy from entering or leaving the calorimeter. A food sample is burned inside the calorimeter, and the heat released is absorbed by the water. A thermometer measures the temperature change. To have the highest degree of accuracy, the calorimeter must be closed. If it were an open system, heat would leak in and out of calorimeter, causing measurements and answers to be no longer correct. Thermodynamically closed systems are not just limited to measuring food calories. An insulated coffee mug is another closed system. The insulated carrier minimizing heat loss from the coffee makes this a closed system.

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STEMscopedia: OPEN AND CLOSED

SYSTEMS

Compare this with an open cup with coffee. It would cool much faster than the insulated coffee cup because it is an open system.

Reflect There is a third type of system, called an isolated system. An open system has a free exchange of matter, energy, and forces with its surroundings. A closed system prevents the exchange of one of those properties, while allowing the others to freely move. An isolated system is completely cut off from its surroundings, no matter or energy or force being exchanged into or out of the system. An open pot of water boiling on the stove is an open system. Energy is being pushed into the system by the stove, while matter escapes in the steam. Put a lid on the pot, and now the system is closed. Energy is still being pushed into the system by the stove, but matter can no longer escape due to the trapped steam. The pot with the lid is not an isolated system, however, because energy is still moving into the system. The calorimeter mentioned on the previous page is an isolated system. It is sealed, so no matter enters or leaves. All heat is absorbed by the water, and it is insulated to prevent the movement of energy in or out. The three types of systems can be summarized in this way: Open system: Matter, energy, and forces are free to move in and out. Closed system: Either matter, energy, or force is prevented from moving in and out. Isolated system: All matter, energy, and forces are prevented from moving in and out.

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STEMscopedia: OPEN AND CLOSED

SYSTEMS

What Do You Know? Classify each of the following as open, closed, or isolated systems: Open System

Closed System

Isolated System

A ball bouncing, eventually coming to a stop Vacuuming the carpet Earth Greenhouse Ice chest/cooler An ocean An aquarium Hot water heater

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STEMscopedia: OPEN AND CLOSED

SYSTEMS

Connecting With Your Child Materials needed: Thermometer Very hot water Ice water Blank sheet of paper Pencil or pen 4 Paper cups or Styrofoam cups with tight fitting lids (Note: You can get the cups and lids from a convenience store or fast food restaurant.) 1. Take the temperature of your very hot water. Record this on a blank piece of paper. 2. Carefully pour the hot water into two of the cups until each are half full. On one of the two cups, place the lid. 3. After five minutes, measure the temperature of the liquids in each cup, recording the data on your sheet of paper. 4. Wait another five minutes and then measure the temperature again, writing down the numbers on your sheet of paper. 5. Repeat steps 1-4 with the ice water and two new cups. Questions: 1. Did the lid make any difference in the temperature change? 2. Did any of the cups act as a closed system? 3. What could you and your child have done to make the system more closed?

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P3A Open and Closed Systems

Reading Science Name:

Date:

Group:

Comparing Open and Closed Systems 1

In physics, a system is defined as the portion of the universe that has been chosen for study. Systems may be complex, such as a whole planet, or simple, such as the water inside a pot. The universe outside the system is called the surroundings. A closed system is one that does not exchange matter with its surroundings and does not experience any outside forces. An open system, on the other hand, can exchange matter with its surroundings and does experience outside forces.

The idea of systems and surroundings was not always part of physics. In 1824, the French physicist Nicolas Carnot applied the idea of systems to thermodynamics. A little later, German physicist Rudolf Clausius added the idea of surroundings. Today, system and surroundings are terms applied also to mechanical systems, as well as used in other scientific fields such as biology.

Examples of open systems are common in everyday life. A car driving down a road is a system. The car engine produces exhaust, which is matter passed to its surroundings. Friction between the car and the road is an outside force that acts on the system. Closed systems are rare in everyday life. They are commonly used in physics laboratories to simplify system analysis and calculations.

So, what questions can help someone decide whether the system under consideration is open or closed? The first question to ask is: Does the system exchange matter with its surroundings? If yes, it is an open system. If no, it is a closed system. The second question is: What is the source of the forces experienced by the system? If all forces originate within the system, the system is closed. If forces act on the system from outside of the system, it is an open system.

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Reading Science 1.

A student has chosen to study a swinging pendulum. The pendulum would be ____________. A.

a system

the surroundings

a universe

a force

Which of the following statements describes a closed system? A.

It exchanges matter with its surroundings.

Its surroundings act on the system.

It experiences only forces originating from within.

None of the above

Which of the following statements about cars indicates that they are an open system? A.

Friction is present between different parts of the engine.

The car burns gasoline and produces exhaust.

The engine heats up as the car is driven.

The faster the car is driven, the faster its tires turn.

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Reading Science 4.

What is the most common use of closed systems? A.

To minimize environmental damage

To create more efficient systems

To simplify system analysis

To predict system structure and behavior

Which of the following questions is important for deciding whether a system is open or closed? A.

Does the system exchange matter with its surroundings?

Is the system composed of multiple parts?

Does the system contain more than one state of matter?

Is the system natural or man-made?

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P3A Open and Closed Systems

Math Connections Name:

Date:

Group:

Open and Closed Systems Energy is the ability to do work or produce heat. It cannot be created or destroyed, but it can be transferred and transformed. There are many types of energy, but two of the most important in physics are kinetic energy and gravitational potential energy. Kinetic energy is the energy of motion. In general, it is directly proportional to both the mass of the object moving and its velocity, but a change in velocity has a larger effect on kinetic energy than does a change in mass. The relationship between kinetic energy, mass, and velocity can be expressed mathematically with the following equation: KE=(1/2)mv2 Where: • KE is kinetic energy in joules (J) • m is mass in kilograms (kg) • v is velocity in meters per second (m/s) 1.

Find the kinetic energy for a 4.00-kg ball rolling down a hallway at 3.00 m/s.

A car driving down a street has a kinetic energy of 32,000 J. If the car has a mass of 1,600 kg, at what velocity is the car moving?

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P3A Open and Closed Systems

Math Connections Potential energy is the energy of position. It is also called stored energy. There are many types of potential energy, ranging from springs to batteries. For this problem, we will be examining gravitational potential energy. Gravitational potential energy is the energy that is stored by moving against the gravitational pull of Earth. In general, it is directly proportional to both the mass of the object and its height above a reference point (usually the ground). The relationship between gravitational potential energy, mass, and height can be expressed mathematically with the following equation: PEg=mgh Where: • PEg is potential energy in joules (J) • m is mass in kilograms (kg) • g is the gravitational acceleration of Earth (always 9.8 m/s2) • h is the height above the ground in meters (m) 3.

Find the potential energy for a 4.00-kg ball resting on a 3.5-m-tall shelf.

A car is at the top of a 112-m hill. If it has 2,200,000 J of potential energy, how massive is the car?

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P3A Open and Closed Systems

Math Connections A system is the object or phenomenon being studied. Systems come in one of three varieties. Open systems freely exchange matter and energy with their surroundings. Closed systems exchange only matter or energy with their surroundings, but not both. Isolated systems do not exchange matter or energy with their surroundings. The energy change in a system is described by the following equation: ΔE=PEg+KE Where: • ΔE is change in energy in joules (J) • PEg is potential energy in joules (J) • KE is kinetic energy in joules (J) 5.

A 1200-kg car travels into a valley that is 50.0 m above sea level at a speed of 12.0 m/s. Determine the total change in energy of the car.

A roller coaster train goes over the crest of a hill at 5.0 m/s. If the train has a mass of 1,000 kg, and the train has a total energy change of 747,500 J, what is the height of the hill?

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Math Connections Closed systems usually do not exchange energy with their surroundings. This means that any kinetic energy lost is a gain in potential energy. This relationship is described by the following equation: PEg=-KE Where: PEg is potential energy in joules (J) KE is kinetic energy in joules (J) 7.

A yo-yo begins to fall from a child’s hand. It is 1.5 meters above the ground. If the yo-yo has a mass of 0.050 kg, find the velocity of the yo-yo right before it hits the ground.

A roller coaster hits 30.0 m/s at the bottom of the hill. If the roller coaster has a mass of 1000.0 kg, how high will it travel up the hill?

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P3A Open and Closed Systems

WRITING SCIENCE Name:

Date:

Group:

Look

THINK A lake is considered an open system because matter and energy are able to move in and out of the system. Animals may come and go thus changing the dynamics of the system. By contrast, a terrarium would be considered a closed system. Think about the components of open and closed systems. WRITE Compare and contrast open systems with closed systems while giving examples of each as they relate to physics.

Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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WRITING SCIENCE

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High School Physics

P3BC

Conservation of Energy and the Work-Kinetic Energy Theorem

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P3BC Conservation of Energy and the Work-Kinetic Energy Theorem

Student Handout Name:

Date:

Directions: Watch your teacher’s and classmates’ demonstrations, and then answer the questions. 1.

What did all of the demonstrations have in common?

What was different about the not work demonstrations?

Work involves both force and movement. In your own words, write a definition of work.

What is something you do every day that is work?

What is something you do every day that feels like work but isn’t because it does not meet the definition?

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P3BC Conservation of Energy and the Work-Kinetic Energy Theorem

Student Journal Name:

Date:

Group:

Part I: Data Collection Mass of the ball ______________ g = _______________ kg First 3-m roll time _________________ s Second 3-m roll time _________________ s Third 3-m roll time _________________ s Average 3-m roll time _______________ s Time force applied to the ball _______________ s

Part II: Analysis Average ball roll velocity ____________________ m/s Average ball kinetic energy _____________________ J 1.

What would the ball’s kinetic energy be if the ball was stationary?

Did the ball’s kinetic energy change?

How much kinetic energy did the ball gain?

Was the ball’s motion parallel with the force?

Was work done on this ball?

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Student Journal Part II: Analysis, continued 6.

Is the hand-ball system an open or closed system?

How much work was done on the ball?

What applied force to the ball?

How much displacement did the force travel through?

10. Calculate the amount of force applied on the ball using the given work equation.

11. Using the time the force was applied to the ball, determine the power.

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P3BC Conservation of Energy and the Work-Kinetic Energy Theorem

Student Journal Part III: How much work is a trip?

1. The equation for work is W = Fd. If the force is increased in the direction of the displacement, what will happen to the amount of work done by the force? If the force applied in a direction perpendicular to the displacement is increased, what will happen to the work done by the force? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 2. State the work-energy theorem. _______________________________________________________________________________ _______________________________________________________________________________ 3. Is energy lost when there are frictional forces present in the system? Does make the system open or closed? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ Use the following information to calculate the work for each step on the next page. A suitcase has a mass of 22 kg. A.

You wheel the suitcase out of the house for a distance of 100 m, applying a force of 4.5 newtons.

The bottom of the trunk of the car is one meter above the ground. You lift the suitcase straight up in the air with a force equal to the weight of the suitcase.

The car travels 20 km to the airport.

At the airport, a porter places the suitcase on the ground, lowering it a distance of 1 m and using a force equal to the weight of the suitcase.

You pull the suitcase for a distance of 500 m to the ticket counter, applying a force of 4.5 newtons.

At the ticket counter, the suitcase is lifted onto a scale placed 25 centimeters above the ground using a force of 215.6 newtons.

The ticket agent attaches the claim check and moves the suitcase directly to the luggage conveyor belt, which is at the same height as the scale.

The conveyor belt transports the suitcase for a distance of 1,200 m at a speed of 12 m/s.

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Student Journal I.

A luggage handler takes the suitcase off the conveyor belt and lifts it straight up to the top of the baggage train 1.5 m above the conveyor belt using a force of 215.6 newtons.

At the plane, the suitcase is taken off the top of the baggage train 1.5 ms above the ground. It is placed onto the ground, and then into the cargo hold so the suitcase is at rest 3 m above the ground.

Calculate Work Use the section below to calculate work for each segment. Indicate whether the work is done by a machine or a person.

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P3BC Conservation of Energy and the Work-Kinetic Energy Theorem

Student Journal Analysis Questions

Use your calculations to answer the following questions. 1.

In which step was the magnitude of the work done on the suitcase the greatest? ___________________________________________________________________________ ___________________________________________________________________________

Which person did the most work? ___________________________________________________________________________ ___________________________________________________________________________

Compare your results to those of another student. How are they different? ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________

If step H took 100 seconds, determine the power exerted on the suitcase at that time. ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________

Reflections and Conclusions 1.

What new insights did you gain into the work-energy theorem as a result of this activity? ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________

What was most surprising about the work done on the suitcase? ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________

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STEMscopedia: CONSERVATION OF ENERGY

AND THE WORK-KINETIC ENERGY THEOREM P3BC

Reflect The sum of the kinetic energy and potential energy in a system is known as the system’s mechanical energy. The law of conservation of mechanical energy states that energy is never created or destroyed in a closed system but only changes form. We are ignoring here the change of energy into mass and the change of mass into energy that occur in nuclear reactions. This activity, for example, is what creates the energy we see as heat and light from the Sun. Accordingly, the total mechanical energy in a closed system remains constant. Within the system, however, kinetic energy and potential energy may change from one to the other. Since there is no energy created or destroyed as the objects travel along on their paths, the forces that do work exchange energy between potential and kinetic according to the energy initially provided to the system. This is the basis for the law of conservation of mechanical energy. When work is done to a system or by a system, the total energy in it changes. Work In physics, work is done when a force acts on an object and causes the object to move over a distance, as shown. The work, W, done on the object is defined as the product of the force, F, on the object and the displacement, d, over which the force acts: W = Fd. Work has units of joules (J), which are units of energy-doing work, changes the total energy. One joule equals one newton-meter. So, if a 10 newton force pushed a block over a distance of 5 meters, the work done on the block would be 10 N × 5 m = 50 N∙m, or 50 J. Note that the quantities of force and displacement are vectors. Because of this, it is important to know in which directions the force and displacement vectors point. To calculate work, you need to know the amount of force that acts on an object and the direction the object moves. If a force pushes an object and the object moves in the direction of the force (as shown above), the work is simply the product of F and d. However, the vectors F and d do not always point in the same direction. For example, a woman may wish to move a box from the left side of the room to the right side, as shown in the diagram on the next page. As she pushes on the box, she might apply a force that acts at an angle θ to the floor, pushing downward and to the right. (The Greek letter theta, θ, is frequently used to represent an unspecified angle.) In this case, you would not use the total magnitude of force to calculate the work done. Instead, you would determine the component of force acting to the right because this is the direction the box will move.

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Note how you can create a right triangle with the total force (F) as the hypotenuse. In this case, the component of force acting to the right is Fx. To determine the magnitude of Fx, or any force that acts at an angle θ to the displacement of the object, you can use the following equation: W = Fd∙cosθ. This equation simplifies in a few common scenarios: • When the vectors point in the same direction, θ is 0 degrees. The cosine of 0 degrees is 1, so the equation becomes W = Fd. This was the case in the first diagram shown. •

When the vectors point in opposite directions, θ is 180 degrees. The cosine of 180 degrees is −1, so the equation becomes W = −Fd. When this happens, the force does “negative work” on the object. This can happen if a box is lifted up a flight of stairs. While a person does positive work to lift the box, the downward force of gravity acts opposite to the motion of the box. Thus, gravity does negative work on the box.

•

When the force points perpendicular to the direction of motion, θ is 90 degrees. The cosine of 90 degrees is 0, so no work is done in this situation. This would happen if you were to hold a box above your head and walk across a room at a constant speed. In this case, the force you apply to the box is in the vertical direction. Because the box moves at constant speed in the horizontal direction, it experiences no net force in that direction. If an object does not experience a net force in the direction it moves, no work is done.

•

Finally, always remember that work is done to move an object. If an object does not move (if d = 0), no work has been done on it, no matter how much force is applied to the object. So you could push on a large piano for a very long time, but if it does not move, no work is No work is done on the car done. if the car does not move.

What Do You Think? In which situation is more work done on the object? Check your answer before the What do you know? section of this companion.

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STEMscopedia: CONSERVATION OF ENERGY

AND THE WORK-KINETIC ENERGY THEOREM

Kinetic, Potential, and Mechanical Energy In everyday language, when we talk about work and energy, we typically say energy is necessary to do work. In physics, the idea of energy is very similar. Energy is defined as the ability to do work. That is, all things with energy have the ability to move over a distance or move something else over a distance. Kinetic energy is the energy of a moving object. Objects with kinetic energy have the ability to bump into other objects, causing them to move. In this way, they have the ability to do work on other objects. Kinetic energy describes many different types of energy in the world around us. For example, when tiny particles (molecules) of water are heated in a pot, they begin to move more quickly as the water gains thermal energy. As the molecules bump into one another, they transfer kinetic energy throughout the pot of water. In fact, temperature is the measure of the kinetic energy of particles in a substance. Other examples of kinetic energy are electrical energy (as electrons move through wire) and sound energy (as vibrating particles transfer a disturbance through a medium). The kinetic energy, K, of an object with mass m (kilograms) and speed v (meters per second) is described with the following equation: KE = ½ mv2 Potential energy is stored energy in an object. Objects with potential energy have the “potential” to do work. Potential energy is typically associated with the position of an object or a particle. Therefore, the equation for potential energy is: PE = m*g*h where PE is measured in Joules, m= mass of the object (kilograms) , g= gravitational force on the object (9.8 meters per second squared), h= height (meters). The Work-Energy Theorem Think again about the definition of energy. Energy is the ability to do work. It may, therefore, make sense that doing work on an object gives it energy. In fact, the work you do on an object is precisely equal to its change in energy. This is a powerful concept in physics known as the workenergy theorem. Objects can obtain energy only when work has been done on them, and energy gives objects the ability to do work. The work-energy theorem is a statement of the fact that energy changes from one form to another. Recall that work is the force applied to an object to move it over a distance. Whenever a force causes an object to move, the object accelerates. In other words, its speed changes. You just learned that the kinetic energy of an object depends on its speed. So when work is done on an object, its kinetic energy changes. The work-energy theorem states that the work, W, done on an object is equal to its change in kinetic energy, ΔK: Work = ΔK Fd = ½ mv2f - ½ mv2i

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AND THE WORK-KINETIC ENERGY THEOREM

In this equation, the force (F) acts over a distance (d) on the object of mass (m). The initial speed of the object is vi, and the force causes the object to accelerate to a final speed of vf. Note this equation applies only when conservative forces do work on the object. If friction is introduced, then some of the work done on the object will be lost as heat to friction. Thus, the total change in kinetic energy will be less than the total work done. This principle can be applied in numerous scenarios to solve problems that can also be solved using kinematics, the science of motion. For example, the brakes of a car apply a force over a distance to stop a car. The work-energy theorem relates the work done by the brakes to the initial and final speeds of the car. Or, the work-energy theorem can describe a pitcher throwing a baseball with force F. If the pitcher winds up over a distance (d), then the speed of the ball (vf) leaving his hand is described by this theorem. (In this case, you could assume the initial speed of the ball, vi, is zero.) A more specific statement of the work-energy theorem applies when work is done against the force of gravity. When work is done on an object against the gravitational field, an object gains gravitational potential energy. For example, a person may apply a force F to move an object along a distance d up a ramp. The object gains gravitational potential energy as it moves up the ramp, and this energy is related to its height, h, above the ground. The object may move from height hi to hf as work is done on it. Thus, the work, W, done by the person on the object is related to the object’s change in potential energy, ΔU: W = ΔU Fd = mghf - mghi Orbits demonstrate the relationship between potential and kinetic energy.

The total amount of energy that is in a comet’s orbit as it goes around the Sun does not change, regardless of where the comet is. The conservation of energy is described using the following equation: E = KE + PEg where KE is kinetic energy, and PEg is gravitational potential energy.

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STEMscopedia: CONSERVATION OF ENERGY

AND THE WORK-KINETIC ENERGY THEOREM

Kinetic energy is a function of the mass and velocity of the object. While comets do lose some mass as they orbit the Sun due to the heat causing some of the ice to melt and vaporize, this is around one percent. We won’t concern ourselves with the change in mass because it affects kinetic energy and gravitational potential energy equally. Kinetic energy is described by the equation KE = ½ mv2, and gravitational potential energy is described by the equation PEg = mgd. V is the velocity, m is the mass of the comet, d is the distance from the Sun, and g is the gravitational acceleration. The mass is more or less constant. If you examine the kinetic energy of the comet at the apoapsis and compare it to the kinetic energy of the comet at periapsis, or point in the orbit closest to the Sun, it will have increased by the same amount that the potential energy has decreased. Since the comet’s mass change is not enough to matter, the increase in kinetic energy causes the comet’s velocity to increase. Halley’s comet obeys the law of conservation of mass!

Look Out The study of energy transfer and measurement is called thermodynamics. The object being studied is called the system, and the rest of the environment is called the surroundings. The combined system + surroundings is called the universe. For the universe, energy cannot be created or destroyed. For the system, though, energy can enter and leave. If the system gains energy, the surroundings have to lose energy and vice versa.

Open system, closed system, isolated system For closed and isolated systems, though, there is no energy moving into or out of the system. A closed system exchanges no energy with its surroundings. An isolated system exchanges no energy or mass with its surroundings. Planets orbiting the Sun are examples of closed systems. They conserve energy as they travel around their orbit, with their velocity changing in response to how close or far they travel from the sun. Another example of a closed system is a Newton’s cradle. A bead on one side is raised up, and then released. The energy from the first bead is transferred through the stationary beads to the other side, causing the far bead to rise up an equal distance from the table. If the Newton’s cradle was in an airless environment, the back-and-forth transfer of energy could go on for a very long time. In a regular, air-rich environment like a desk, the air provides some resistance, causing energy to be lost to drag. Slowly, the beads will rise less and less, until finally they stop moving altogether and are stationary.

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AND THE WORK-KINETIC ENERGY THEOREM

The conservation of energy in a closed system was first discovered by a scientist named James Joule. He created a device that showed that mechanical energy was the same thing as heat energy, or rather that mechanical energy could be transformed into heat energy. His device was simple. An insulated container of water had a paddle running down the middle. This paddle was attached to a string that ran to a heavy weight. When the weight was released, it would fall, pulling the string. This in turn would spin the paddle inside the container of water, causing friction and turbulence. Joule reasoned that the gravitational potential energy of the weight would be transformed into heat energy in the water. After repeated experimentation, Joule determined that not only was this true, but that there was a consistent distance he could raise the weight to generate enough energy to change his container of water by one degree Fahrenheit. He found that heat energy could be generated by mechanical motion, because mechanical energy and heat energy are the same thing. Power Power is the rate that work is done, or the rate energy is transferred. It is measured in watts, so an 80-watt light bulb transfers energy twice as fast as a 40-watt light bulb. One form of power is horsepower, which is associated with cars and other internal combustion engines. One horsepower is equal to 746 watts. The more horsepower a car has, the faster it can transfer energy to the road to propel the car. The equation for power can take a couple of different forms: P=Wt P=Fv P=Fd/t Where P is power in watts, W is work in Joules, t is time in seconds, F is force in newtons, v is velocity in meters per second, and d is distance in meters. An example problem would look like this: A 2,000 kilogram elevator has to be lifted at 4 meters per second. How much power does this require? Well, the best equation to solve this will be P=Fv, because we have velocity. The force isn’t given, but it is being lifted. This means that the force is most likely equal to the weight of the elevator. Weight is Fg = mg, so we substitute in our mass: Fg = (2,000 kg)(9.8 m/s) = 19,600 N We substitute this force back into our original equation and get: P = (19,600 N)(4 m/s) = 78,400 W

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AND THE WORK-KINETIC ENERGY THEOREM

What Do You Know? Observe this diagram of a pendulum, then answer the three questions on the next page. The pendulum bob has a mass of two kilograms. Assume that at location 3, the pendulum bob is just above the ground such that its height can be approximated as zero. Use the value g = 10 m/s2 for any calculations. 1. How much work is done to lift the pendulum bob to a height of five meters above the ground at location 5?

2. What force must a person apply to lift the bob to location 5?

3. The pendulum is raised to location 5, then released from rest. What is the speed of the pendulum bob at location 3? (Note that the initial velocity of the pendulum, vi, is 0 m/s.)

Connecting With Your Child Investigating Work and Potential and Kinetic Energy Transformations To help your child understand how potential and kinetic energy change forms, have him or her design an experiment to measure the initial and final energy of an object rolling down a ramp. Your child may wish to use the following materials: • Books • Paper towel tubes • Tape • Triple-beam balance • Marble • Stopwatch • Ruler

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To construct the ramp, your child can stack many books on top of one another on the floor. Then he or she can tape a few paper towel tubes from end to end to create a longer tube through which the marble can travel. The top of the tube should begin at the top of the books, and the bottom of the tube should end at the floor. At the top of the ramp, the marble is not moving, so it has only potential energy. The potential energy, U, at the top of the ramp can be calculated using the equation U = mgh, where m is the mass of the marble, g is the acceleration due to gravity (approximately 9.8 m/s2), and h is the height of the ramp. As it moves along the ground at the bottom of the ramp, the marble will have only kinetic energy. Have your child think about how to measure the kinetic energy of the marble. To do this, your child will need to measure the marble’s speed. The speed can be approximated by measuring the time it takes the marble to travel a particular distance once it exits the ramp tube. To calculate speed, your child can divide the distance traveled by the time it takes to travel that distance. Then kinetic energy, K, can be calculated using the equation K = ½ mv2, where m is the mass of the marble and v is the speed. Your child can modify the height of the ramp to observe how the potential energy and kinetic energy change. Here are some questions to discuss with your child: 1. What type of energy does the marble have at the top and bottom of the ramp? 2.

How can you measure the energy of the marble at the top and bottom of the ramp?

How does the energy of the marble at the top of the ramp compare with its energy at the bottom? Does this change when you change the height of the ramp?

Does the energy of the marble change from one form to another as it moves down the ramp? What evidence supports your answer?

How does work on the object change for both potential and kinetic energy throughout the investigation?

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P3BC Conservation of Energy and the Work-Kinetic Energy Theorem

Reading Science Name:

Date:

Group:

Conservation of Energy Experiments 1

The law of conservation of energy is one of the laws of physics. It was updated by Einstein's theory of relativity. The theory of relativity states that energy and mass are interchangeable. Therefore, it is actually “mass-energy” that is conserved, not energy by itself. For large objects not traveling near the speed of light, conservation of energy is a good approximation.

Conservation of energy does not mean that it will always have the same form and location in an isolated system. Energy can change form and location. For example, gravitational potential energy can transform to kinetic energy as a ball rolls down a ramp. Friction is a force that opposes motion. In a mechanical system, friction causes some of the kinetic energy to be transformed to another type of energy. The greater the amount of friction, the greater the reduction of kinetic energy. Other types of energy frequently seen in mechanical systems include sound and heat. As a cannon ball travels down the bore of the cannon, the bore heats up. Some of the kinetic energy of the cannon ball is converted to heat in the bore. Let’s look at three experiments used to demonstrate conservation of energy.

For Experiment 1, a 2 m long piece of foam pipe insulation is cut in half lengthwise to create a track. The length is measured accurately and the halfway point is marked. The piece of foam is then bent so only the middle rests on the table. Figure 1 shows the setup. Along the side of the track near Point A, a mark is made to indicate the starting point for all experiments. A marble of mass 10 g is placed onto the track at the starting point and released. It travels down the length of the track and up the other side. At the end of its travel, the highest point it reached is marked and measured. Marbles of mass 1 g and 100 g are also tested.

For Experiment 2, another series of three balls is tested. While they have the same mass as the marbles, each of these balls is covered with sand. Each ball was dipped in glue and then rolled in sand, so the sand covers the ball uniformly. The sand is glued on very tightly, so it does not come off during the experiment. Each of these balls is also placed on the track at the starting point, and the maximum height reached is recorded.

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Reading Science 5

For Experiment 3, a child with mass 20 kg is sitting on a swing with mass 3 kg. The swing is old and creaks as it swings. A student holds onto the child and pulls the child up 1 m to his chest. He lets go of the child on the swing. The swing swings freely and returns, almost touching his chest. He catches the child on the swing and this time pushes it away from him. The child swings, and on the return, the student must step back to avoid getting hit.

Each of these experiments illustrates aspects of the conservation of energy. Each involves an isolated system. Conversion of energy from one form to another is also common to each of these experiments. Think about the conservation of energy as you answer the questions that follow.

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Reading Science 1.

Which of the following statements is true about mass-energy in an isolated system? A.

Mass-energy remains the same.

Mass-energy can be created or destroyed.

Mass-energy increases over time up to a maximum.

Energy has to remain in the same form and location in the system.

A marble of mass 10 g is placed on the track at the starting point. The height attained by the marble on the opposite side is measured. This is repeated five times. Which of the following experimental results would support the explanation of conservation of energy given in paragraph 2? A.

All measurements are the same or higher than the starting point.

All measurements are the same or lower than the starting point.

All measurements are exactly the same height as the starting point.

here is no pattern to the measurements. Some are higher and some are lower than T the starting point.

When comparing a marble of 10 g and a “sandy ball” of 10 g, which is likely to reach a greater height on the track? A.

The marble

The sandy ball

Both are likely to reach the same height

Can’t be predicted

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Reading Science 4.

In all three experiments, an unbalanced force may be acting on the objects (the marbles, “sandy balls,” or swing). What is the name of this force? A.

Momentum

Sound

Impulse

Friction

Which of these statements describes a similarity in the situations investigated by Experiments 2 and 3? A.

Some energy is lost from the system due to friction.

Some kinetic energy is transformed into heat or sound energy.

he potential energy remains the same at the highest points of the object’s movement T compared to the starting point.

All of the above.

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Math Connections Name:

Date:

Group:

The law of conservation of energy states that the total amount of energy in a system remains constant in a closed system, although energy within the system can be changed from one form to another or transferred from one object to another. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. When a force acts upon an object to cause a displacement of the object, it is said that work was done upon the object. In order for a force to qualify as having done work on an object, there must be a displacement and the force must cause the displacement. The following variables and formulas will be used to answer questions about energy, force, and work. Symbol

Variable

Unit

mass

velocity

m/s

height

acceleration due to gravity

9.8 m/s2

Formulas

Potential energy (joules)

PE = mgh

Kinetic energy (joules)

KE = ½ mv 2

Work-energy theorem (joules)

Wnet = ∆KE

1. If a 1,300-kg car with no people inside is on the edge of a cliff 1,500 m above the ground, what is the potential energy?

2. What is the car’s kinetic energy?

3. The car starts to fall. What is the potential energy when it is 1,000 m above the ground?

4. As the car falls, it loses height and gains velocity. What is the kinetic energy of the car when it has fallen 500 meters? What is its velocity?

5. What is the kinetic energy of the car just before it hits the ground? What is its velocity?

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Math Connections 6. Think about the formula for kinetic energy: • If the speed of an object doubles, by what factor does the kinetic energy increase? • If the speed of an object triples, by what factor does the kinetic energy increase? • What is the relationship between the kinetic energy of an object and its speed? 7. Calculate the kinetic energy of a 790-kg rollercoaster traveling at a velocity of 20.7 m/s.

8. Create a formula for the work-energy theorem knowing that it describes the relationship of the net work and the change in kinetic energy of an object as it moves.

9. Use the work-energy theorem to calculate the potential energy, kinetic energy, and velocity at different points on the diagram below. The mass of the ball is 5 kg. PE = 250 J KE = 0 J

d. PE = ___ J e. KE = ___ J f. v = ___ m/s

PE = 0 J KE = 250 J v = 10 m/s

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PE = 125 J g. KE = ___ J h. v = ___ m/s

a. PE = ___ J b. KE = ___ J c. v = ___ m/s

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WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK Roller coasters are commonly used in physics as demonstrations of motion and the transformation of energy. Energy can be transformed from one type of energy to another and back again. Since the law of conservation of energy states that energy cannot be created or destroyed, it must constantly change energy types. Energy can change from potential energy to kinetic energy to thermal energy to electrical energy to mechanical energy, to name just a few examples. The roller coaster above shows one of the most common transformations of energy. WRITE What are the energy transformations that occur during a roller coaster ride? Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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WRITING SCIENCE

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High School Physics

P3D

Conservation of Momentum

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Student Handout Name:

Date:

Momentum Card Sort Activity

Momentum (p) is the motion of a moving object. We know that it’s harder to stop a large truck than a small car when both are moving at the same speed. We say the truck has more momentum than the car. By momentum, we mean inertia in motion.

Part I Your teacher will give you six cards. Using the definition given above, estimate how much momentum you think each object has. Then sort the cards from the most momentum to the least momentum. Write your order below: 1)____________________2) ____________________3)____________________ 4)____________________5) ____________________6)____________________

Part II Your teacher will write the equation for momentum on the board. Calculate the momentum for each of the six cards, and write your answers below. Aircraft Carrier: ____________ Subway Train: ____________ Semi: _____________ Car:______________ Bullet: ____________ Baseball: _______________ Now sort the cards based on their calculated momentum from the most momentum to the least momentum. Write your order below: 1)____________________2) ____________________3)____________________ 4)____________________5) ____________________6)____________________

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Student Journal Name:

Date:

Group:

Part I: Elastic vs. Inelastic 1.

What is the definition of an elastic collision?

Is an egg hitting the ground an elastic or inelastic collision? Why?

Part II: Free-Fall Velocity and Momentum 1.

What was the result when the egg hit the ground?

What distance did your egg fall?

Using the equation from your Student Guide, what is the velocity of the egg at the moment of impact with the ground?

What is the mass of the egg? What is this mass in kilograms?

What is the momentum of the egg at the moment of impact?

Part III: Use the Force 1.

State Newton’s third law.

What is the egg’s change in momentum (or impulse)?

Using the equation from your Student Guide and an impact time of 0.0001 s, what is the force experienced by the egg at the moment of impact?

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Student Journal Part IV: Don’t Break the Egg 1.

Write the equation for impulse below.

What are the variables in this equation?

What is the maximum force the egg can experience?

Based on the variables, how will you reduce the force on the egg?

Using the provided resources, design a catching apparatus that will catch the egg after it falls 2 m without breaking. Outline your design below.

Have your teacher put his or her initials here after he or she has approved it. _________

Did both eggs survive the drop intact? What was the result of both drops?

Reflection 1.

What is the relationship between impact time and force?

How does a car’s airbag reduce the force on a person in a car wreck?

How would you improve your egg drop design to allow you to drop an egg from a second-story balcony?

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MOMENTUM P3D

Reflect If you are standing on the sidewalk and a small three year old is rolling toward you on roller blades at a pace of one meter per second and his dad is also rolling toward you traveling three meters per second, which person will be easier for you to stop? If you said the little boy, you are correct. Why? Because the little boy has less momentum than his dad. Read on to find out more about momentum.

Momentum What is momentum? Momentum is the product of an object’s mass and velocity. The formula for momentum is: p = mv P is momentum and is commonly measured in kg⋅m/sm, mass is measured in kilograms, and velocity is measured in meters per second. Why is it important to note that velocity (rather than speed) is included in the momentum formula? The direction in which an object is traveling is very important in regards to momentum. Often when an object moves to the right, momentum is considered positive; when it moves to the left, momentum is considered negative. Think back to the situation presented in the “Reflect” section above. Using the formula, why would the dad have more momentum than the child? The dad has a greater mass than the child, and the dad was traveling at a higher velocity. Let us now specify the masses of both people from the example above. If the dad has a mass of 100 kilograms and is traveling at three meters per second directly at you, what is his momentum? If the child has a mass of 20 kilograms and is rolling at a velocity of one meter per second toward you, what is his momentum? If you use the momentum formula, you will figure out that the dad’s momentum is 300 kg⋅m/s or 300 N⋅s, and the child’s momentum is 20 kg⋅m/s or 20 N⋅s. [Hint: Remember, one Newton (N) is equivalent to one kg⋅m/s2.] Imagine a different scenario. What if there were twin sisters moving toward you, both with the same mass of 25 kilograms? One of the sisters is traveling at three kilometers per hour and the other is traveling at eight kilometers per hour. Which sister would have the greater momentum? The sister traveling at eight kilometers would have the greater momentum. The momentum of the slower sister is 20.83 N⋅s, while the momentum of the faster sister is 55.56 N⋅s. (Hint: Remember to convert units to meters and seconds when necessary.)

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How can the momentum of an object change? Momentum changes when mass or velocity is altered. The most likely scenario is a modification of velocity. How does velocity of an object vary? A force is responsible for causing an alteration of the velocity of an object. How much the velocity of an object changes depends upon two things: the strength of the force and the amount of time the force is applied upon the object. Force multiplied by the time of application is called impulse. The formula for impulse is: Ft = mvf - mvi Therefore, impulse (Ft), or force multiplied by the amount of time the force was applied, is equal to the change in momentum (the product of mass and initial velocity subtracted from the product of mass and final velocity). What are some examples of impulses that would change the momentum of an object by changing the velocity? (Hint: Remember, velocity is changed when either the speed or direction of the moving object is altered.) The following circumstances are examples of impulses that change the momentum of an object: • A batter hitting a pitched baseball • Someone pushing a car stalled in the road • Serving a tennis ball • A roller skater pushing off the wall at the roller rink • A fan blowing a mosquito away from someone’s arm • A parent beginning to jog while pushing a stroller

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What Do You Think? 1. What is the momentum of a goose with a mass of 1.8 kilograms migrating south at 72 kilometers per hour? (Remember that p = mv.)

2. Which has a greater momentum: a 1,000 kilogram car traveling forward at one meter per second or a 15 gram bullet traveling at 750 meters per second? (Check that your units are uniform.)

3. A net force of five newtons is applied for .1 seconds to a .5 kilograms soccer ball at rest. What is the speed of the soccer ball at the end of the .1 seconds? (Remember, the formula for impulse is Ft = mvf - mvi.)

4. How long should it take to increase the speed of a five kilogram bike from five meters per second to 10 meters per second if applying a force of 5 Newtons? (Remember: Ft = mvf - mvi.)

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Newton’s Third Law of Motion Most people have heard of Newton’s third law of motion: For every action force, there is an equal and opposite reaction force. What does this law mean? It denotes that each force that exists has a reaction force that is equal in magnitude but opposite in direction. In other words, forces come in pairs. When an entity exerts a force on an object, that object exerts an equal and opposite force on the entity. If this is true, do the forces just cancel each other out, resulting in a net force of zero? The answer is no because the forces are not acting on the same object. They are acting on each other. What are some examples of pairs of action and reaction forces? • The force of a racket hitting a tennis ball and the tennis ball pushing back against the racket • A bird standing on the sidewalk (force of weight pushing down) and the sidewalk pushing up (support force) to keep the bird from falling through the sidewalk • Two people on roller skates on a roller rink pushing against each other to separate themselves (each applying force to the other person) • Catching a ball (the hand applies force that slows the ball’s velocity, while the force of the ball pushes the hand back)

How do you know which force is the action force and which force is the reaction force? They are actually interchangeable. The action force could technically be said to “create” the reaction force, but since the forces are created simultaneously, either force can be the action or reaction force. Sometimes action and reaction forces can be difficult to comprehend. You know the forces are there, but it’s hard to picture what exactly transpires. Here are some helpful hints about action and reaction forces: • They always occur in pairs. • They are always forces of equal strength. • They always act in opposite directions. • They never act on the same object. Drawing a picture of the scenario with arrows to show the directions of the action and reaction forces can be a useful visual aid.

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The Law of Conservation of Momentum The law of conservation of momentum states that if no outside forces act on a system, the total momentum in a system remains constant. Since action and reaction forces are joined as a pair, the momentum in the system is conserved. If one object in the pair gains momentum, the other object loses the same amount of momentum. In other words, the total momentum before the change is equal to the total momentum after the change. Here is a formula for calculating conservation of momentum: m1u1 + m2u2 = m1v1 + m2v2 m1 = mass of object 1 m2 = mass of object 2 u1 = initial velocity of object 1 u2 = initial velocity of object 2 v1 = final velocity of object 1 v2 = final velocity of object 2 Think of this example in a situation where there are no outside forces. An astronaut floating in space kicks a football with a mass of one kilograms to the right at a velocity of 20 meters per second. The astronaut has a mass of 75 kilograms. What direction and what speed will the astronaut move after kicking the football? Although it makes no difference which object is which, we will choose the football to be object 1 and the astronaut to be object 2. (Hint: Both objects were at rest before the astronaut kicked the football. Also, remember that movement to the left is considered negative.) (1 kg)(0m/s) + (75kg)(0m/s) = (1 kg)(20 m/s) + (75 kg)(x) 0 = 20 kg m/s + 75 kg(x) -20 kg m/s ÷ 75 kg = 75 kg (x) ÷ 75 kg -.267 m/s = x The astronaut will move to the left at .267 m/s.

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What Do You Know? Reflect upon the following situation regarding conservation of momentum. Pretend there are no outside forces acting upon the objects in the scenario. Use the conservation of momentum formula to solve the problem where both bodies were originally at rest. A brother and a sister are standing on ice skates facing each other and not moving. They decide to see how far apart they can get with just one strong push. The sister gives one hard shove. The younger brother (with a mass of 34 kilograms) travels backward to the left at a rate of 1.4 meters per second. The older sister has a mass of 42 kilograms. She moves to the right. At what rate does she move?

Let’s alter the scenario just slightly. Still pretend there are no outside forces acting upon the objects in the situation. Use the conservation of momentum formula to solve the problem where both bodies were originally at rest. A brother and a sister are standing on ice skates facing each other and not moving. They decide to see how far apart they can get with just one strong push. They put their hands together and give one hard shove at the same time. The younger brother (with a mass of 30 kilograms) travels backward to the right at a rate of 3.0 meters per second. The older sister moves backward to the left at a rate of 1.8 meters per second. What is the mass of the older sister?

Collisions Most of the time when people hear the word “collision,” they immediately envision a car crash. However, collision simply means an object striking another object. Because of conservation of momentum, momentum that exists before a collision is conserved after a collision. Energy is also conserved, though (depending on the type of collision) perhaps not as kinetic energy. Though momentum and energy are conserved, they may change form or transfer to another object or form.

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There are two types of collisions: elastic and inelastic. Elastic collisions means the kinetic energy of the two objects involved in the collision is maintained before and after the collision. Inelastic collisions, however, involve a loss of some kinetic energy due to a change in shape, sound, heat, or other transformation of energy. An elastic collision in its purest form cannot actually occur on Earth because there is always some kind of friction or loss of energy due to sound or heat with a collision. However, swinging steel balls are extremely close to an elastic collision. This is evidenced by how long the balls remain in motion. An inelastic collision occurs when two objects collide and kinetic energy is not maintained. Objects will usually change their shapes. Examples of inelastic collisions are car crashes, striking a watermelon with a hammer, and hitting someone over the head with a pillow during a pillow fight.

Look Out Most collisions that occur on Earth are a combination of elastic and inelastic collisions. When no forces outside the system act upon the objects in the collision, momentum is conserved. This may be hard to visualize when kinetic energy is not conserved and is instead transformed into another form. Remember, total momentum before a collision equals the total momentum after a collision. When you are determining the answer to a momentum conservation problem, figure out whether the collision is elastic or inelastic, and then draw a picture of the situation. It will help you to visualize what is physically happening. Here is a sample problem of conservation of momentum after a collision: A 4,000 kilogram truck driving at 80 kilometers per hour doesn’t stop and plows into the back of a car stopped at a red light. The car has a mass of 1,200 kilograms. The truck carries the car forward. What is the speed they travel after the collision? Use the law of the conservation of motion: m1u1 + m2u2 = m1v1 + m2v2 Hint: Because the vehicles are stuck together after the collision, they will have one combined mass (m1 + m2) and one velocity (v3). Hint: Don’t forget to convert kilometers per hour to meters per second! (4,000 kg)(22.22 m/s) + (1,200 kg)(0 m/s) = (4,000 kg + 1,200 kg)(v3) 88,880 kg∙m/s + 0 = (5,200 kg)(v3) 88,880 kg∙m/s ÷ 5,200 kg = (5,200 kg)(v3) ÷ 5,200 kg 17.09 m/s = v3

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Try Now A man is driving his 1,000 kilogram car down his street at 10 meters per second. He doesn’t notice the 10 kilogram empty trashcan that has blown into the street and is stopped there blocking his path. He drives his car right into the trashcan, which sticks to the front of his car. What is the speed the car and trashcan travel together after the collision?

Connecting With Your Child These activities will help you to understand the similarities and differences between elastic and inelastic collisions. Feel free to look up questions, answers, concepts, and ideas on the Internet. Answer the following questions: • Is momentum conserved during inelastic collisions? •

Is momentum conserved during elastic collisions?

•

Which type of collision conserves kinetic energy?

•

What type of collision most often happens on Earth?

Decide whether each of the following collisions is elastic or inelastic: • You drop a glass on the floor and it shatters. • You step on a banana and it flattens. • You bounce a basketball on a basketball court. • Two cars crash into each other and their bumpers crumple. • A hockey puck ricochets off the wall. • A baseball player catches a fly ball in his glove.

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Try performing the following collisions and try to think of how momentum was conserved: Elastic: Hold an egg high above the sink. Drop it and observe what happens when it hits the sink.

Inelastic: Roll two billiard balls quickly at each other and watch what happens when they collide.

Questions: 1. What did you notice that was similar about the two collisions? 2.

What differences did you notice regarding the collisions?

How do you think momentum was conserved in each of the collisions?

What would be three more examples of each type of collision?

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P3D Conservation of Momentum

Reading Science Name:

Date:

Group:

Physics of Car Crashes 1

The simplest collision to analyze is a head-on collision between a car with a driver and a stationary concrete wall. The characteristics of the driver include instantaneous velocity and mass. If the driver is wearing a rigid seatbelt, the distance in which the driver stops depends on deformation of the car’s hood and the passenger compartment. 1 m is a common distance. An equation relates the average force on the driver (Favg ) to the stopping distance (d), mass (m), and instantaneous velocity (v): Favg * d = −0.5 * m * v2

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Reading Science 4

Computer simulations allow engineers to test the crash performance of cars without using actual cars. The inputs to the model include the structural geometry of the parts and the basic material properties. For example, windshield glass has different material properties than automotive steel and plastic. Mathematical techniques divide the car into more than one million small units. Each unit is connected to its neighbors through nodes. Forces are then applied. The spatial position of each unit is analyzed as a function of time. The most important output of a simulation is the forces experienced by the occupants of the car. Based on human biology, survivable limits for force have been established. For example, the force to the chest cannot exceed a certain value, otherwise the rib cage will collapse, and the person is likely to die.

One way to simulate this modeling process is to take a sheet of graph paper and use it to wrap a small box. Use glue to attach the paper tightly to the box. Each square of the graph paper would be one unit, while the line intersections on the paper are the nodes. Use your hand to partly crush the box without tearing the paper. Notice how the relative position of the squares has changed where the box is crushed. Your simulation provides the time points at the beginning and at the end. A computer simulation is analyzed with many steps to account for the motion of car parts and occupants during the crash.

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Reading Science 1.

Automotive engineering programs at college – A.

are frequently associated with mechanical engineering programs.

don’t require an understanding of math and physics.

interact only with the business school.

are only available in Michigan.

Pam is driving a car, and Dave is riding in the front passenger seat. Both are wearing seatbelts. Pam crashes head on into a concrete barrier driving 50 kph. Assuming that Dave’s mass is 1.5 times that of Pam’s, which statement below describes the force experienced by Dave? A.

Dave experiences 3 times the force that Pam experiences.

Dave experiences 1.5 times the force that Pam experiences.

Dave experiences the same force as Pam.

Dave experiences half the force that Pam experiences.

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Reading Science 1.

Bill is driving a very old car with a hood designed to be rigid in a crash. Linda is driving a new car with a hood designed to crumple in a crash. Both have the same mass and are wearing seatbelts. In a head-on collision at the same speed with a stationary wall, which driver will experience greater force? A.

Both will experience the same force.

Linda will experience the greater force.

Bill will experience the greater force.

It cannot be determined from the information provided.

Deformation of the hood in a head-on collision – A.

increases the mass of the car and increases the force on the occupants.

decreases the mass of the car and decreases the force on the occupants.

decreases the stopping distance and increases the force on the occupants.

increases the stopping distance and decreases the force on the occupants.

Using a box covered with graph paper allows a student to simulate which aspect of a car crash? A.

The impact on occupants

The stiffness of car materials

The computer modeling

The kinematic equations

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Math Connections Name:

Date:

Group:

Momentum is an object’s quantity of motion. The amount of momentum depends on the object’s mass and velocity. The following equation can be used to calculate the momentum of an object: Momentum (p) = mass (m) × velocity (v) 1. If an object’s mass is measured in kg and its velocity is measured in m/s, what is the unit for momentum?

2. The mass of a fully loaded Boeing 747 is about 4,082,331.33 kg. If it cruises eastward at a velocity of 253 m/s, what is its momentum?

3. How fast must a 142 g baseball travel to achieve a momentum of 3.905 kg × m/s?

4. Japan’s 500 Series Shinkansen (bullet train) travels between Tokyo and Hakata. If it heads north with a momentum of 13194098.64 kg × m/s at a velocity of 261.8 km/h, what is its mass?

5. What is the momentum of a water balloon with a mass of 0.035 kg traveling through the air at a velocity of 11.176 m/s?

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Math Connections Use the following information to answer questions 6–9. The following table was used to collect data about the effects of mass on the amount of momentum a horse has when racing. The masses of the jockeys, the masses of the horses, and the velocities of the horses are recorded below. Riders

Mass of jockey (kg)

Mass of horse (kg)

Velocity (m/s)

Rider 1

110

489.88

0.82

Rider 2

115

489.88

0.82

Rider 3

120

489.88

0.82

Rider 4

125

489.88

0.82

Momentum (kg × m/s)

6. Calculate the momentum for each rider, and input the data in the table.

7. Plot the mass of the horse and rider compared to the momentum on the graph below.

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Math Connections 8. Which horse and rider would be the hardest to stop? Why?

9. What is the relationship of the mass and the momentum of an object with a constant velocity?

In a collision, the momentum of an object is changed. The object experiences a force for a certain amount of time that results in this change. When an impulse is encountered, the object’s mass either speeds up or slows down. We can describe the impulse-momentum change using the equation below. F ∙ t = m ∙ ∆v 10. If a car with a mass of 1,279 kg is moving at a velocity of 26.82 m/s when it hits a truck exerting a 20,000 N force that slows it down to 10 m/s, for how long did the car experience the force?

11. If a 110 kg go-cart traveling at a velocity of 13.41 m/s has a collision with an impulse of 615 N × s, what is the change in velocity?

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WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK When accidents occur, damage to both vehicles usually occurs. However, that amount of damage can be very different depending on the mass and speed (momentum) of the vehicles. When two vehicles collide, the kinetic energy can be transferred completely or change to heat and sound. The amount of momentum each vehicle has determines which of those scenarios will happen. The following scenarios show three different collisions. • Two smart cars collide at 5 miles per hour. • A semi truck traveling at 50 mph collides with an SUV traveling at 60 mph. • A midsize sedan backs into a parked car. WRITE Which collision will create the most damage and why? Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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WRITING SCIENCE

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High School Physics

P4ACD

Mechanical and Electromagnetic Waves

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P4ACD Mechanical and Electromagnetic Waves

Student Handout Name:

Date:

Properties of Waves Access Prior Knowledge 1. What is a wave? 2. What is the difference between a sound wave and an electromagnetic wave?

Activity Waves carry energy. Think about the waves at the beach. The larger the wave, the more energy it carries. This is true for all energy that travel in waves, from a sound to a spring. Your teacher will ask you to download an oscilloscope app onto your smartphone. Search in the app store for “oscilloscope” and download the first free app listed. They all function in more or less the same way, so it does not matter which one. Open the oscilloscope in one hand and have you or your partner make a constant tone, like a middle C note, with his or her voice. Using the ruler, measure the distance between two crests on the oscilloscope. Then repeat the process making a higher tone, like a high F note. Measure as before. Finally, perform the process one more time making a low tone, such as a low C note.

Analysis 1.

Which tone had the longest wavelength?

Which tone had the shortest wavelength?

What conclusion can you draw on the relationship between the pitch of a sound and its wavelength?

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P4ACD Mechanical and Electromagnetic Waves

Student Journal Name:

Date:

Group:

Part I: Frequency vs. Pitch 1.

What happened to the sound produced as the sound tube was twirled faster?

A specific frequency of vibration will produce a specific sound. What is producing the frequency for the sound tube?

If pitch is how high a note is, what is the connection between frequency and pitch?

Is the relationship between frequency and pitch direct or inverse?

Part II: Doppler Effect 1.

What happened to the sound the tube made as the source student moved toward the observer?

What happened to the sound the tube made as the source student moved away from the observer?

What happened to the sound the tube made as the observer moved toward the source student?

What happened to the sound the tube made as the observer moved away from the source student?

Would the sound change be greater or lesser if the source student was moving faster, as if he or she was sprinting or riding in a car?

Using the information from this section, predict how an ambulance siren will sound as the ambulance approaches and then passes you while you stand by a road.

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Student Journal Part III: Amplitude of a Sound wave 1.

What was the height of the sound wave with only one student making the tone?

What was the height of the sound wave with two students making the tone?

What was the height of the sound wave with three students making the tone?

Graph the three sound waves on the provided graph paper.

Part IV: Standing Waves 1.

What happened to the sound when you switched from the one meter pipe to the 0.5-m pipe?

What happened to the sound when you switched from the one meter pipe to the 1.5-m pipe?

Summarize the effect of the length of pipe on the sound produced.

Part V: Standing Waves 1.

In Part I, you produced a sound wave with the sound tube. The wavelength of this wave was 1.32 m and it had a frequency of 261 Hz. Determine the speed of sound.

Using the speed of sound from question 1 in this section, what would be the frequency if the wavelength was doubled to 2.64 m?

Using the speed of sound from question 1 in this section, what would be the wavelength if the frequency was doubled to 522 Hz?

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Student Journal Analysis 1.

Summarize the relationship between frequency and pitch you determined in Part I.

In Part II, did it make any difference to doppler shift if the observer was stationary or the source was stationary?

In Part III, sound’s power was examined. One sound wave has an amplitude of three centimeters, and a second sound wave has an amplitude has an amplitude of six centimeters. If all other things are identical, what is the primary difference between the waves?

Considering what was learned in Part IV, why does a bass guitar have longer strings than a regular guitar?

State whether the relationship between frequency and wavelength is a direct or inverse relationship.

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Student Journal Date:

Name:

Group:

Part II: The Relationship Between Wavelength, Frequency, and Speed 1.

The wavelength of the infrared wave ___________ cm = ______________m

The wavelength of the visible light-green wave ___________ cm = ______________m

The wavelength of the ultraviolet wave ___________ cm = ______________m Time

# IR waves

# Vis waves

# UV waves

Freq. IR

Freq. Vis

Freq. UV

Speed IR

Speed Vis

Speed UV

2s 3s 4s

What do you notice about the speed of your waves?

If you had a fourth wave, a radio wave, with a wavelength of 25 cm, how would you predict its frequency for the 2 s trial?

Part III: Light Frequency and Energy 1.

What is your solar-powered object?

What is its behavior under normal light?

What is its behavior under no light?

What is its behavior under red light?

What is its behavior under green light?

What is its behavior under blue/violet light?

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Student Journal Part III: Light Frequency and Energy, continued 7.

What is its behavior under ultraviolet light?

Which color of light produced the strongest response?

Spend a few moments researching the frequency of red, green, blue, and ultraviolet light, then write them down here.

10. Using the equation provided in your Student Guide, calculate the energy of each type of light from question 9 above.

11. Did the highest energy light from question 10 match your answer to question 8? Give reasons for this result.

Analysis 1.

Given that the speed is constant for all kinds of light in Parts I and II, what is the relationship between frequency and wavelength, direct or inverse? Give specific evidence in support of your answer.

The actual speed of light is 3 x 108 meters per second. If a radio wave has wavelength of 3.23 m, what is its frequency?

Which color of light gave the most energy to the solar-powered object?

Even though the black light appeared dimmer to our eyes, it still powered the object. Explain.

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Reflect Consider the following situations, and think about what they all have in common: • As a police siren approaches, the siren has a high pitch. Then as the siren passes, its pitch sounds like it decreases. • After a rainstorm, people can see a rainbow in the sky as the Sun emerges from behind clouds. • When a woman yells over a large canyon, she can hear an echo of her voice. • On a hot, sunny day, a distant location along a road appears to be wet. However, when one approaches the location, the road is completely dry.

What do a rainbow and a heat mirage have in common?

Each of these situations is an example of wave behavior. Unlike particles, which move in straight lines, waves oscillate or vibrate as they travel through space and time. Wave motion produces some very interesting—and sometimes difﬁcult to explain—phenomena in the world around us. This is partly due to the fact that our senses of sight and sound are dependent upon the behavior of two different types of waves: light waves and sound waves. Because waves can behave in unusual ways, we may sometimes be surprised or confused by what we are seeing or hearing. Sound waves require a medium to travel. All waves transmit energy, not matter. Nearly all waves travel through matter. Waves are created when a source (force) generates a vibration. Vibrations in materials set up wavelike disturbances that spread away from the source of the disturbance. This means that every wave starts somewhere. Different types of waves can be compared by the ways they behave. Waves have a repeating pattern that gives them a shape and length. These characteristics allow us to describe wave behavior and categorize waves with our descriptions. Waves change their behavior as they travel through different types of matter. Waves are moving energy. The type of matter that the wave travels through determines the frequency (speed) of the wave. As a source of energy begins the vibration of the wave, the matter around it is disturbed. Each disturbance passes the disturbance to the matter next to it, and thus energy flows away from the source in a wave. What are some different ways that waves can behave? How does our understanding of wave behavior help explain various phenomena in the world?

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Reflection The most commonly observed wave behavior is reflection. You observe this phenomenon whenever you see your image in a mirror, a glass window, or on the surface of a lake. Reflection occurs whenever a wave strikes a boundary between two medium: a substance media, such as air and water, and then bounces back into the medium through which a wave from which it originated. For example, when light travels through the air moves and strikes the surface of a lake, some of the light is reflected at this boundary. Reflect Light reflecting off a lake’s surface can cause a bright glare on a lake or an ocean on a sunny day. It is also the reason we can observe the images of objects in water. Similarly, sound waves reflect off surfaces, creating a reverberation—or an echo— effect. The reflection of waves from a boundary is similar to the way a billiard ball strikes and bounces away from a wall. If a ball strikes a wall “head on” (meaning it is traveling perpendicular to the wall), the ball will bounce back in exactly the same direction from which it traveled. However, if a ball strikes a wall at an angle to the perpendicular (called the angle of incidence), The reflection of hot air balloons is seen on the surface of a still lake. it will bounce away from the wall at the same angle to the Some of the light that has reflected perpendicular (the angle of reflection). Waves behave in the from the hot air balloon travels same way, as shown below. In fact, this is called the law of through the air to the lake. When reflection. While a wave’s direction changes during reflection, this light strikes this boundary, its speed does not. some of it reflects back into the air. This causes an image of the hot air balloon to appear on the lake surface.

A wave (red arrow) strikes a barrier (blue line) at an angle θi to the perpendicular line. This is the angle of incidence. The wave bounces away at an angle θr. The law of reﬂection states that the angle of incidence is equal to the angle of reﬂection.

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Look Out Light waves reflect from surfaces in different ways. For example, mirrors reflect all the light that strikes them. However, light behaves differently on other surfaces. For example, opaque surfaces do not allow light to pass through them. Light striking an opaque surface is either absorbed by the surface or reflected from it. Some objects absorb certain frequencies (colors) of light and reflect other frequencies. The particular frequencies of light that an object reflects determine the color of the object. For example, grass absorbs all frequencies of light except for green. That is, grass reflects green light. This is why grass appears green. White objects reflect most of the light striking them, while black objects absorb most of the light. frequency: the number of times a wave cycles (or vibrates) in a given unit of time

Look Out Refraction A wave can also be transmitted through a boundary, meaning that it passes through the boundary from one medium to another. In fact, at most boundaries, part of the wave is reﬂected and part is transmitted. Most waves move at different speeds through different media. For example, light moves quickly through air, but more slowly through water. Thus, waves change speeds as they transmit from one media to another. This change in speed usually causes a wave to refract, or bend, as it passes through the boundary.

The black dots in this diagram represent a group of students marching across a room. The students represent a light wave. The left side of the room represents air (a relatively fast medium), and the right side represents water (a relatively slow medium). When the students pass from left to right, one student crosses the boundary ﬁrst. This student begins moving slowly, but the rest of the group still travels quickly, causing the students to change direction, or bend, as they move into the new medium. This is known as refraction.

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To understand how refraction happens, think of a light wave as a group of students marching shoulder-to-shoulder from the bottom left corner of a room to the top right corner. Imagine that the left side of the room is one medium, such as air, and the right side of the room is another medium, such as water. As they march diagonally across the room, they step at the same pace. However, once they pass over the boundary into the right side of the room, they begin to walk more slowly through the new medium. Because the entire group approaches the boundary at an angle, one person will cross the boundary ﬁrst and begin walking more slowly on the right side, but the rest of the group will continue walking at the faster pace on the left side. This will cause the line of students to swing into a new direction, pivoting around the ﬁrst student to cross over the boundary. Then, as the remainder of the students pass into the slower medium, they will begin walking at the slower pace, and the students will march in a straight line again. A wave behaves in the same way as the marching students. If it transmits from one medium to another at an angle to the medium, it will refract and change directions. (Note: If it strikes the new medium “head on,” it will not change directions.) Refraction causes white light from the Sun to spread out into different colors as it passes from air into new media, such as water or glass. For example, the different wavelengths of sunlight all refract at different angles when they pass through a raindrop. This causes sunlight to spread out into a rainbow as it refracts through raindrops after a storm.

Look Out Diffraction and Interference Have you ever watched water waves pass through a narrow slit in a barrier? When the waves pass through, they spread out radially. This is known as diffraction. For example, when a light bulb is turned on in a dark room, light waves spread out radially from the light bulb. However, once the waves have traveled a certain distance, they can be thought of as plane waves that move in parallel “sheets,” like in the image on the right. When a plane wave passes through a narrow slit or a barrier, the wave will act as though it is originating from a point source again. Thus, the wave spreads out, or diffracts.

Plane waves (left) spread out radially (right) when they pass through a slit in a barrier.

This can also happen when a wave approaches a solid barrier. In these cases, when the wave passes along any edge of the barrier, it will spread out radially around the barrier. In this way, waves will appear to “bend” around barriers. This is the reason you can hear sounds that are emitted from behind a wall or large building.

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An interesting aspect of wave behavior is that two waves can occupy the same space at the same time. This is called a superposition of waves. The same types of waves can superimpose whenever they cross paths through the same medium. For example, if two sound waves cross paths in the air, they will superimpose. When this happens, interference will occur. Interference is the net effect of two or more superimposed waves. Recall that the amplitude, or displacement, of a wave changes depending on where the wave is in its cycle. When the displacement of two waves is in the same direction, their amplitudes add together and constructive interference takes place. So if two identical sound waves interfere with one another, the amplitudes of the waves add together and the sound becomes louder. Similarly, if two identical light waves interfere, the amplitudes add together and the light appears brighter. Sometimes, however, two waves with very similar characteristics are out of phase with each other. (The phase of a wave simply refers to its position in the wave cycle.)

Waves A and B are identical, meaning the parts of each wave are displaced in the same directions. When they cross paths, they interfere, and the amplitude of each wave adds together. This is called constructive interference.

Look Out If two waves begin their cycles at the same time, they will be in phase with each other. However, if one wave begins its cycle ﬁrst and then another wave begins slightly later, the waves will be out of phase. In this case, when the waves interfere, the displacement of each wave might cancel the other one out. When the displacement of waves is in opposite directions, destructive interference takes place. Most waves in the real world are out of phase with each other to some extent. In these cases, there will always be some amount of constructive interference and some destructive interference when the waves cross paths.

Waves A and B are similar but out of phase. The displacement of Wave A is always opposite that of Wave B. When the waves cross paths, they interfere, but the amplitude of each wave cancels out the other. This is called destructive interference.

Career Corner: Acoustical Engineering Acoustical engineers apply their understanding of the physics of sound (acoustics) to minimize or maximize the behavior of sound waves. They may apply this understanding to the construction of a recording studio or concert hall. For example, in a recording studio sound waves may reﬂect from the walls of the room, creating an unwanted reverberation. An acoustical engineer may cover the walls in a specialized foam padding to absorb some of the sound wave energy so that it does not reverberate as much in recordings.

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Similarly, an acoustical engineer may want to enhance the behavior of sound waves in a large, outdoor music pavilion. For example, sound waves may refract in unwanted ways if they travel from a colder region to a warmer region in the pavilion, causing “dead zones” where no music can be heard. An acoustical engineer may want to position speakers and audience seats to account for this behavior so that no audience seats will be located in dead zones. Furthermore, sound waves will diffract and decrease in quality as they travel around barriers between the sound source and audience members. As a result, an engineer may want to design a stadium seating venue so sound will not diffract through many audience members before reaching listeners in the back. The Doppler Effect Earlier you reﬂected on what happens when a police car moves past you. As the car approaches, its siren has a high-pitched sound. As the car passes, the siren’s pitch seems to decrease. This phenomenon is called the Doppler effect. The Doppler effect is the apparent change in frequency of a wave moving relative to an observer. It happens when the source of a wave is moving and an observer is standing still. It also happens when the observer is moving and the wave source is still.

Look Out If the police car were at rest, the siren would release sound waves at a particular frequency, and each wave would travel a particular distance before the next wave is released. The waves would move away from the car at the speed of sound in air. However, when a police car approaches a stationary observer, the source of the sound wave is moving relative to the observer. As a result, the apparent distance between each sound wave decreases. As this happens, it will appear to the observer that the sound waves are arriving more frequently. In other words, it will appear that the frequency of the pitch is higher than it would be if the police car were stationary. Conversely, when the police car passes by and begins moving away from the observer, the distance between successive sound waves appears to increase. Thus, it will appear to the observer that the sound waves are arriving less frequently, so the sound’s pitch will appear to be lower. A police car with a siren moves to the right. Each circle represents a sound wave from the siren. As the siren moves toward an observer on the right, the distance between waves is shortened, so an observer will notice a higher pitched frequency. An observer on the left will notice a lower pitched frequency.

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The Doppler effect is commonly observed with sound waves, though it is also observed in water waves when objects such as boats or animals move through water. Furthermore, it is observed with light waves that are emitted from moving sources.

What Do You Know? The higher the frequency of the sound, the higher the pitch. Similarly, the slower the frequency of the sound, the lower the pitch.

What Do You Think? An astronomer observing objects in deep space notices that electromagnetic radiation from a distant star appears to have a lower frequency than it is expected to have. This is called redshift because the frequency is shifted toward the red end of the visible light spectrum. What could redshift indicate about the motion of a star? You can check your answer on the next page. Resonance Have you ever wondered why a tuned guitar string always produces a particular sound? No matter how quickly or forcefully you pluck the string, it produces the same pitch. The reason for this is called resonance. To understand resonance, you must know that sound waves with larger amplitudes produce louder sounds, while sound waves with smaller amplitudes produce softer sounds. Resonance occurs when an object or a system oscillates at a large amplitude only when it is oscillating at a certain frequency or frequencies. Resonance occurs when a wave The frequencies that cause the system to oscillate at a large oscillates at its resonant frequency, amplitude are called resonant frequencies. Consider the guitar ω0. At this frequency, the wave will string. When it is plucked, it will vibrate with a large amplitude have a large amplitude. at its resonant frequency. This means that it will produce a loud sound with one particular frequency, or pitch. The string may vibrate at other frequencies, but the amplitudes of those vibrations will be much smaller, so those frequencies of sound may be too soft to hear. Other musical instruments, such as trumpets, ﬂutes, and pianos, work in the same way. For example, air will vibrate through chambers of a brass instrument at a particular set of resonant frequencies. The musician must vibrate his or her lips at one of these frequencies through the mouthpiece of the instrument in order to cause the air in the chambers to vibrate. If the musician does not vibrate his or her lips at one of these frequencies, the air will not vibrate very loudly, and no sound will be heard. Resonance is also observed in buildings and bridges. Different structures have resonant frequencies at which they will vibrate. Engineers must understand resonance to ensure that the wind does not cause the structure to vibrate at a resonant frequency and collapse.

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In 1940, the Tacoma Narrows Bridge in Washington state collapsed due to vibrations at resonant frequency. You can search for videos of the collapsing bridge online.

What Do You Think? Redshift is an example of the Doppler effect as it applies to visible light waves. As explained previously, if a source of sound waves emits waves at a lower frequency than expected, the source must be moving away from the observer. Similarly, if a star is emitting light waves at a lower frequency than expected—that is, if a star is exhibiting redshift—it must be moving away from observers on Earth. Mechanical waves and electromagnetic waves transport energy in the world around us. Mechanical waves are caused by a disturbance or vibration in matter, whether solid, gas, liquid, or plasma. The matter that a wave travels through is called a medium. Two examples of mechanical waves are waves in water and sound waves in air. A water wave is formed by vibrations in a liquid, and a sound wave is formed by vibrations in a gas (air). These mechanical waves travel through a medium by causing the molecules to bump into each other, like falling dominoes transferring energy from one to the next. Sound waves cannot travel in the vacuum of space because there is no medium to transmit these mechanical waves. The strength of a wave is dependent upon the energy of the wave. The energy relates to the wavelength and the frequency of the wave. The shorter the wavelength and higher the frequency, the higher the energy. The longer the wavelength and the lower the frequency, the lower the energy. Waves are grouped by how they behave. All waves have repeating patterns that give them each a shape and length, which we use to describe wave behavior and, therefore, categorize waves according to these descriptions. Waves change their behavior as they travel through different types of matter. To apply these wave properties, we must first understand how each wave is measured. Do you see any characteristics in the waving rope above that might help us describe a wave? Wave behavior is measured by the distance between peaks (wavelength), the size of the peak (amplitude), and the speed of the peaks (frequency). Sound and earthquake tremors are examples of how waves appear and are measured differently. These and other waves move at different speeds in different materials.

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What Do You Know? How do you think these processes can be mathematically modeled? The following formula shows the connection between velocity (V), wavelength (ʎ), and frequency (f). V=ʎ∙f

Two waves cross a path in a medium, as shown below. Determine whether the interference is constructive or destructive at each location indicated. A. B. C. D.

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Connecting With Your Child Investigating Wave Behavior With a Spring To help students learn more about various wave behaviors— including reflection, interference, and resonance—have them observe the behavior of a long spring. For this investigation, a A transverse wave moves helical spring is best but a long traditional spring or a spring toy perpendicular to the direction of will also work. First, challenge your child to produce a transverse its vibrations. wave along the spring. This can be done by quickly moving one end of the spring up and down or left and right. A transverse pulse will then travel along the spring as a wave. To observe a reflected wave, have your child fix one end of the spring to a stationary object (such as a table). Then have your child produce a transverse pulse along the free end of the spring. He or she should notice that the pulse travels to the fixed end and is then reflected back to the free end. To observe interference, two people must hold opposite ends of the spring. To produce constructive interference, each person must produce a pulse in the same direction. For example, both people must move their hand up and then down to produce the pulse. Your child should notice that the waves add together when they meet, producing a pulse that is the sum of the height of each individual pulse. Similarly, to observe destructive inference, one person must produce a pulse that is in the opposite direction of the other pulse. For example, if one person moves his or her hand up and then down, the second person would move his or her hand down and then up. Your child should notice that the pulses cancel each other out when they meet. Finally, to observe resonance, your child will create a standing wave. Explain that a pulse produced at a certain frequency causes a standing wave that travels along the spring and then reflects back. When the pulse is produced at particular frequencies, the pulse will appear to be vibrating in one position along the spring. To produce a basic standing wave, have your child fix one end of the spring to a table. Then have your child produce a continuous pulse so the middle part of the spring begins to oscillate up and down in a steady rhythm. Your child can create additional standing waves by creating a faster pulse (at a higher frequency). Here are some questions to discuss with your child: 1. What happens when you fix one end of the spring and then produce a single pulse on the free end? What is this called? 2. When two identical pulses are produced at each end of the spring, what happens when the pulses meet? What happens when the pulses are opposite one another? What is this called? 3. When a trumpet player vibrates her lips at a particular frequency into the mouthpiece of a trumpet, air begins to vibrate through the trumpet at this frequency. This produces a sound with a particular pitch. How is this similar to the standing waves that you observed on the spring?

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Reading Science Name:

Date:

Group:

The Electromagnetic Spectrum and Redshift 1

Astronomers use spectral analysis to investigate the spectrum of incoming light from distant celestial objects to determine their composition, age, surface gravity, and motion. The spectrum consists of all of the invisible and visible wavelengths of electromagnetic radiation. Telescopes are mounted with special spectroscopes that capture the incoming light from, for example, distant stars or galaxies.

Astronomers know that when certain chemicals are heated or charged, they emit radiation in specific wavelengths as emission or absorption lines (dark bands). Spectral analysis also shows if an object is moving toward or away from Earth by the change in the frequency of the wavelength, which appears as a shift in the emission and absorption lines to the blue or red end of the spectrum. A shift toward the blue end means the object is moving closer, while a shift to the red end of the spectrum means it is moving away from Earth.

The shift is based on the same principle as the Doppler effect when the sound of an approaching train whistle seems to go higher in pitch as the sound waves are compressed. The sound of a departing train whistle seems to go lower in pitch as the sound waves are stretched out. The same phenomenon occurs with approaching wavelengths of light from a distant object that compress into a shorter frequency toward the blue end of the spectrum, while the light from receding objects appears to have a longer frequency toward the red end of the spectrum, thus the term “redshift.”

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Reading Science 4

Astronomers measure redshift by using spectroscopy. When the white light from a distant star or galaxy passes through a prism, it separates into its various rainbow wavelengths (spectrum). If the absorption or emission lines are shifted, they know the object is moving toward or away from Earth.

Astronomers use the redshift parameter Z. This is calculated using the following equation: z = (λobserved - λrest) /λrest where λ observed = observed wavelength of a spectral line λ rest = wavelength the spectral line would have if its source was not in motion z = redshift parameter

For example, if a galaxy emits a wavelength of light that is 400 nm (violet), by the time it reaches us, the wavelength is redshifted to 2000 nm in the infrared. You can calculate the Z parameter as Z = (2000 - 400)/400. So that Z parameter = 1600/400 or 4.

With a Z parameter of 4, the light from a galaxy traveled 12.094 billion years and is 20.745 billion years away. Due to the expansion of the universe since the light left the distant object, it is now farther away. As the universe expands, space between galaxies expands. The more distance between Earth and a galaxy, the faster it will appear to be moving away. Astronomer are careful to realize that, the galaxy itself is not traveling so fast. Its motion away from us is due to the expansion of the space between us.

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Reading Science 1.

All the wavelengths of visible and invisible light make up the _________. A.

redshift

cosmological constant

astronomical unit

electromagnetic spectrum

How do astronomers determine properties of celestial objects such as composition, age, and distance? A.

Light-year analysis

Spectral analysis

Telescope analysis

Celestial analysis

How do astronomers determine if a celestial object is moving away? A.

The spectral lines shift toward blue.

The spectral lines shift toward red.

The spectral lines stay constant.

The spectral lines shift toward black.

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Reading Science 4.

How do astronomers know if a celestial object is moving toward Earth? A.

AThe spectral lines shift toward blue.

The spectral lines shift toward red.

The spectral lines stay constant.

The spectral lines shift toward black.

In the table in Image 2, all of the distances that light has traveled are different from the actual distance of the object. How can that be? A.

Margin of error occurred.

The object is smaller than it appears.

The object is larger than it appears.

Space is expanding.

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Math Connections Name:

Date:

Group:

Use the following information to answer questions 1–4. The speed of a wave can be calculated using the equation v = f x λ, where v is the wave speed in meters/second, f is the frequency in Hz, and λ is the wavelength in meters. 1.

Middle C, also known as Do on the fixed do-solfège scale, is a note used when playing or singing music. The frequency of Middle C is 261.63 Hz and the wavelength is 131.87 cm. What is the speed of sound for Middle C?

Dolphins communicate using various sounds including whistles, clicks, and squeaks. Lower frequency vocalizations are likely used in social communication, and high frequency vocalizations are likely used in echolocation. If a dolphin is producing a vocalization with a frequency of 35 Hz, traveling at 1500 m/s, what is the wavelength of the sound?

A sound wave with a wavelength of 2.5 m, travels 660 m in 2 sec. Calculate the frequency of the wave. (To calculate the speed of sound, remember: speed = distance/ time.)

A tsunami is a series of huge waves caused by earthquakes under water. If a tsunami is traveling at 970 km/h with a wavelength of 450 km, what is the frequency of the wave?

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Math Connections Use the following information to answer questions 5–8. The frequency of a wave is the number of cycles in a given unit of time. The number of cycles in one second is called one Hertz (Hz). The period of a wave is the time it takes a wave to complete one cycle (two successive waves passing through the same point) and is measured in seconds. The table below shows several wave frequencies and their corresponding periods. Frequency (Hz) 0.5 1 5 10

Period (seconds) 2 1 0.2 0.1

Plot the given points on the graph below.

Create an equation to describe the relationship between a wave’s frequency and period.

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Math Connections 7.

The D string on a violin has a frequency of 293 Hz when it is in tune. Calculate the period.

In a classroom demonstration, students are using a slinky to observe and learn about wave properties. If the slinky has a period of 0.333 seconds, what is the frequency?

Use the following information to answer questions 9–10. The amplitude of a wave is the distance from the equilibrium position to the top of a crest or to the bottom of a trough. It is measured in meters. The amplitude helps to describe how much energy is in a wave; greater amplitude means greater energy to produce the wave. 9.

Look at the graph below. What is the amplitude? How do you know?

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Math Connections 10. Look at the following graphs and their equations. Fill in the amplitude for each figure. Figure 1.

Figure 2.

Equation of Wave: y = 2sin(2x)

Equation of Wave: y = 4sin(1/2x)

Amplitude:

Figure 3.

Figure 4.

Equation of Wave: y = 4cos(5x)

Equation of Wave: y = 2.5cos(3x)

Amplitude:

11. What is the relationship between the function describing a wave and its amplitude?

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WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK Binaural beats are said to be therapeutic and can increase concentration. The process of binaural beats involves playing a certain frequency in one ear and a close, but different, frequency in the other ear. For example, in your left ear you could be listening to a tone at a frequency of 125 Hz, while in the left ear you could be listening to a tone of 130 Hz. The difference of the two tones is 5 Hz and that is the beat that you would hear. Some people argue that since music can have different frequencies present in a single song, the sound waves used in binaural beats would not create a separate beat in your brain. WRITE Construct an argument to either defend or debunk the process of binaural beats based on the characteristics and production of sound waves. Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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WRITING SCIENCE

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High School Physics

P4BG

Interference and Diffraction of Waves

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P4BG Interference and Diffraction of Waves

Student Handout Name:

Date:

A fundamental law of physics is that two objects cannot occupy the same space at the same time. The same is not true of waves. Since waves are actually energy that propagates through space, two or more waves can pass through each other without being affected. The point where the waves pass each other is called interference. The oscillating medium or field is affected by both waves passing. The effect is the sum of the amplitudes of the waves at that point. Interference can be constructive or destructive. Constructive interference is when the crest of one wave meets the crest of another, increasing the wave’s amplitude. Destructive interference is when the crest of one wave meets the trough of the other, decreasing the wave’s amplitude. Practice making sharp pulses with the spring on the floor. Then make two pulses simultaneously, one from each end, so that the pulses meet in the middle. Do several trials each with the pulses on the same side and with the pulses on opposite sides. Safety note: Keep the spring in contact with the floor or table to avoid damaging it. Sketch what the spring looked like when the pulses met on the same side and when they met on opposite sides.

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P4BG Interference and Diffraction of Waves

Student Journal Name:

Date:

Group:

Part I: Single- and Double-Slit Experiments 1.

What is the appearance of the wave in the wave pond when the water is dripping?

Sketch the wave on the graph below.

What is the appearance of the wave in the wave pond when the water is dripping and there is only one slit?

Sketch the wave pattern in the tank. Don’t forget to include the slit!

What is the appearance of the wave in the wave pond when the water is dripping and there are two slits?

Sketch the wave pattern in the tank. Don’t forget to include the slits!

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P4BG Interference and Diffraction of Waves

Student Journal Part I: Single- and Double-Slit Experiments, continued 7.

What is the appearance of the wave in the wave pond when the water is dripping and the double slit is set very narrow?

Sketch the wave pattern in the tank. Don’t forget to include the slit!

What is the appearance of the wave in the wave pond when the water is dripping and the double slit is very wide?

10. Sketch the wave pattern in the tank. Don’t forget to include the slits!

Part I Analysis 1.

What was the difference between the single-slit wave pattern and the double-slit wave pattern?

Why did the wave propagate in a fan-like pattern for the single slit? Why did it not travel in a straight line?

Why did the double slit produce a double-fan pattern?

In the narrow double slit, what property caused the change in pattern, interference or diffraction? Give evidence in support of your answer.

In the wide double slit, there was almost no change in the wave pattern. Why?

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P4BG Interference and Diffraction of Waves

Student Journal Part II: Lasers and Diffraction 1.

What is the distance from the diffraction grating to the wall in centimeters?

What is the distance from the 0 dot to the 1 dot in centimeters?

What is the distance from the 0 dot to the 2 dot in centimeters?

Using tan-1, determine the angle of light for diffraction beam 1.

Using tan-1, determine the angle of light for diffraction beam 2.

What is the wavelength of your laser pointer?

What is the distance for the slits of your diffraction grating using the angle for dot 1?

What is the distance for the slits of your diffraction grating using the angle for dot 2?

How much difference is there in your two sets of measurements?

Part II Analysis 1.

Compare your results with the results from another group. How close is your data?

What caused the difference in your numbers and their numbers?

What would be the difference in the diffraction pattern if a shorter wavelength laser pointer (like blue or violet) had been used instead?

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STEMscopedia: INTERFERENCE AND

DIFFRACTION OF WAVES P4BG

Reflect Did you know that you observe waves interacting with each other on a regular basis? Not just at the beach, but EVERYWHERE! Consider these common events: • • • •

As a police siren approaches, the siren has a high pitch. Then as the siren passes, its pitch appears to decrease. After a rainstorm, people can see a rainbow in the sky as the Sun emerges from behind clouds. When a woman yells over a large canyon, she can hear an echo of her voice. On a hot, sunny day, a distant location along a road appears to be wet. However, when one approaches the location, the road is completely dry.

All of these happen because of wave interactions. We know that waves travel in straight lines and oscillate. It is the oscillation (repeated vibrations) that cause the waves to behave the way they do. Waves are very interesting, and we can only detect them via seeing and hearing. What are some different ways that waves can behave? How does our understanding of wave behavior help explain various phenomena in the world? When waves interact, they do so by reflecting, refracting, and diffracting. Reflection The most commonly observed wave behavior is reflection. You observe this phenomenon whenever you see your image in a mirror or a glass window, or on the surface of a lake. Reflection occurs whenever a wave strikes a boundary between two media, such as air and water, and then bounces back into the medium from which it originated. For example, when light travels through the air and strikes the surface of a lake, some of the light is reflected at this boundary. Light reflecting off a lake’s surface can cause a bright glare on a lake or an ocean on a sunny day. It is also the reason we can observe the images of objects in water. Similarly, sound waves reflect off surfaces, creating a reverberation—or an echo—effect. The reflection of waves from a boundary is similar to the way a billiard ball strikes and bounces away from a wall. If a ball strikes The reflection of hot air balloons is seen on a wall “head on” (meaning it is traveling perpendicular to the wall), the syrface of a stilllake. Some of the light that has reflected from the hot air balloon the ball will bounce back in exactly the same direction from which travels through the air to the lake. When it traveled. However, if a ball strikes a wall at an angle to the this light strikes this boundary, some of it reflects back into the air. This causes an perpendicular (called the angle of incidence), it will bounce away image of the hot air balloon to appear on from the wall at the same angle to the perpendicular (the angle of the lake surface. reflection). Waves behave in the same way, as shown below. In fact, this is called the law of reflection. While a wave’s direction changes during reflection, its speed does not.

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STEMscopedia: INTERFERENCE AND

DIFFRACTION OF WAVES A wave (red arrow) strikes a barrier (blue line) at an angle θi to the perpendicular line. This is the angle of incidence. The wave bounces away at an angle of θr. The law or reflection states that the angle of incidence is equal to the angle of reflection.

Look Out Light reflects off of things in different ways. Some frequencies (colors) are absorbed, and some are reflected. Only reflected frequencies are seen. For instance, grass reflects green and absorbs all other visible light. This is why the grass appears green to us. Refraction A wave can also be transmitted through a boundary, meaning that it passes through the boundary from one medium to another. In fact, at most boundaries, part of the wave is reflected and part is transmitted. Most waves move at different speeds through different media. For example, light moves quickly through air, but more slowly through water. Thus, waves change speeds as they transmit from one media to another. This change in speed usually causes a wave to refract, or bend, as it passes through the boundary. To understand how refraction happens, think of a light wave as a group of students marching shoulder to shoulder from the bottom left corner of a room to the top right corner. Imagine that the left side of the room is one medium, such as air, and the right side of the room is another medium, such as water. As they march diagonally across the room, they step at the same pace. However, once they pass over the boundary into the right side of the room, they begin to walk more slowly through the new medium. Because the entire group approaches the boundary at an angle, one person will cross the boundary first and begin walking more slowly on the right side, but the rest of the group will continue walking at the faster pace on the left side. This will cause the line of students to swing into a new direction, pivoting around the first student to cross over the boundary. Then, as the remainder of the students pass into the slower medium, they will begin walking at the slower pace, and the students will march in a straight line again. The black dots in this diagram represent a group of students marching across a room. The students represent a light wave. The left side of the room represents air (a relatively fast medium), and the right side represents water (a relatively slow medium). When the students pass from left to right, one student crosses the boundary first. This student begins moving slowly, but the rest of the group still travels quickly, causing the students to change direction, or bend, as they move into the new medium. This is know as refraction.

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STEMscopedia: INTERFERENCE AND

DIFFRACTION OF WAVES

A wave behaves in the same way as the marching students. If it transmits from one medium to another at an angle to the medium, it will refract and change directions. (Note that if it strikes the new medium “head on,” it will not change directions.) Refraction causes white light from the Sun to spread out into different colors as it passes from air into new media, such as water or glass. For example, the different wavelengths of sunlight all refract at different angles when they pass through a raindrop. This causes sunlight to spread out into a rainbow as it refracts through raindrops after a storm. Diffraction and Interference Have you ever watched water waves pass through a narrow slit in a barrier? When the waves pass through, they spread out radially. This is known as diffraction. For example, when a light bulb is turned on in a dark room, light waves spread out radially from the light bulb. However, once the waves have traveled a certain distance, they can be thought of as plane waves that move in parallel “sheets,” like in the image on the right. When a plane wave passes through a narrow slit or a barrier, the wave will act as though it is originating from a point source again. Thus, the wave spreads out, or diffracts. This is how you can hear sound from someone in another Plane waves (left) spread out radially (right) room or see a light from around a corner This can also when they pass through a slit in a barrier. happen when a wave approaches a solid barrier. In these cases, when the wave passes along any edge of the barrier, it will spread out radially around the barrier. In this way, waves will appear to “bend” around barriers. An interesting aspect of wave behavior is that two waves can occupy the same space at the same time. This is called a superposition of waves. The same types of waves can superimpose whenever they cross paths through the same medium. For example, if two sound waves cross paths in the air, they will superimpose. When this happens, interference will occur. Interference is the net effect of two or more superimposed waves. Recall that the amplitude, or displacement, of a ave changes depending on where the wave is in its cycle. When the displacement of two waves is in the same direction, their amplitudes add togetherand constructive interference takes Waves A and B are identical to one place. So if two identical sound waves interfere with one another, another, meaning the parts of each the amplitudes of the waves add together and the sound wave are displaced in the same becomes louder. Similarly, if two identical light waves interfere, directions. When they cross paths, the amplitudes add together and the light appears brighter. they interfere, and the amplitude of Sometimes, however, two waves with very similar characteristics each wave adds together. This is called constructive interference. are out of phase with each other. (The phase of a wave simply refers to its position in the wave cycle.)

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STEMscopedia: INTERFERENCE AND

DIFFRACTION OF WAVES

If two waves begin their cycles at the same time, for example, they will be in phase with each other. However, if one wave begins its cycle first and then another wave begins slightly later, the waves will be out of phase. In this case, when the waves interfere, the displacement of each wave might cancel the other one out. When the displacement of waves is in opposite directions, destructive interference takes place. Most waves in the real world are out of phase with each other to some extent. In these cases, there will always be some amount of constructive interference and some destructive interference when the waves cross paths. This is how noise-canceling headphones work. It takes in the waves coming into the headphones and emits an opposite wave to create destructive interference.

Waves A and B are similar to each other but out of phase. The displacement of Wave A is always opposite that of Wave B. When the waves cross paths, they interfere, but the amplitude of each wave cancels out the other. This is called destructive interference.

The Doppler Effect Earlier you reflected on what happens when a police car moves past you. As the car approaches, its siren has a high-pitched sound. As the car passes, the siren’s pitch seems to decrease. This phenomenon is called the Doppler effect. The Doppler effect is the apparent change in frequency of a wave moving relative to an observer. It happens when the source of a wave is moving and an observer is standing still. It also happens when the observer is moving and the wave source is still. If the police car were at rest, the siren would release sound waves at a particular frequency, and each wave would travel a particular distance before the next wave is released. The waves would move away from the car at the speed of sound in air. However, when a police car approaches a stationary observer, the source of the sound wave is moving relative to the observer. As a result, the apparent distance between each sound wave decreases. As this happens, it will seem to the observer that the sound waves are arriving more frequently. In other words, it will appear that the frequency of the pitch is higher than it would be if the police car were stationary. Conversely, when the police car passes by and begins moving away from the observer, the distance between successive sound waves seems to increase. Thus, it will appear to the observer that the sound waves are arriving less frequently, so the sound’s pitch will seem lower. A police car with a siren moves to the right. Each circle represents a sound wave from the siren. As the siren moves toward an observer on the right, the distance bwtween the waves is shortened, so an observer will notice a higher-pitched frequency. An observer on the left will notice a lower-pitched frequency.

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STEMscopedia: INTERFERENCE AND

DIFFRACTION OF WAVES

Resonance Have you ever wondered why a tuned guitar string always produces a particular sound? No matter how quickly or forcefully you pluck the string, it produces the same pitch. The reason for this is called resonance. To understand resonance, you must know that sound waves with larger amplitudes produce louder sounds, while sound waves with smaller amplitudes produce softer sounds. Resonance occurs when an object or a system oscillates at a large amplitude only when it is oscillating at a certain frequency or frequencies. The frequencies that cause the system to oscillate at a large amplitude are called resonant frequencies. Consider the guitar string. When it is plucked, it will vibrate with a large amplitude at its resonant frequency. This means that it will produce a loud sound with one particular frequency, or pitch. The string may vibrate at other frequencies, but the amplitudes of those vibrations will be much smaller, so those frequencies of sound may be too soft to hear. Other musical instruments such as trumpets, flutes, and pianos work in the same way. For example, air will vibrate through Resonance occurs when a wave chambers of a brass instrument at a particular set of resonant oscilates at its resonant frequency, ω0. frequencies. The musician must vibrate his or her lips at one of At this frequency, the wave will have a these frequencies through the mouthpiece of the instrument in large amplitude. order to cause the air in the chambers to vibrate. If the musician does not vibrate his or her lips at one of these frequencies, the air will not vibrate very loudly, and no sound will be heard. Resonance is also observed in buildings and bridges. Different structures have resonant frequencies at which they will vibrate. Engineers must understand resonance to ensure that the wind does not cause the structure to vibrate at a resonant frequency and collapse. In 1940, the Tacoma Narrows Bridge in Washington state collapsed due to vibrations at resonant frequency. You can search for videos of the collapsing bridge online.

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STEMscopedia: INTERFERENCE AND

DIFFRACTION OF WAVES

Try Now Observe the image below.

Label A, B, C, and D as constructive or destructive interference and indicate whether each would sound louder or softer. A. B. C. D.

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STEMscopedia: INTERFERENCE AND

DIFFRACTION OF WAVES

Connecting With Your Child Investigating Wave Behavior With a Spring To help students learn more about various wave behaviors— including reflection, interference, and resonance—have them observe the behavior of a long spring. For this investigation, a helical Image 10 goes here spring is best, but a long traditional spring or a spring toy will also work. First, challenge your child to produce a transverse wave along the spring. This can be done by quickly moving one end of the spring up and down or left and right. A transverse pulse will then travel alongthe spring as a wave.

A transverse wave moves perpendicular to the direction of its vibrations.

To observe a reflected wave, have your child fix one end of the spring to a stationary object (such as a table). Then have your child produce a transverse pulse along the free end of the spring. He or she should notice that the pulse travels to the fixed end and is then reflected back to the free end. To observe interference, two people must hold opposite ends of the spring. To produce constructive interference, each person must produce a pulse in the same direction. For example, both people must move their hand up and then down to produce the pulse. Your child should notice that the waves add together when they meet, producing a pulse that is the sum of the height of each individual pulse. Similarly, to observe destructive interference, one person must produce a pulse that is in the opposite direction of the other pulse. For example, if one person moves his or her hand up and then down, the second person would move his or her hand down and then up. Your child should notice that the pulses cancel each other out when they meet. Finally, to observe resonance, your child will create a standing wave. Explain that a pulse produced at a certain frequency causes a standing wave that travels along the spring and then reflects back. When the pulse is produced at particular frequencies, the pulse will appear to be vibrating in one position along the spring. To produce a basic standing wave, have your child fix one end of the spring to a table. Then have your child produce a continuous pulse so the middle part of the spring begins to oscillate up and down in a steady rhythm. Your child can create additional standing waves by creating a faster pulse (at a higher frequency). Here are some questions to discuss with your child: 1. What happens when you fix one end of the spring and then produce a single pulse on the free end? What is this called? 2. When two identical pulses are produced at each end of the spring, what happens when the pulses meet? What happens when the pulses are opposite one another? What is this called? 3. When a trumpet player vibrates her lips at a particular frequency into the mouthpiece of a trumpet, air begins to vibrate through the trumpet at this frequency. This produces a sound with a particular pitch. How is this similar to the standing waves that you observed on the spring?

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P4BG Interference and Diffraction of Waves

Reading Science Name:

Date:

Group:

Doppler Effect and the Universe 1

In 1842, Christian Doppler proposed that there is a change in frequency of a wave depending on the motion of the observer relative to the source of the wave. The observed frequency is higher than the emitted frequency when the source is moving toward the observer. The observed frequency is equal to the emitted frequency at the instant of passing by, and the observed frequency is lower than the emitted frequency when the source is moving away from the observer.

We are most familiar with the Doppler effect as it relates to sound. As a police car approaches, the sound waves generated by its siren are compressed. The waves reach your ears with higher frequency, and you hear them as higher pitched. Once the police car passes, the sound waves reaching your ear are stretched apart, reaching your ear with lower frequency. You hear the sound as being lower pitched. As frequency and wavelength have an inverse relationship, higher frequency sound has a shorter wavelength, while lower frequency sound has a longer wavelength. Velocity of the sound wave depends on the medium, so it is not affected by the relative motion of source and observer. The loudness of the siren, or amplitude of the wave, depends on the amount of energy the siren has.

Light waves behave similarly, although sensitive instruments are required to detect the shifts in wavelength. Telescopes, such as the Hubble telescope in orbit, detect light from stars and galaxies. If a star is approaching Earth, its light will be shifted toward higher frequency blue light. This phenomenon is known as blueshift. On the other hand, if a star is moving farther away from Earth, the light coming from it will be shifted toward lower frequency. Since red light has the lowest frequency in the visible spectrum, the light will be redshifted.

Telescopes in space have several advantages over telescopes on Earth. Earth’s atmosphere absorbs much of the infrared and ultraviolet light making it impossible for Earth-mounted telescopes to use these frequencies to study stars and planets. Furthermore, atmospheric turbulence limits the sharpness of images. The disadvantage of space telescopes is that they are very difficult to upgrade and repair.

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Reading Science 5

Astronomers studying the dimensions of the universe use the shift in frequency to determine the direction of motion of stars and galaxies relative to Earth. All galaxies seen from Earth display a redshift, meaning that they are moving away from us. Moreover, galaxies located farther from Earth have a stronger redshift. So the farther a galaxy is from us, the faster it is moving away from us.

Studying the light coming from stars shows that the universe is expanding. The rate of expansion appears to be increasing with time. Whether the universe will continue to expand indefinitely or reverse direction and contract again is not clear at this time. What is clear is that no one alive today will have to worry about being part of the next Big Bang, if there is one!

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P4BG Interference and Diffraction of Waves

Reading Science 1.

The Doppler shift can be defined as – A.

change in amplitude of a wave depending on the relative motion of wave source and A receiver.

change in frequency of a wave depending on the relative motion of wave source and A receiver.

A change in quality of a wave depending on the relative motion of wave source and receiver.

A change in energy of a wave depending on the relative motion of wave source and receiver.

A siren in the middle of town warns of an approaching tornado. A student is in a car traveling directly away from the siren toward their house. How is the sound the student hears while in the car different from what a person hears standing right next to the siren? A.

The student hears a lower pitched sound.

The student hears a higher pitched sound.

The student hears the same pitch.

The student hears a louder sound.

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Reading Science 3.

Most people have experienced the Doppler shift and sound waves, but humans don’t have direct experience with the Doppler shift and light waves. Why? A.

Only light from stars is subject to the Doppler shift.

Earth’s atmosphere blocks the Doppler shift.

The Doppler shift is too large for humans to perceive.

The human nervous system is not sensitive enough to detect the Doppler shift in light waves.

Proxima Centauri is one of the stars nearest Earth. Its light is redshifted. Therefore, it is – A.

Moving away from Earth.

Moving toward Earth.

Moving parallel to Earth.

Stationary with respect to Earth.

While Proxima Centauri is relatively close to Earth, Procyon A is farther away. Which star’s light has a larger redshift? A.

Procyon A

Proxima Centauri

Neither, their redshifts will be the same

Can’t be answered from the information provided

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Reading Science 6.

What are advantages of telescopes in space as opposed to telescopes on Earth? A.

They are easier to repair.

They can be bigger.

They can detect unimpeded infrared and ultraviolet light.

They are sturdier.

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P4BG Interference and Defraction of Waves

Math Connections Name:

Date:

Group:

Use the following information to answer questions 1–8. Diffraction, reflection, refraction, resonance, and interference all describe different wave behaviors. Match the following words with their definitions. 1.

______ Diffraction

a. The change in direction of a wave

______ Reflection

b. Occurs when frequency of forced vibrations on any object matches the object’s natural frequency and an increase in amplitude

______ Refraction

c. The bending of a wave around a barrier

______ Resonance

d. A pattern formed by the overlapping of two or more waves

______ Interference

e. The bouncing back of a particle or wave

What is the Doppler effect?

What happens to the conical angle of the shock wave of a supersonic aircraft when the aircraft gains speed?

How far behind the mirror is Samantha’s image if she is 1.7 m tall and is standing 8 m from that flat mirror?

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P4BG Interference and Defraction of Waves

Math Connections Use the following information to answer questions 9–10. Refraction is the bending of the path of a light wave as it passes through the boundary separating two media, that is, air and water. We can measure how much the light refracts as it crosses that boundary. The incident ray is a ray that shows the direction that light travels as it approaches the boundary. The refracted ray is a ray that shows the direction that light travels after it crosses the boundary. The angle that the incident ray makes with the surface of the boundary is called the angle of incidence, and the angle that the refracted ray makes with the boundary line is called the angle of refraction. θr = angle of refraction θi = angle of incidence n = index of refraction 9.

θr = θi nsinθi = n’sinθr

Krista is playing with the newly installed light beams in her front yard. She notices that one of the beams is aimed towards the front bedroom window at a 45° angle with the ground (n = 1.23 and n’=1.54). Find the following: a. The angle to the ground (normal) of the light beam after being refracted on the glass window (Once sinθr is found, take the inverse to find θr.):

b. The angle to the ground (normal) of the light beam after it exits the other side of the glass into the air:

10. A shark is swimming around and looks up at the fish ahead at a 20° angle to the water’s surface (normal: n = 1.45). Find the following: a. Can the shark see into the air? If so, what is the shark’s line of sight outside the water? (Hint: n’ = 100) b. What if the angle is 45°? Calculate the shark’s line of sight outside of the water.

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P4BG Interference and Diffraction of Waves

WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK Diffraction is when a wave spreads out radially or bends as it moves around the edge of an obstacle. When looking at the picture of the water, you can see the waves are distorting what is seen under the moving water as it meets obstacles or slits. The characteristics of diffraction change in single and double slits. WRITE Discuss the differences between single and double slit diffraction in regard to their characteristics and the process by which diffraction is calculated. Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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WRITING SCIENCE

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High School Physics

P4EF

Light and Lenses

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P4EF Light and Lenses

Student Handout Name:

Date:

Directions: Look at your reflection on both sides of a silver spoon. 1. Describe your reflection when you looked at the concave side of the spoon.

Describe your reflection when you looked at the convex side of the spoon.

Flip the spoon around so you are staring into the concave side. Slowly bring it forward until you see a giant, magnified view of your nose. Describe what happened to the image in the spoon as you brought it closer:

Directions: Hold the plane mirror up to your face. 4. Describe the image that you see in the mirror.

Directions: Hold the plane mirror to the Teacher Supplemental. Angle it in such a way that the text becomes perfectly readable. 5. Describe the image that you see in the mirror.

Explain the difference between a convex mirror and a plane mirror.

A real image is always inverted. Virtual images are always upright. What type of image did the concave side of the spoon make: real or inverted?

What type of image did the convex side of the spoon and the plane mirror make: real or inverted?

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P4EF Light and Lenses

Student Journal Name:

Date:

Group:

Part I: Polarization 1.

How does your vision change when you look through one polarizing filter?

How does your vision change when you look through two polarizing filters that are properly aligned?

How does the image change when one of the filters is rotated 90 degrees?

Part II: Apparent Color of Light 1.

Move the red slider to its maximum setting. What color does the person see?

Click the orange reset button on the bottom right side. Move the green slider to its maximum setting. What color does the person see?

Click the orange reset button on the bottom right side. Move the blue slider to its maximum setting. What color does the person see?

Move the red slider to its maximum setting while blue is also at maximum. What color does the person see?

Move the green slider to its maximum setting while blue and red are also at maximum. What color does the person see?

Play around with the color sliders some more. Fill in the color wheel below.

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P4EF Light and Lenses

Student Journal Part III: Speed of Light and Refraction 1.

What is c as a property of light?

What is the speed of light in air?

How does the speed of light change as the color of light change?

What is the speed of light in water?

How does the light change from glass to water or water to air?

Notice the path of the light beam. What happens to its path as the material is changed?

Does the path change when the color of light is changed?

Part IV: Snell’s Law and Refraction 1.

What is the incident angle of light?

Using Snell’s law and the provided indexes of refraction, determine the angle of light after it passes into water.

Using the protractor, measure the angle of the light after it passes into water.

How accurate was your calculation compared to the measured value?

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P4EF Light and Lenses

Student Journal Plan Your Investigation My question of inquiry _______________________________________________________________________________ _______________________________________________________________________________ What do you need to do to answer this question? _______________________________________________________________________________ _______________________________________________________________________________ What are the variables that you will observe? _______________________________________________________________________________ _______________________________________________________________________________ What do you predict will occur? _______________________________________________________________________________ _______________________________________________________________________________ Tools and equipment _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ Safety precautions _______________________________________________________________________________ _______________________________________________________________________________ Procedure List the steps of your procedure. Use additional paper, as needed. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

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Student Journal Results 1.

Read your prediction from your plan. Was your prediction correct or incorrect? Explain.

Was there a relationship between the variables you observed?

_______________________________________________________________________________ _______________________________________________________________________________ 3.

Where could errors have been made while collecting or organizing data?

_______________________________________________________________________________ _______________________________________________________________________________ 4.

What do you conclude about this investigation?

What would you do differently if you were to conduct this experiment again?

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Student Journal Name:

Date:

Group:

Background 1.

What is an image?

What is a focal point? What is focal length?

Describe what you know about lenses, both concave and convex, and the images they form. Draw illustrations below to support your descriptions.

4. What is the difference between a real image and a virtual image? Explain your reasoning. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

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Student Journal Part I: Plan Your Investigation 1.

My question of inquiry

_______________________________________________________________________________ _______________________________________________________________________________ 2.

What do you need to do to answer this question?

_______________________________________________________________________________ _______________________________________________________________________________ 3.

What are the variables that you will observe?

_______________________________________________________________________________ _______________________________________________________________________________ 4.

What do you predict will occur?

_______________________________________________________________________________ _______________________________________________________________________________ 5.

Tools and equipment

Safety precautions

_______________________________________________________________________________ _______________________________________________________________________________ 7.

Procedure List the steps of your procedure. Use additional paper, as needed.

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Student Journal Part II: Implement Your Investigation Collect, Record, and Organize Data Station

Observations-1

Observations-2

Conditions:

A Focal Length: Conditions:

B Focal Length:

Conditions:

C Focal Length:

Conditions:

D Focal Length:

Conditions:

E Focal Length:

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Student Journal Part II: Implement Your Investigation, continued Analyze Data 1.

Compare and contrast your observations from Stations A, B, and C. What conclusions can you make about how focal length affects image formation? Make a claim, cite specific evidence, and explain your reasoning.

_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 2. At Station D, explain what happened to the ray of light as the convex lens moved back and forth. _______________________________________________________________________________ _______________________________________________________________________________ 3. At Station E, describe the image type (real or virtual), orientation (upright or inverted), and magnification when the object is three focal lengths away from a converging lens. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 4. Describe lenses you have encountered in your daily life. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 5. Name four careers that use lenses and describe how they use them. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 6. When you look through a glass window, the images of the objects outside the window do not appear to be distorted. What characteristics of a lens cause an image to be distorted? Explain. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 7. Summarize the similarities and differences between the images formed by convex lenses and the images formed by concave lenses. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

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Student Journal Reflections and Conclusions 1.

Read your prediction from Part I. Was your prediction correct or incorrect? Explain.

On a separate sheet of paper, use all of the following terms to develop a graphic organizer. Terms: real image, virtual image, concave lens, convex lens, focal length, focal point

Additional Practice 1.

A candle is positioned 10 centimeters from a thin convex lens that has a focal length of six centimeters. How far from the lens will the image appear?

An object is placed 15 centimeters from a thin convex lens and its image appears three centimeters from the lens. What is the focal length of the convex lens?

An object is located 30 centimeters from a thin convex lens with a focal length of 15 centimeters. How far from the lens will the image appear?

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STEMscopedia: LIGHT AND LENSES P4EF

Reflect Imagine what it would be like to wake up, look outside your window, and not be able to see all the colors of the rainbow. Surprisingly, about one in 12 males has some form of color blindness. About one in 200 women suffer from color blindness. What is color blindness? It is the decreased ability to see colors. There are different forms of color blindness—where it is difficult for people to see certain types of colors—such as red/green or blue/yellow. However, complete color blindness (the lack of ability to see any colors) is extremely rare. What kind of behavioral adaptations would you have to develop if you were color blind? What kind of situations would be tricky for you? Would there be situations that might be dangerous for you? Why? When we think about light, we cannot help but think about its many characteristics and the questions it invokes. How fast does light travel? Are there different types of light? What would happen without light? How is light related to color? How does light behave when it encounters something? What is the temperature of light? Color In order to understand what color is you must understand that color cannot be seen without light. In the absence of light, there are no colors. With dim light, colors look to be shades of gray and black. Light comes to your eyes directly from something that creates light or from something that has reflected light. What are examples of objects that produce light? Answers include natural sources such as the Sun, stars, fireflies, fires, lightning, and the aurora borealis. Man-made (or artificial) objects also produce light, such as electric lights, gas lamps, fireworks, and flashlights.

People commonly think of light as white light. In reality, there is a very large range of light called the electromagnetic spectrum. For the purposes of this companion, we will be referencing the small section of visible light. White light is the type of light we see most often. This kind of light comes from the Sun, lightning, and light bulbs. White light occurs when all the colors of the rainbow are combined. Isaac Newton was the first scientist to understand that white light was composed of red, orange, yellow, green, blue, and violet light. He refracted white light using a prism.

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STEMscopedia: LIGHT AND LENSES So, how do we actually see different colors of visible light? The color of light depends upon the energy level of light. The lowest energy of light is red, and the highest energy of light is violet. For example, think about a campfire that has just been started that burns with a red flame versus a grill with a blue gas flame that burns much hotter. What happens is that the atoms in the red flame move rapidly, but not nearly as rapidly as the atoms in the blue flame. Therefore, the blue flame has more energy.

How do varying amounts of energy help people differentiate between colors of light? Human eyes possess special cells that are sensitive to light called photoreceptors, which are special cells that detect light on the retina. People have two kinds photoreceptors: rods and cones. Rods specialize in black, white, and gray colors, and also excel when light is dim. Cones are the color experts. There are three types of cone detectors that respond to red, blue, and green light, respectively. The cones work together to create all the colors that normal, healthy human eyes can see. Depending upon which types of cone cells are stimulated by light and how much they are stimulated, the result is the color you see for each object. The light that is reflected off objects is the result of objects absorbing some colors and reflecting others. People see the colors that are reflected. People actually have superior black and white vision versus color vision. This is true because people have almost 20 times more rod cells than cone cells in their eyes! People have about 130 million rod cells and seven million cone cells in each eye.

Wavelength, Frequency, and Speed of Light The wavelength and frequency of visible light are inversely related. In other words, as wavelength increases, frequency decreases, and as frequency increases, wavelength decreases. Lower frequency waves have less energy, and higher frequency waves have more energy. Red light has a wavelength of 650 nm and a frequency of 462 THz, while violet light has a wavelength of 400 nm and 750 THz.

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STEMscopedia: LIGHT AND LENSES Energy Level

Color

Low Low Medium Medium Medium Medium High High

Red Orange Yellow Green Blue Violet

Wavelength (nm) 610-700 590-610 570-590 500-570 450-500 400-450

Frequency (THz) 450 500 520 550 650 750

To clarify, all light travels through a vacuum at the same speed (3.00 x 108 meters per second), regardless of color. Red light simply has a longer wavelength and a slower frequency, and violet light has a shorter wavelength and a faster frequency while traveling at the same speed. Polarization Polarization is the motion in which a wave oscillates. It is perpendicular (either horizontally or vertically) to the direction the wave is traveling. To simplify it, when a wave is traveling forward, it can be polarized up or down, or right or left. Therefore, light is a transverse wave, which is a wave that oscillates in a movement perpendicular to the direction the wave travels. However, most light appears to be unpolarized because it travels in all directions and oscillates in all directions. Thus, no single polarization governs light waves. Have you heard of polarized sunglasses? A polarizer permits light of only one polarization to pass through it. If light has passed through a polarizer, it then only possesses light with a single orientation of light. That light is defined as polarized light. Polarized sunglasses screen out the horizontal orientation of light and let the vertical orientation of light through. That makes it easier to see because the glasses block out much of the glare that reflects horizontally. Plane Mirrors In physics, a flat mirror is called a plane mirror. The law of reflection says that the angle of incidence equals the angle of reflection. Look at the image on the right to understand what each of the following terms means: normal line, incident ray, angle of incidence, angle of reflection, and reflected ray. • normal line: the line perpendicular to the mirror • incident ray: the ray of light that approaches and hits the mirror • angle of incidence: the measurement of the angle between the incident ray and normal line • angle of reflection: the measurement of the angle between the normal line and the reflected ray • reflected ray: the ray of light that that is reflected off the mirror and travels away from it

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STEMscopedia: LIGHT AND LENSES The diagram on the right shows how a plane mirror creates a virtual image. The symbols do and di represent the object distance and image distance, respectively, from the mirror. The symbols ho and hi represent the height of the object and the height of the image. The image is said to be virtual because it cannot be projected onto a screen. Note the orientation of the image; that is, the direction the image is facing relative to a defined point. The image, like the object, is upright. In addition, the image height is the same as the object height, and the image distance is the same as the object distance.

A plane mirror always produces an upright, virtual image that is the same size as the object.

Properties of Images Produced by a Plane Mirror Orientation Upright Height hi = ho Type Virtual A ray diagram is a diagram used to show how an image is formed by a mirror or a lens. In the diagram of a plane mirror, above, the lines show two light rays coming from the top of the object. One ray reflects back on itself, and the other ray reflects to the observer’s eye (in the lower-left corner of the diagram). Extensions of these rays through the mirror intersect at the top of the image. These extensions, which are not actual light rays, are shown with dashed lines. If similar rays were drawn from the bottom of the object, their extensions would intersect at the bottom of the image.

Look Out When you look in a mirror, your image seems to be reversed left to right. When you raise your right hand, the image raises its left hand, but what happens if you move your hand up and down? Your image also moves its hand up and down. How can a mirror reverse left and right but not up and down? It can’t. The answer to the puzzle is that your image in a plane mirror is not reversed left and right but it is reversed front to back. To understand this effect, hold your hand with the palm facing the mirror and think about how each point is reflected. Refraction Light travels at slightly different speeds through different materials. It is fastest through a vacuum. What happens when light is traveling through air on Earth and then shines through a glass of water? Because the air, glass, and water are all different media, the light behaves differently as it enters each of them. The law of diffraction (also known as Snell’s law) explains how the angle of incidence and the angle of refraction are related when light passes through two different media, like air, glass, and water. Each material has its own index of refraction. It is a value assigned to each medium to describe how much or little it bends light. Look at the chart below to see how some common materials refract light.

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STEMscopedia: LIGHT AND LENSES Material Vacuum Air Water Glass Vegetable Oil

Index of Refraction 1.0 1.0003 1.33 1.5 1.57

The index of refraction for any material can be calculated by using the following formula: n = speed of light in a vacuum ÷ speed of light in a medium. Why does light slow down when it enters into various materials? It must be absorbed and re-emitted by every particle in the medium as it passes through. Therefore, it travels faster through gases, slower through liquids, and finally slowest through solids. Solids are slowest because the particles are packed so closely together that light must be absorbed and emitted many more times than it does in a less dense gas. Lenses A lens is a transparent material through which you view an image. A concave lens is thinner in the middle and thicker on the edges. A convex lens is thicker in the middle and thinner on the edges. One or both sides of a lens may be curved. A light ray that passes directly through the center of a curved lens passes straight through, but a light ray that strikes a lens anywhere but the center changes direction. Above, a concave or Recall that refraction is the change in direction of a light ray that passes at diverging lens. Below, a an angle from one material into another. Side views of two lenses are shown convex or converging lens. in the diagrams on the right. With a real lens, refraction occurs as the rays enter and exit the lens, but we will consider only thin lenses and use an approximation of a single refraction. Notice that light rays passing through a concave lens diverge, or move apart, while rays passing through a convex lens converge, or come together. As a result, a concave lens is often called a diverging lens, and a convex lens is often called a converging lens.

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STEMscopedia: LIGHT AND LENSES Images Produced by Convex Lenses You can draw a ray diagram to determine the image produced by a curved lens. The figure on the right shows an image that can be produced by a convex lens. Keep in mind that you view images through a lens, so you should imagine yourself on the right of the figure looking through the lens to the object on the left. An object placed more than two focal lengths from a convex lens produces a real image that is inverted and smaller than the object. A line that extends horizontally through the center of the lens is called the principal axis. The point labeled F is the focal point of the lens. Each lens has a specific focal point determined by how curved the lens is. Light rays that reflect off an object through the focal point will refract parallel to the principal axis. Other symbols in the diagram represent the same quantities as in the mirror diagram on the first page of this companion. The distance from the focal point to the lens is the focal distance, f. Both sides of a lens have a focal point. To determine the size and orientation of an image, draw Ray 1 parallel to the principal axis to the lens and then toward the other focal point. Draw Ray 2 from the tip of the object through the focal point to the lens and then parallel to the principal axis. The rays intersect at the point of the image that corresponds to the same point on the object. Notice on the diagram that the image we see through the lens, in this case is, inverted and smaller than the object. You can also see this effect in the photograph on the right. For convex lenses, if the object distance (do) is greater than the focal distance (f), the image will be real. If do is less than f, the image will be virtual. You can also determine whether the image is real or virtual by comparing the placements of the object and the image. If the image is on the same side of the lens as the object, the image is virtual. If the image is on the opposite side of the lens as the object, the image is real. In the diagram on the previous page, the image is real because it is on the side opposite the object. Remember, for real images, light rays converge at the image, and the image could be seen if you placed a screen at its location. In the example just shown, the object was placed more than two focal lengths from the lens. What type of image is produced if the object is placed at other distances from the lens? Consider, for example, an object placed between the focal point and the lens, as shown in the diagram on the right.

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STEMscopedia: LIGHT AND LENSES Here, Ray 1 is refracted by the lens through the focal point, as before. Ray 2 does not pass through the focal point, but the focal point is used to find its direction. Because the rays do not converge on the other side of the lens, they must be drawn back to the point of intersection. Because the rays converge on the object side, the image is virtual. The image is also larger than the object and is upright. The image that is produced by a convex lens depends on the placement of the object. The following table summarizes the types of images a convex lens can produce. Notice, in particular, that no image is produced if the object is placed exactly at the focal point.

An object placed less than one focal length from a convex lens produces a virtual image that is upright and larger than the object.

Properties of Images Produced by a Convex Lens Placement of Object

do > 2f

do = 2f

2f > do > f

Orientation

Inverted

Height

Smaller

hi = ho

Enlarged

Type

Real

do = f

do < f Upright

No image

Smaller Virtual

What Do You Think? While looking through a convex lens, you slowly move the lens closer to and then farther from an object. Suddenly, the image you see through the lens disappears! What has happened? Check your anser below. Images Produced by Concave Lenses Unlike convex lenses, concave lenses produce only one type of image. Regardless of the placement of the object, the images are always virtual, upright, and smaller than the object. Here we see an image created by a concave lens. A concave lens produces a virtual, upright Ray 1 is refracted upward as it passes through the image smaller than the object. lens. The refracted ray is then drawn back through to the focus on the object side of the lens. Ray 2 passes through the center of the lens. Because the lens causes the rays to diverge, the intersection is on the object side of the lens, and the image is virtual. Answer: The image disappeared because the object was exactly one focal length from the lens at that moment. © Accelerate Learning Inc. - All Rights Reserved

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STEMscopedia: LIGHT AND LENSES Getting Technical: Eyeglass Lenses Our eyes act as lenses, forming images of the objects we see in the world around us. Images form on the retina, which is located at the back of the eye. Nearsightedness (myopia) happens because a person’s lens is too wide, so the image is focused in front of the retina. This causes distant objects to appear blurry. Wearing glasses with concave lenses diverges the light rays entering the eye, moving the point of focus back to the retina. Farsightedness (hyperopia) happens because a person’s lens is too thin, so the image is focused behind the retina. This causes nearby objects to appear blurry. Wearing glasses with convex lenses converges the light rays entering the eye, which moves the point of focus forward to the retina. Equations for Predicting Image Properties We have assumed the lenses in the diagrams in this companion are very thin. To calculate properties of images, we can use the thin lens equation. (This same equation can be used for mirrors, in which case it is sometimes called the mirror equation.)

Suppose we have a lens with a focal length of 4.00 centimeters that produces the image of an object that is 9.00 centimeters tall and located 5.50 centimeters from the lens. What other properties does the image have? Insert each known quantity into the lens equation and rearrange to solve for the unknown, which in this case is di:

The distance of the image from the lens, di, is about 14.7 centimeters. Because di is positive, it is on the same side of the lens as the viewer, and the image is real. We use another relationship to determine the height of an image. The magnification equation predicts the size of an image. If M is the magnification of the image, we can use this equation:

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STEMscopedia: LIGHT AND LENSES In this case, we know ho, do, and di, so we can solve for the relationship for hi:

Because the height is negative, we know the image is inverted. Because 24.1 centimeters is greater than 9.0 centimeters, we know the image is magnified. We can now calculate the magnification of the image:

The negative result indicates the image is inverted. The height of the image is more than twice the height of the object. What Do You Know? A lens and its focal points are shown below. Also shown are an object and two light rays. Draw the extensions of the rays after they pass through the lens past the point where they intersect. Insert image 22 of ray diagram for student to complete. Now circle the underlined word that answers each question. 1. Will the image be real or virtual? 2. Will the image be larger or smaller than the object? 3. Will the image be upright or inverted?

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STEMscopedia: LIGHT AND LENSES Connecting With Your Child Characteristics of a Convex Lens For this investigation, you will investigate the behavior of light with lenses. Materials: Convex lens, such as a magnifying glass White, flat object, such as a piece of paper Procedure: Hold the lens between a bright light and a white surface. The surface should be parallel to the face of the lens. Look for the image of the light on the paper. Move the lens back and forth between the light and the white surface. Continue moving the lens until you find the point at which the light projected onto the paper is smallest and clearest. If the light has a distinct shape, such as a lamp with a shade, the shape should be recognizable on the paper and it should be upside down. The fact that the image is projected onto the paper means it is a real image. Next, look through the lens at a small image drawn on a piece of white paper, such as a black arrow. Move the lens until the object comes into sharp focus. If you see an image that is vertical and larger than the object, it is virtual. Slowly move the object away until you see an inverted image of the object. It may take some time to locate this image because directions will be reversed. This image is real. Questions: 1. How is the image formed by a mirror like the object it reflects? How is the image formed by a mirror different from the object? 2. How is the image formed by a lens like the object it refracts? How is the image formed by a lens different from the object? Does it matter if the lens is convex or concave? 3. How do light rays change direction when they pass through a convex lens? How do light rays change direction when they pass through a concave lens?

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P4EF Light and Lenses

Reading Science Name:

Date:

Group:

The Physics of Mirrors 1

Because light behaves in a very predictable manner, its interaction with a reflective surface can also be predicted. The light ray traveling toward the mirror is called the incident ray; the light ray traveling away from the mirror is called the reflected ray. The angle between the incident light beam and a line perpendicular to the mirror is called the angle of incidence. The angle of incidence is exactly equal to the angle of reflection. To see an image, your eye must be positioned in the path of the reflected light beam. Multiple mirrors at an angle to each other result in multiple images. Flat surfaces such as mirrors, ponds, or glass doors all obey the law of reflection. So do curved surfaces, although the effects can be more interesting.

Two different curved surfaces are easy to analyze. Concave surfaces can produce a stretched image. Standing in front of a concave mirror will make you appear very tall and thin. The location of the object determines whether an image is right-side up or upside down, and if it is larger or smaller than the object. In contrast, convex mirrors produce a squashed image. Standing in front of a convex mirror will make you appear short and wide. Regardless of where the object is relative to the convex mirror, the image will always be right-side up and reduced in size. Funhouse mirrors installed in fair or carnival attractions often have a wavy surface, combining concave and convex sections. However, funhouses are not the only places where curved reflective surfaces are used.

Satellite dishes are a common sight in many cities. The dishes have a concave reflective surface that focuses the signal at a single point in front of the dish. The receiver mounted at this focal point collects the signal and transmits it via a cable to the television. However, very large spherical surfaces do not focus all collected signals to a single point. Therefore, very large dishes have a parabolic reflecting surface. Radio telescopes are another application of concave reflecting surfaces. Radio telescopes are used to track satellites and other spacecraft.

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Reading Science 4

If (or when) you drive a car, you will take advantage of another curved reflective surface. The side view mirrors in most cars are convex reflective surfaces. The field of view is the area from which light is collected and focused on your eye. The field of view is wider for a convex mirror than for a flat mirror allowing the driver to see more of the road behind the vehicle. Many of these mirrors are labeled, “Warning! Objects in mirror are closer than they appear!” The image you see in the mirror is smaller than the actual object behind you. Your brain usually interprets smaller as farther away. However, with relatively little experience, drivers get used to this distortion. Looking directly out the driver’s side and rearview windows allows a driver to judge distances more accurately before changing lanes, for example.

Reflections and mirrors feature prominently in many artworks. Two famous drawings by M. C. Escher use mirror surfaces. Hand with Reflecting Sphere depicts the artist in his office holding a mirrored sphere in his hand. His 1956 Print Gallery uses distortions similar to curved mirrored surfaces. Contemporary sculptor, Anish Kapoor, has used both concave and convex surfaces in his works. Cloud Gate at the Millennium Park in Chicago reflects both skyline and sky along its concave upper surface. Nature photographers such as David Muench often use reflections from natural surfaces such as rivers and lakes. For example, his 2009 Canyon Reflection photograph takes advantage of the flat Rio Grande river and the reddish cliffs of Santa Elena Canyon in Big Bend National Park.

No matter what type of material a mirror is made of, natural or man-made, rigid or flexible, as long as it is smooth, it will obey the law of reflection. Reflective surfaces are used in many applications from fun, to safety, to art. Experiment with different mirrors as you come across them in your daily life!

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Reading Science 1.

The ray of light traveling toward the mirror is called the – A.

Incident ray.

Accidental ray.

Normal ray.

Reflected ray.

A sculpture named Sky Mirror in New York City reflects skyscrapers upside down and smaller than they are in real life. What type of reflective surface does this sculpture most likely have? A.

Convex

Concave

Flat

Wavy

What type of mirror could have resulted in this image of a giraffe? A.

Convex

Concave

Flat

Wavy

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Reading Science 4.

Side view mirrors in many cars are convex. What is one advantage of convex mirrors for this use? A.

Convex mirrors are more sturdy than flat mirrors.

Convex mirrors show the image at the actual size of the object.

Convex mirrors have a very narrow field of view.

Convex mirrors always show the image right-side up.

The rearview mirror in most cars is flat. What driving situation is it most useful for? A.

Judging actual distance of traffic behind you

Making sure no small child is sitting behind your car when you back up

Seeing a car in your blind spot

Putting on makeup while driving

Which of the following natural surfaces would make a good mirror? A.

A fast moving river

A blade of grass

A still lake

The ocean during a storm

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Math Connections Name:

Date:

Group:

The following terms and equations will be used to answer questions throughout this worksheet: 1 1 1 + = i o f f = focal length i = image distance o = object distance 1. How far from the lens is the image of the house if the house is 16 feet from the thin convex lens with a focal length of 8 feet?

2. What is the distance from the vase of flowers to the mirror if the distance between the vase of flowers and image is 40 cm?

3. State the type of lenses below. a.

b. W hat does point X represent in the diagram below?

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Math Connections 4. Four physics students are working on an experiment with convex lenses, placing objects at different distances from the lenses. Below is a table of the results. Help out these physics students by filling in the missing information. Beyond 2F

At 2F

Between F & 2F

Between lens & F

object distance

50 cm

35 cm

30 cm

15 cm

image distance

30 cm

50 cm

real or virtual

real

upright or inverted

inverted

upright

5. How far from the lens will the image of the vase of flowers appear if the distance between the vase of flowers and the thin, convex lens is 35 cm with a focal length of 25 cm?

6. What is the distance of the soap dispenser’s image if the soap dispenser is 5 cm tall and the distance from the double convex lens is 45 cm (focal length = 17 cm)? Round to the nearest hundredth.

7. Angela is far-sighted, thus she is more comfortable reading at a distance of 70 cm from her eyes. She went to the eye doctor recently for corrective lenses which now allow her to read at a distance of 35 cm. Angela is walking past a few signs in the mall and notices that one of the signs is 70 cm from her and the image distance is 35 cm from her. Find the focal length of the corrective lens.

8. A glass of water is set down 20 cm from a thin, convex lens with a focal length of 10 cm. How far is the glass of water from the lens (or what is the object’s distance from the lens)?

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P4EF Light and Lenses

WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK The location and magnification of the image depend on the location of the object relative to the focal length of the thin convex lens. Thin convex lenses are used for magnifying small objects. Naturalists of all ages use magnifying lenses to examine insects. Some toy insect habitats come with magnifying lenses built in. Missy and Juan want to look more closely at a very small ant. The walls of the habitat are too slick for it to climb up. Mrs. Jones has made the following habitats available: • Habitat 1: Focal length of lens 5 cm, depth of habitat 3 cm • Habitat 2: Focal length of lens 5 cm, depth of habitat 10 cm • Habitat 3: Focal length of lens 5 cm, depth of habitat 8 cm WRITE Which habitat should they choose and why?

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WRITING SCIENCE

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High School Physics

P5A

Electrical and Gravitational Forces

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P5A Electrical and Gravitational Forces

Student Handout Name:

Watch the demonstration.

Describe what happened.

Explain what happened.

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Date:

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P5A Electrical and Gravitational Forces

Student Journal Name:

Date:

Group:

Background 1.

What force is holding the yarn against the table before you start, gravity or electromagnetism?

Write out Coulomb’s law and define each variable.

Investigation 1.

What is the length of your first piece of yarn?

What is the mass of your first piece of yarn?

What is the distance between the charged object and the first piece of yarn in meters?

What is the length of your second piece of yarn?

What is the mass of your second piece of yarn?

What is the distance between the charged object and the second piece of yarn in meters?

In order for the yarn to be picked up, the balloon or rod must generate enough electrostatic force to overcome ________________________.

Using Fg = mg, determine the gravitational force on the two pieces of yarn.

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Student Journal Investigation, continued 9.

What electrostatic force did it take to lift the first piece of yarn?

10. What electrostatic force did it take to lift the second piece of yarn? 11. Draw a force diagram for the first piece of yarn the moment it began to lift off the table. Label all vectors with the numerical values.

12. Draw a force diagram for the second piece of yarn the moment it began to lift off the table. Label all vectors with the numerical values.

13. Which piece of yarn experienced the greatest electrostatic force? Why?

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Student Journal Final Analysis 1.

What is the magnitude of the electrostatic force between the two charged spheres below? (The line between them is a measuring stick, and the balls are not in contact. The μ is the micro prefix and means 10-6.)

If the sphere on the left had a mass of 2 kg and the sphere on the right had a mass of 4 kg, what would be the gravitational force between the two spheres?

Which force is greater between the two spheres, gravitation or electrostatic?

What if both masses of the spheres had been doubled, would that have changed the answer to question 3?

Under what conditions would the gravitational force always be greater than the electrostatic force?

Under what conditions would the electrostatic force always be greater than the gravitational force?

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STEMscopedia: ELECTRICAL AND

GRAVITATIONAL FORCES

P5A

Reflect Have you ever thought about what holds the planets in our solar system in orbit around the Sun? The answer—gravity—may sound simple, but it is a little more complicated than you might think.

Newton’s law of universal gravitation and Coulomb’s law provide the mathematical models to describe and predict the effects of gravitational and electrostatic forces between distant objects. Gravitational Forces vs. Electrical Forces Gravitational and electrical forces have several things in common but two main differences. Their similarities include the following: • Both utilize a field to operate in. • Similar equations are used to solve for their values. • Distance determines the strength of both forces. Their main differences are: • Electrical forces have both an attraction and repulsion, whereas, gravity is only an attractive force. • Gravitational forces can extend infinitely, but electrical forces are limited in their distance. Force Fields and Attraction/Repulsion Electrical forces are caused by the charges of the subatomic particles in atoms. The protons in the atom have a positive charge, the electrons have a negative charge, and the neutrons are neutral. These charges create a force field in the space around the atom. When these charges come in contact with each other, the like charges will repel one another and opposite charges attract one another. Gravity is the force that draws you back to the ground when you jump; specifically, it is an attractive force between all objects with mass. This attractive force between two objects pulls the objects toward each other and creates a field between them. Two objects with mass exert a gravitational pull on each other. The force on one of the objects in the pair has the same magnitude, or strength, as the force on the other object, but it points in the opposite direction. The force on the first object points toward the second object. The force on the second object points toward the first object. Both objects feel the same magnitude of force.

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STEMscopedia: ELECTRICAL AND

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Equations • Electrical Force Scientists can measure electric forces. Charles-Augustin de Coulomb (pronounced: KOO-lom) studied electrostatic forces in the late 18th century. He measured these forces with a device called a torsion balance. Two identical balls are suspended by a thin wire. First, the scientist determines how much force is needed to twist the wire a given number of degrees. Next, the balls are given a charge. When another charged ball is brought near one of the balls, the electrostatic force can be calculated by measuring how far the wire twists.

A torsion balance consists of two metal balls on a rod You can calculate electric forces. Coulomb’s measurements revealed suspended by a fine wire. two relationships. First, electrostatic force (F) is proportional to the In this diagram, all the balls product of the two interacting charges, q1 and q2. You can state this have positive (+) charges. relationship as follows: F µ q1q2. (The symbol µ means “is proportional to.”) As the strengths of the electric charges increase, the strength of the electrostatic force increases. Second, electrostatic force is inversely proportional to the square of the distance between the charges, d2. You can state this relationship as follows: F µ 1/d2. As the distance between the electric charges increases, the strength of the electrostatic force decreases. You can combine these two relationships like this: F = K q1q2. d2 This visually represents In this equation, the electric charges (q1 and q2) are measured in 18 Coulomb’s law equation. coulombs (C). One coulomb equals the combined charge of 6.25 × 10 electrons. Distance (d) is measured in meters (m). K is a constant equal to 9 × 109 N·m2/C2. Force (F) is expressed in newtons (N), the metric unit of force. • Gravitational Force How can we calculate the force of gravity between two masses? In the 17th century, the physicist Isaac Newton answered this question with his law of universal gravitation. This law says that any two objects with mass feel a gravitational force between them. The force on each object has the same magnitude. The magnitude is proportional to the product of the objects’ masses. It is inversely proportional to the square of the distance between them. (When two values are inversely proportional, if one value increases, the other decreases by the same proportion.)

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STEMscopedia: ELECTRICAL AND

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As an object’s mass increases, its gravitational force increases. Compare the first and second diagrams: gravitational force (F) between the masses (m1 and m2) is twice as large when m1 is twice as massive. As the distance between two objects increases, the gravitational force between them decreases. Compare the first and third diagrams: gravitational force (F) between the masses (m1 and m2) DONE ES 6/2/17 is four times smaller when the distance (r) between the masses is doubled. Newton wrote this equation to express his law: F = G m1m2 r2 In this equation, the gravitational force (F) is equal to the product of the two masses (m1 and m2). It is inversely proportional to the square of the distance (r) between the objects. G is a universal constant called the gravitational constant. It is approximately equal to 6.67 × 10–11 m3·kg–1·s–2. Gravitational force is measured in units called newtons (N). A newton equals 1 kg·m·s–2.

Look Out Distance Both of the equations for gravitational and electrical forces discussed the importance of the distance between the two objects. Both forces’ strength depends on the distance of the objects from one another. This is due to the inverse square relationship between the force and distance in each equation. The closer the objects are to one another, the stronger the force. The further away from each other they are, the weaker the force. Even though the mathematical relationship between the forces and their distance is the same, the limitations of the forces due to their distance is not. Gravity is known as universal force, meaning that there are gravitational forces between all objects no matter how far away from each other in proportion to the masses of the objects in question. Electrical forces on the other hand, are very sensitive to the distance between two objects. This is due to the extremely small size of the subatomic particles that are exerting this force. If the particles are spaced at too great a distance, they cannot have an interaction between them.

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STEMscopedia: ELECTRICAL AND

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What Do You Know Use Newton’s law and Coulomb’s law to solve the appropriate problems below. 1. The Sun has a mass of 2.0 × 1030 kilograms. The distance between Earth and the Sun is about 1.5 × 1011 meters. Calculate the force of gravity on Earth due to the Sun. (Recall that Earth’s mass is 6.0 × 1024 kilograms.)

2. Two charges are separated by a distance of 3 meters. Charge A has a charge of 2 C, and charge B has a charge of 1 C. What is the force between these two charges?

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STEMscopedia: ELECTRICAL AND

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Connecting With Your Child Make an Electroscope You can make an electroscope—a tool that reveals the effects of electrostatic charge—with your child. You will need these materials: • About 1 foot of heavy copper wire (10 or 12 gauge), without insulation • Clear bottle • Cork that fits the bottle • A few square inches of light-duty aluminum foil • Drill and a small drill bit or a screw or nail Follow these steps, using the model at right as your guide: 1. Drill a small hole through the cork lengthwise, or make a hole by putting the nail or screw through the cork and then removing it. 2. Force the wire partway through the hole in the cork so that about two inches of wire comes out the bottom. 3. Bend the top of the wire into a spiral coil and the bottom into a small hook. (This may be easier if you wrap the wire several times This electroscope is around a pencil to create the coil and halfway around a pencil to carrying an electrostatic create the hook.) 4. Cut two identical strips of aluminum foil about 0.5 × 2 inches. Hook charge. The charge causes the metal strips at the one end of each strip over the hook in the wire. bottom of the tool to repel 5. Insert the cork into the bottle so that the foil strips are roughly each other. centered in the bottle. Try charging objects by rubbing them on fabrics, hair, and plastics. Bring the charged object near the coiled wire at the top of the electroscope and observe the motion of the foil strips. Discuss with your child what happens in terms of electrostatic forces. Here are some questions to discuss with your child: 1. Why are charged objects attracted to uncharged objects? 2. The foil strips of an electroscope have moved apart two centimeters. What else would you need to know to calculate the electrostatic charge? 3. The leaves of an electroscope are repelled by like charges. What could you do to the electroscope to make the leaves fall back together? Explain your answer in terms of the movement of electric charges.

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P5A Electrical and Gravitational Forces

Reading Science Name:

Date:

Group:

Comparing Coulomb’s Law and Newton’s Law 1

Coulomb’s law on electrostatic forces and Newton’s law of gravitational forces have similar formats as inverse square laws. Both describe mathematical relationships in which the force is directly proportional to the product of the charges (Coulomb’s law) or the product of the masses (Newton’s law of gravity) and proportional to the inverse of the square of their separation. Both forces can be infinite. This means both static electric force and the force of gravity fall off with the square of the distance between objects. The force equations of the two laws show similar relationships: interacting masses behave like interacting charges.

Coulomb’s law of electrostatic forces calculates static electric force between two charged bodies and is proportional to the product of the charges and inversely proportional to the square of the distance between them.

The electrostatic force equation describes the force of attraction between particles of opposite electrical charge. It also represents the force of repulsion for like charges: F = keqQ/r2 where F is the force of attraction or repulsion between two electrically charged particles ke is the Coulomb force constant q and Q are point charges of the two particles r is the separation between the particles

Static charges have practical applications. For example, they are used in inkjet printers and photocopiers where the printing powders initially adhere electrostatically to the paper. However, those same static charges can range from being annoying (static cling on fabric) to being hazardous (ruining electronic equipment and software). Consequently, anti-cling dryer sheets and innovative packing for electronic materials have been developed to reduce static charges.

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Reading Science 5

The gravitational force between two particles is calculated using Newton’s law of gravity. The force between two masses is proportional to the product of the masses and inversely proportional to the square of the distance between them. Newton’s law of gravitation equation explains the force of attraction between two objects, where the mass is concentrated at the centers of each object: F = GMm/R2 where F is the force of attraction between two objects G is the Universal Gravitational Constant M and m are the masses of the two point objects R is the separation between the centers of the objects

Some similarities exist between Coulomb’s law and Newton’s law. The two laws have a similar format as inverse square laws. Both describe mathematical relationships where the force is directly proportional to the product of the charges (Coulomb’s law) or the product of the masses (Newton’s law of gravity) and proportional to the inverse of the square of their separation. Both forces can be infinite. This means both static electric force and the force of gravity fall off with the square of the distance between objects. Both forces act along a central line between the two bodies. Both forces are conservative where the work done does not depend on the path followed, and both can operate in a vacuum. Lastly, the equations for both laws show similar relationships: interacting masses behave like interacting charges.

There are differences between the electrostatic force and the force of gravity. The electrostatic force can attract or repel. Similarly charged particles repel and opposite charges attract. However, between all masses in the universe, gravitational forces are always attractive. This means that gravity is classified as a monopole force, while electrostatic is classified as a dipole force. Another difference is the value of the constant used in the equation. The gravitational constant G does not change, while the electrical constant K depends on the medium.

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P5A Electrical and Gravitational Forces

Reading Science 1.

What similar mathematical relationship do Coulomb’s law of electrostatic force and Newton’s law of gravity show in their equations? A.

Inverse cube law: force decreases with distance cubed.

Inverse cube law: where force increases with distance cubed.

Inverse square law: force increases with distance squared.

Inverse square law: force decreases with distance squared.

Coulomb’s Law and Newton’s Law show similar relationships in that __________. A.

both forces are dipole

interacting charges behave like interacting masses

both forces are finite

interacting charges are not like interacting masses

A direct relationship exists between the electrostatic force and __________. A.

the product of their separation

the constant G

the product of the charges

gravity

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P5A Electrical and Gravitational Forces

Reading Science 4.

Unlike electrostatic forces, gravitational forces are __________. A.

always attractive

sometimes repulsive and sometimes attractive

always repulsive

neither attractive nor repulsive

Electrostatic forces can be helpful with __________. A.

software

delicate electronic equipment

fabric cling

printers and copiers

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P5A Electrical and Gravitational Forces

Math Connections Name:

Date:

Group:

Gravitational force is one of the four fundamental forces of nature. It always involves attraction between two bodies, and it acts between all particles of matter. The gravitational force of one object on a second one acts in the opposite direction and is equal to the force exerted by the second object on the first one. The gravitational force between two objects can be calculated: it is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Gm The surface gravity, g, on a planet can be calculated using the formula: g = 2 , where r N•m2 −11 • G = gravity = 6.673×10 kg 2 • m = mass in kg • r = radius in m

Characteristics of Solar System Objects Solar System Object

Mass (kg)

Radius (m)

Surface gravity (m/s2)

Mercury

3.30×1023

2,440,000

3.70

Venus

4.87×1024

6,051,000

Earth

5.97×1024

Moon

7.35×1022

1,738,000

Mars

6.42×1023

3,397,000

Jupiter

1.90×1027

71,492,000

Saturn

5.69×1026

Uranus

8.66×1025

25,559,000

Neptune

1.03×1026

24,764,000

Pluto (dwarf planet)

1.31×1022

1,160,000

9.79 1.62

10.45 8.84 .65

Use the table above to answer the following problems. Insert your answers into the spaces in the table. 1.

Calculate the surface gravity on the following planets: a. Venus b. Jupiter c. Neptune d. Mars

Calculate the radius of the following planets: a. Earth b. Saturn 329

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P5A Electrical and Gravitational Forces

Math Connections 3.

Use the table on previous page to answer the following problems: a. Calculate your mass on Earth using the formula W = mg, where m is your mass in kg, and g is the surface gravity on Earth. (1 pound = 2.2 kg).

b. Calculate your weight and mass on Mercury (the unit for weight is Newtons).

c. Calculate your weight and mass on the Moon.

d. Calculate your weight and mass on Uranus. 4.

Calculate the surface gravity at a height of 2 Earth radii above Earth’s surface. (Note: The distance of 2 Earth radii is measured as 3 Earth radii from Earth’s center.) g=

Gm r2

Review of one- and two-dimensional motion: 5.

How much time would it take for a brick to free-fall 50 m on Mercury? Since velocity = 0, use the following equation: d = ½ gt 2, where d is distance in meters, g is surface gravity, and t is time in seconds.

You can throw a baseball straight up with a velocity of 25 m/s. a. Find the baseball’s maximum height on Earth. V = v0 + gt d = ½ gt 2

(Hint: max height is when v0 = 0; use g = 10 m/s2.)

b. Find the baseball’s maximum height on Mars.

c. On which planet would the brick in question 5 travel highest?

d. On which planet would that brick spend the least amount of time in the air? 330

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P5A Electrical and Gravitational Forces

WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK Gravitational force between objects depends upon the mass of each object and the distance between their centers. Gravity is proportional to the product of two masses and inversely proportional to the square of the distance between them. The modern statement of the equation is: Fg = G (m1m2 / d 2), in which G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between the centers of the balls. A spherical object behaves as if all of its mass is in its center, which simplifies calculations for gravity. Billiard balls’ sizes and weights vary depending on the country and the type of game played. Assume that all billiard balls involved in this problem have the same mass and diameter. WRITE Describe how the gravitational force varies between the different billiard balls. Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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WRITING SCIENCE

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High School Physics

P5B

Charge Transfer

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P5B Charge Transfer

Student Handout Name:

Date:

Shocking! Directions: Search for “John Travoltage” on your smartphone, tablet, or computer. Open up the app. Explore what happens when you move various parts. Be sure to use the orange reset button! 1.

What happened when you moved his foot?

What happened when you moved his hand?

What happened when you moved his foot and then his hand?

What happened when you moved his hand and then his foot?

What do the blue spheres represent?

What is a real-world example of this simulation?

What causes your answer to number 6?

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P5B Charge Transfer

Student Journal Name:

Date:

Group:

Scientific Investigation Develop a procedure that will illustrate how charge is transferred by friction, conduction, and induction. In your investigation, you will first experiment with the equipment to see which combination can generate enough force to lift little pieces of graph paper. Once you find a combination that works well, you will then investigate how to transfer this charge to another object or to induce a charge in another object and have that lift the squares of graph paper. Procedure Step 1. Question of inquiry

Step 2. Relevance Step 3. Variables Independent variable (also known as the manipulated variable) Dependent variable (also known as the responding variable) Control variable(s) or group (also known as constants) Step 4. Hypothesis How will the responding variable change when the manipulated variable changes? Step 5. Materials

Step 6. Safety considerations

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P5B Charge Transfer

Student Journal Step 7. Procedures 1. Cut graph paper into sections: 1 x 1, 2 x 2, 3 x 3, and 4 x 4. 2.

Develop a data table for your scientific investigation.

Experiment by trial and error to see which might generate the greatest static charge. Consider such ideas as using a glass or plastic rod, silk or fur, wool, etc.

See how far away the lifting object can be above each section of graph paper. Do a few trials and record the greatest distance.

Try to determine a way to transfer the charge to a different object. Can this transferred charge lift the graph paper the same amount?

Assemble the pith ball electroscope, as shown by your teacher. Explore charge transfer by conduction and induction.

Analyze your data.

Data Collection Place your data table and any other data below.

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P5B Charge Transfer

Student Journal Data Analysis

Conclusion Provide a scientific explanation using evidence from your experiment to make a claim of how charge transfer by induction, friction, and conduction works.An object is placed 15 centimeters from a thin convex lens and its image appears three centimeters from the lens. What is the focal length of the convex lens?

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STEMscopedia: CHARGE TRANSFER P5B Reflect You know that sparks can sometimes jump through the air. You may have noticed a spark jump from your finger to a metal doorknob, and you have surely seen the spectacular sparks called lightning. These sparks are explained by the properties of static electricity. Static means “stationary.” Something that is static does not move (or, in the case of static electricity, moves less compared to current electricity, which flows along a path called a circuit). Static electricity is different from current electricity, which refers to the flow of electricity through complete circuits. Current electricity is what powers the electrical devices in your home. In this companion, we will study the forces exerted by static electrical charges. What do you think causes these charges? What factors determine whether a charge is strong or weak? Electric forces are caused by subatomic particles. Static electricity was not well understood until the basic atomic model was developed around the beginning of the 20th century. To explain static charges clearly, we must refer to this model. Every atom is made up of smaller particles. A neutral atom—or one without an electric charge—includes equal numbers of electrons and protons and a similar number of neutrons. An atom’s neutrons carry no charge and are not involved in This diagram represents electrostatics. The protons have a positive (+) charge and are packed six electrons (green circles) tightly into the nucleus. The electrons have an equal but opposite circling the nucleus of a negative (−) charge and circle the nucleus at a large distance, compared to the size of the nucleus. Protons are tightly bound by strong carbon atom. The nucleus contains six neutrons (pink nuclear forces, but electrons can easily be removed from or added to the atoms of many elements. “Free-range” electrons not associated with circles) and six protons (blue circles). individual atoms may also be added to a material. Not all atoms are neutral. If an atom has more electrons than protons, it has a negative charge. If an atom has fewer electrons than protons, it has a positive charge. Similarly, if an object has more negatively charged atoms, it has a negative charge. If an object has more positively charged atoms, it has a positive charge. Both types of charges are created by moving electrons (never protons) into or out of an object. Electrical charges exert forces. Remember, like charges repel each other, and opposite charges attract each other. Attraction or Repulsion: The direction of the electrical force is not always attractive; it could be either repulsive or attractive. The direction depends on the intrinsic properties of the charged objects. If the two objects carry different charges, one positive and the other negative, the direction is attractive. If both charges are the same, the electrical force is repulsive.

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STEMscopedia: CHARGE TRANSFER Look Out The rule for electrical charges—“like charges repel, opposite charges attract”—may sound familiar. This is also the rule for magnetic poles. (The north pole of one magnet repels the north pole of another magnet but attracts the south pole.) Do not confuse magnetic and electrical forces just because the rules are very similar. Although the forces both involve electrons, they arise in different ways. Scientists can measure electric forces. Charles-Augustin de Coulomb (pronounced: KOO-lom) studied electrostatic forces in the late 18th century. He measured these forces with a device called a torsion balance. Two identical balls are suspended by a thin wire. First, the scientist determines how much force is needed to twist the wire a given number of degrees. Next, the balls are given a charge. When another charged ball is brought near one of the balls, the electrostatic force can be calculated by measuring how far the wire twists. A torsion balance consists You can calculate electric forces. of two metal balls on a rod Coulomb’s measurements revealed two relationships. First, electrostatic suspended by a ﬁne wire. force (F) is proportional to the product of the two interacting charges, q1 In this diagram, all the balls and q2. You can state this relationship as follows: F μ q1q2. (The symbol have positive (+) charges. means “is proportional to.”) As the strengths of the electric charges μ increase, the strength of the electrostatic force increases. Second, electrostatic force is inversely proportional to the square of the distance between the charges, d2. You can state this relationship as follows: F μ 1/d2. As the distance between the electric charges increases, the strength of the electrostatic force decreases. You can combine these two relationships like this: F μ q1q2. In this equation, the electric charges (q1 and q2) are measured in coulombs (C). One coulomb equals the combined charge of 6.25 × 1018 electrons. Distance (d) is measured in meters (m). K is a constant equal to 9 × 109 N·m2/C2. Force (F) is expressed in newtons (N), the metric unit of force.

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STEMscopedia: CHARGE TRANSFER What Do You Think? Let’s review Coulomb’s relationships using a simple example. Two charges are separated by a distance of three meters. Charge A has a charge of two coulombs, and charge B has a charge of one coulomb. To calculate the electrostatic force between these objects, set up the equation like this:

The electrostatic force between charges A and B is 2 × 109 newtons. 1. What happens to the electrostatic force if charge B increases in strength to two coulombs? 2. What happens to the electrostatic force if the distance between the charges doubles? You can check your answers on the next page. Scientists in the Spotlight: Charles-Augustin de Coulomb Coulomb was a French engineer who lived from 1736 to 1806. Trained as an engineer, he spent much of his early career designing large construction projects, including military forts. Later in life, he became more and more interested in experimental physics, where he made a number of important discoveries. Coulomb was greatly aided in his investigations by his excellent grasp of mathematics. In 1777, he invented the torsion balance, which allowed scientists to make accurate measurements of very small forces. (The English geologist John Michell also invented a torsion balance about 25 years before Coulomb. Coulomb invented his tool without knowledge of Michell’s.) He applied this device to the study of magnetic and electrostatic forces. Coulomb also made important contributions to the understanding of friction and of current electricity. The unit of electrical charge, the coulomb, is named in his honor. Electric forces affect matter. There are a number of ways to transfer an electrical charge to common household objects by simply rubbing two different materials together. Rubber objects will pick up a charge when rubbed on most fabrics. Combing hair can charge a comb. Walking across certain carpets in your socks can even give you an electric charge that you can pass to other people by touching them. (Be careful not to touch metal objects while charged, though, or you may shock yourself.)

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Lightning appears when a large static charge discharges.

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STEMscopedia: CHARGE TRANSFER Ways to Transfer Charge Friction: Sometimes kinetic energy can heat up objects. Friction requires objects to be touching and in motion to act. Friction occurs when two objects that are neutral rub against one another, which can cause a pull on each other’s electrons. This results in one positively charged object and one negatively charged object. Different materials work better than others for transferring charge. We can look at a list called the triboelectric series to compare substance types. Conduction: Conduction is the process of using a charged object to touch and cause the same charge on another object. The newly charged object will have the same type but a weaker charge than the original. So if the charged object is negative, it will cause the neutral object it touches to also be negative, but weaker. Electrons will move from the charged object to the neutral object when touched.

The Triboelectric Series is a comparison between substance types that have a tendency toward either positive or negative charges

Induction: In the process of induction, there is one charged object and one neutral object, similar to conduction. But the two objects are not touching in order for the charged object to affect the neutral one. The charged object simply has to be near the neutral object to force the electrons in the neutral object to move and collect on one side. The side they move to depends on if the charged object is positively or negatively charged. If it’s positively charged, the electrons in the neutral object will move toward the charged object. If it’s negatively charged, the electrons will move away from it. This movement causes an imbalance in the charges of the object even though, as a whole, it is technically still neutral because it hasn’t gained or lost any protons or electrons.

The negatively charged balloon is attracted to the induced positive charge in the wall.

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STEMscopedia: CHARGE TRANSFER What Do You Think? To test whether an object is charged, see if small pieces of tissue paper are attracted to it. The tissue paper will stick to the charged object because it has become charged by induction. For example, if the object has a negative charge, it will repel the electrons in the paper. This leaves a positive charge on the side of the paper nearest the charged object, creating a positive-negative attraction. Inflated rubber balloons pick up a charge easily. Because a balloon is light, electrostatic attraction is strong enough to hold one to a wall. An electroscope is a common laboratory device used to observe electrostatic charges. This tool consists of a metal rod. On top of the rod is a metal ball, and at the bottom of the rod are two metal leaves. When a charge is added to the ball, it spreads to the leaves via the rod. Because the leaves have like charges, they repel each other. What happens to the electrostatic force in each case? Plug the new values into the charge equation, like this: a.

If charge B (q2) doubles from one coulomb to two coulombs, then the electrostatic force (F) also doubles:

If distance (d) doubles from three meters to six meters, then the electrostatic force (F) is four times weaker:

What Do You Know? The three balls suspended by strings from the left-hand rod have static electrical charges; two charges are positive (+), and one charge is negative (−).

In real life, balls with these charges would not hang straight down as shown. Show how the electrostatic forces would make the balls move by drawing their ﬁnal, at-rest positions on the righthand bar.

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STEMscopedia: CHARGE TRANSFER Connecting With Your Child Make an Electroscope You can make an electroscope—a tool that reveals the effects of electrostatic charge—with your child. You will need the following materials: • About 1 foot of heavy copper wire (10 or 12 gauge), without insulation • Clear bottle • Cork that ﬁts the bottle • A few square inches of light-duty aluminum foil • Drill and a small drill bit, or a screw or nail Follow these steps, using the model to the right as your guide: 3. Drill a small hole through the cork lengthwise, or make a hole by putting the nail or screw through the cork and then removing it. 4. Force the wire partway through the hole in the cork so that about 2 inches of wire comes out of the bottom. 5. Bend the top of the wire into a spiral coil and the bottom into a small hook. (This may be easier if you wrap the wire several times around a pencil to create the coil and halfway around a pencil to create the hook.) 6. Cut two identical strips of aluminum foil about .5 × 2 inches; hook one end of each strip over the hook in the wire. 7. Insert the cork into the bottle so that the foil strips are roughly centered in the bottle.

This electroscope is carrying an electrostatic charge. The charge causes the metal strips at the bottom of the tool to repel each other.

Try charging objects by rubbing them on fabrics, hair, and plastics. Bring the charged object near the coiled wire at the top of the electroscope and observe the motion of the foil strips. Discuss with your child what happens in terms of electrostatic forces. Here are some questions to discuss with your child: 1. Why are charged objects attracted to uncharged objects? 2. The foil strips of an electroscope have moved apart two centimeters. What else would you need to know to calculate the electrostatic charge? 3. The leaves of an electroscope are repelled by like charges. What could you do to the electroscope to make the leaves fall back together? Explain your answer in terms of the movement of electric charges.

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P5B ChargeTransfer

Reading Science Name:

Date:

Group:

Putting Static Electricity to Work 1

Objects can receive a static charge in three ways: • • •

Friction – Applying friction can charge insulators. By rubbing two materials against each other (a plastic ruler and paper towel, glass and silk, PVC and fur, etc.), electrons can be transferred. Conduction – Touching an object to a conductor can result in some charge being transferred when charging metals and other conductors. This method charges the conductor with the same charge sign as the other object. Induction – Bringing a charged object close to a conductor, but not touching it, can be used to charge metals and other conductors. When the conductor is grounded, electrons can flow to or from the object. If grounding is taken away, the conductor receives a charge opposite to that of the charged object.

Static electricity can be applied to pollution control by using electrostatic forces to charge dirt particles in the air and collect them on a plate with the opposite electrical charge. These machines are called electrostatic precipitators. Factories that burn products use static electricity to reduce smokestack pollution. The smoke particles are charged and are attracted electrodes with an opposite charge. This minimizes the particulate matter from escaping into the atmosphere.

Household ionizers work on the same principle. The machines strip electrons from the molecules of smoke, dust, or pollen. This particulate matter becomes charged and is attracted to a plate inside the ionizer with the opposite charge. The plates require periodic cleaning and replacement of their carbon filter.

Photocopiers use static electricity to transfer charged ink powder either to a page or a rotating drum, which transfers the image to paper. To begin copying a document, a copying plate is electrically charged. Then a light falls on the plate, and some of the charge falls off. The parts that remain charged attracts toner powder with an opposite charge. The black power is transferred to paper where it is heated, melts, and sticks permanently. Copy machines need periodic replacement of their powder toner as it is used up.

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Reading Science 5

Inkjet printers operate differently. As an ink mist is sprayed, it is electrically charged and passes between a negative plate and a positive plate. The charged mist is attracted to the oppositely charged plate. The voltage is controlled so that each droplet is deflected to a particular place on the paper and produces a final image made up of imperceptible tiny dots.

In the automobile industry, some manufacturers apply an electric charge to the paint. In a paint booth, the paint mist is attracted to the car. When the paint dries, it adheres permanently. Electrostatic forces create an even distribution of paint molecules.

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P5B ChargeTransfer

Reading Science 1.

Rubbing glass and silk together is an example of applying a charge through ___________. A.

friction

translation

induction

conduction

Conduction creates a same-sign charge when touching ___________. A.

wood

metal

plastic

rubber

Induction is different from conduction because the ___________. A.

object is touched

object is not charged

object is not touched, but the charged object comes close

charge is not touched, but the object is touched

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P5B ChargeTransfer

Reading Science 4.

Why are dust and pollen attracted to the metal plate in an electrostatic precipitator? A.

They have no charge.

They have the same charge as the plate.

They have a double charge.

They have an opposite charge as the plate.

In which application are charged particles heated until they stick permanently? A.

Inkjet printers

Photocopiers

Smoke stacks

Autopainting

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P5B Charge Transfer

Math Connections Name:

Date:

Group:

Charge Transfer: Conduction, Friction, and Induction The unit used for measuring electric charge is the Coulomb (C). A single Coulomb is equal to 6.25 x 1018 electrons. Objects typically have no charge but can be charged through three different methods: • Friction – Occurs when electrons transfer between two objects without touching • Conduction – Occurs when electrons transfer between two objects by touch; one of the objects must be previously charged • Induction – Occurs when a charged object causes the neutral charges in an object to separate Look at the diagrams below. A

Calculate the percentage of positive and negative charges in each object. Object

Positive Charge

Negative Charge

A B C D

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P5B Charge Transfer

Math Connections 2.

Based on your data, create a circle graph for each diagram. Make sure you include a key. A.

What process do the diagrams demonstrate?

What is your evidence to support your claim?

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P5B Charge Transfer

WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK Traditionally, people have used gas or electricity to cook food on a stovetop. The advantages of using gas over electricity is the speed and efficiency of cooking. However, gas is not always an option. To remedy the problem of speed with electricity, induction cooktops were created. In order to use an induction stove, users must cook with a pot containing iron for induction to occur properly. If a pan that does not contain iron is used, the stove will not operate. One of the reasons why using electricity is slower is because the metal coil underneath is heated and then tries to heat the pot, the food, and the air in the room. With induction, the pot is heated directly thus causing the food to heat up much more quickly in comparison. WRITE Describe an investigation demonstrating charge transfer through conduction, induction, or friction. Explain the processes acting in the investigation to explain charge transfer. Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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P5B Charge Transfer

WRITING SCIENCE

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High School Physics

P5C

Behavior of Charges

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P5C Behavior of Charges

Student Handout Name:

Date:

Potential Energy and Fields Directions: Take two of the magnets and bring them slowly together. Then carefully and slowly separate them until you can no longer feel the magnets attract each other. Measure this distance. 1.

Distance:

Rotate one magnet end for end, and then slowly bring the magnets back together. There should be repulsion. Continue until the two magnets are touching, but do not let either flip! Make sure they are still trying to repel each other. 2.

What would happen if you let one of the magnets go?

Remember that work is force applied over distance. 3.

In the first step, did you do work? How do you know?

In the second step, did you do work? How do you know?

Potential energy is stored energy. In which step was the potential energy the greatest?

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P5C Behavior of Charges

Student Journal Name:

Date:

Group:

Background 1.

What is the equation for electric potential energy?

What is the value of Coulomb’s constant?

If a number has the unit of joules, is it measuring electric potential energy or electric potential?

If a number has the unit of volts, is it measuring electric potential energy or electric potential?

What is the primary difference between electric potential energy and electric potential, other than the unit?

Part I 1.

Given that your positive charge is equal to 1 x 10-9 C and your detector has a charge equal to 1 C, what would be the potential energy present if they were one meter apart? Show your work.

What was the measured value on the detector? Were the units what you expected?

What would happen to the PEE if the detector was moved to 2 m away?

Was your prediction from question 3 correct? Why or why not?

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Student Journal Part II There are two positive charges. Distance between the two charges _____________________ Distance from left—most charge 0.5 m

Electric Potential (volts)

Electric Potential Energy (joules)

1.0 m 1.5 m 2.0 m There are two negative charges. Distance between the two charges _____________________ Distance from left—most charge 0.5 m

Electric Potential (volts)

Electric Potential Energy (joules)

1.0 m 1.5 m 2.0 m There is one positive and one negative charge. Distance between the two charges _____________

Distance from left—most charge 0.5 m

Electric Potential (volts)

Electric Potential Energy (joules)

1.0 m 1.5 m 2.0 m

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P5C Behavior of Charges

Student Journal Analysis 1.

When was the potential energy the highest? When was the potential energy the lowest?

What do you think the significance is of the negative voltage versus positive voltage?

If you dropped a positive charge between the positive and negative charges in trial 3, which direction would it want to move?

What happened to the electric potential energy when both charges were positive?

What happened to the electric potential energy when both charges were negative?

What happened to the electric potential energy when one charge was negative and one was positive?

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STEMscopedia: BEHAVIOR OF CHARGES P5C Reflect Think about what you have already learned about potential energy in reference to gravity. If a ball is sitting motionless at the edge of a platform 30 meters above the surface of Earth, does it have any potential energy? Its kinetic energy is zero, but it does have potential energy, which can be converted to kinetic energy. Electricity behaves in the same way in reference to charged particles. A charged particle will build up potential energy based on its surrounding particles. Electrical Potential Energy Potential energy is a measure of an object’s ability or capacity to do work, and it is in reference to its location in a fixed field. In essence, energy is being stored in an object due to its location or configuration around other objects. With electric potential energy, it is all about its location and its dependency on the amount of potential energy charge at that location.

Each of these dominoes has potential energy due to the fact that the surrounding dominoes may fall into it, transforming its potential energy into kinetic energy.

Since electrical charges can either be positive or negative, we know that two charges will interact with each other depending on the type of charges. Electrical potential energy is when electrical charges are being repelled from each other because they both have the same charge, giving it stored, or potential, energy. If the charge has a small amount of potential energy, then the charge has a low amount of potential energy. However, if the charge has a high amount of potential energy, then the charge has a large amount of potential energy. Remember, since the charges are moving, a force is involved. In addition, work is being done on the charges since the force is moving them a certain distance. Recall that work is the product of an applied force (F) across a distance (d), and potential energy is the ability to do work. Charges move because of an electrical field that has been created by other charges. For example, in dry cold air, negative charges can build up on a person when they rub across a carpet or car seat. When the person goes and reaches for a positively charged door handle, the electrical potential energy associated with each charge moves when there is a static discharge.

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STEMscopedia: BEHAVIOR OF CHARGES In a uniform electric field, the direction the charge is moving will determine if the potential energy will increase or decrease. For example, if a negative charge is moving with the electric field, then the potential energy decreases. However, if the negative charge is moving against the electric field, then the potential energy increases. Electrical Potential Energy and Electric Fields Electric fields are areas or regions around a charge that point outward if the charge is positive and inward if the charge is negative. The direction of the field is the same direction of the force. When you place a positive charge in an electric field that has its field lines all moving in the same direction, the charge will move in the same direction as the electric field. Since the charge is moving across the electric field, the potential energy will change as a result. The change in the potential energy is associated with the change of the charge’s position. How much of that change will depend on a few factors such as the charge on the particle, the strength of the field, and how far the charge moved. When a negative charge is placed in a uniform electric field, the potential energy will increase, and if you place a positive charge in the field, the potential energy will decrease.

Plasma ball

Look Out Volt is the unit for electrical potential, and since electrical potential difference is expressed with the unit of volts, it is also known as or referred to as voltage. Do not confuse voltage with current. Voltage is like the force that moves the electrons (current) to different places. Current cannot move itself like water cannot move itself. Voltmeter

Try Now So now that we have some background information, let’s see if you can explain the main points of electric potential difference.

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STEMscopedia: BEHAVIOR OF CHARGES 1. Explain what electric potential difference is. 2. Explain how work is involved to move a charged particle. 3. Explain how potential difference affects current. 4. Explain how the amount of energy is directly related the distance the charge moves.

Connecting With Your Child Materials needed: • • • • •

Chalk (different colors if possible) Dice Black paper (or any dark paper that chalk will show up clearly on) If chalk or black paper are not available, use small white boards with different dry erase markers instead. Cup of Fruit Loops

Procedure On the black or colored paper, use the chalk to draw two electrostatic balls with the first ball coated with a positive (+) charge. Draw a negatively (-) charged wand that is close to the positively charged ball. On the second electrostatic ball, coat the ball and wand with the new charges if the negatively charged wand touches the first electrostatic ball. On another piece of black or colored paper, use the chalk to draw a positive and a negative charge that are at least 20 centimeters apart. Use the die to determine the distance between charges by rolling the die and then multiplying the number by 5. For example, if they roll a “2” on the die, the distance would be 10 centimeters as you multiply the “2” x 5 = 10 centimeters. Using a different colored piece of chalk, draw in the force field lines to represent the attraction between the positive and negative charge showing the direction with arrow points. Students can also repeat the same situation but with the same charges. On the black or colored paper, draw a uniform electric field with a piece of chalk between two images of metal. Draw positive charges on one side of the paper and negative charges on the other side of the paper. Draw in the uniformed field. On a separate piece of paper, explain the relationship between the charge and the field it is in. Draw a charge moving through the field. On the separate piece of paper, explain how the potential energy increases or decreases as it moves through the field.

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P5C Behavior of Charges

Reading Science Name:

Date:

Group:

Alessandro Volta 1

Everyone is familiar with the huge number of items that require a battery with a particular voltage, but how many know that the unit of voltage, called a volt, was named after the Italian scientist Alessandro Volta? Most people are also unaware that it was Volta who invented the battery!

How is voltage related to electric potential? Voltage is the change in electric potential energy per unit charge––the measure of the force that moves electric current. Basically, an electric charge changes its surrounding space through a vector called the electric field and through a scalar called voltage or the electric potential.

Electric fields and voltages are two different ways of saying the same thing. More specifically, electric potential is the effect of an electric field of a source depending on its location within the electric field. Three factors affect electrical potential: the charge of the object, the electric field strength, and the distance the charge has moved parallel to the field.

Electric potential (V) is the change in potential energy (U) per charge (q) moved. This means that electrical potential energy changes depending on the amount of charge moved. The formula for electric potential is: V= U / q. Another way to describe that relationship is: electric potential = Δ energy / unit of charge moved. Because energy is measured in units of joules and charge in units of coulombs, then the unit for electric potential is measured in joules per coulomb, which is equal to a volt. Electric potential is used to predict and calculate energies needed to move charges, and is found on different-sized batteries.

Alessandro Volta (1745-1827), the Italian physicist, invented the battery through a series of controversies with another scientist, Luigi Galvani. When Galvani conducted experiments with frog legs that moved when connected to pieces of metal, he concluded that animal tissue contained a form of electricity. Volta disagreed and built a voltaic pile to prove that electricity did not come from the animal tissue but was generated by the contact of different metals, brass and iron, in a moist environment.

To make his voltaic pile in 1800, Volta assembled alternating disks of zinc and copper coins with pieces of cardboard soaked in salt water between the metals. It produced electricity. Alessandro Volta’s voltaic pile was the first “wet cell battery” and the first to produce a steady current of electricity.

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Reading Science 1.

Who invented the battery? A.

Alessandro Baterria

Alessandro Volta

Luigi Galvani

Benjamin Franklin

The unit pf change in electric potential energy per charge is known as the ____________. A.

watt

coulomb

joule

volt

A synonym for voltage is ____________. A.

electric potential

electric potential energy

coulomb

watt

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P5C Behavior of Charges

Reading Science 4.

The formula for voltage, V= U / q, means which of the following? A.

Electrical potential energy changes depending on the amount of charge moved.

Gravitational potential energy changes depending on the amount of charge moved.

The electric field stays the same as the charge moves.

Voltage increases as q increases.

Why was Volta’s voltaic cell (wet cell battery) such an important invention? A.

He proved Galvani’s assertion that tissue contained electricity.

He made the first device that could produce static electricity.

He made the first device that could produce steady current.

He proved that metals, such as zinc and copper, when used with saltwater would not create current.

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P5C Behavior of Charges

Math Connections Name:

Date:

Group:

The following terms and equations will be used to answer questions throughout this worksheet: d = distance qq FE= kc 12 2 e = elementary charge of an electron = -1.602 x 10-19C d FE = electrical force or electrostatic force kc = Coulomb’s constant = 8.99 x 109 Nm2/C2 f kcq q = charged object E= = -19 p = elementary charge of a proton = -1.602 x 10 C q d2 μ = 10-6 E = electric field (electric force in Newtons per unit charge in Coulombs (N/C) 1.

Find the electrostatic force between two protons 2.0 m apart.

Two balloons are tied to the back of the birthday boy’s chair 0.1 m apart. Find the electrostatic force between these two balloons given that each balloon carries a charge of 4.6 μC (4.6 x 10-6 C or 0.0000046 C).

Find the electric field 1.3 m from an isolated electron.

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Math Connections 4.

Find the electric field 1.3 m from an isolated proton.

An unshielded small electrical generator is near a charge of 0.0070 C and experiences 10 N of electrostatic force. What is the strength of the electrical field at that point in space? Round to the nearest hundredth.

There is an electrical field of 7,000 N/C in which I place a charged object that sees 40 N of electrostatic force. What is the charge on the object? Round to the nearest hundredthousandth.

Two equally negatively charged spheres are placed close to each other. If the distance between the two spheres is tripled, what is the force acting on the spheres decreased by?

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P5C Behavior of Charges

Math Connections 8.

In the diagram below, what is the magnitude of the force between the two charged spheres?

0.42 m 5.2 μC

4.5 μC

Given the table below, which pair of spheres exerts the greatest force on each other? Explain your answer.

Pair

Charge on A (μC)

Charge on B (μC)

C H S R

3.3 3.3 5.5 5.5

4.2 4.2 4.2 4.2

Distance from A to B (m) 0.3 1.4 0.3 1.4

10. Two charges exert a force of 60 N on each other and are separated by a distance of 2 m. What would be the new force on each charge if the charges were pulled to a distance of 4 m?

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P5C Behavior of Charges

WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK A plasma ball can be used to understand more about electrical fields. An LED can be lit using the oscillating electric field being emitted from the plasma ball and into the air outside of the glass. The closer the bulb is to the plasma, the brighter it gets; the farther away from the plasma ball it gets, however, the less likely the bulb is to light up. Think about what is occurring at the charge level. WRITE Using your knowledge of the behavior of charges, explain the electrical field present in the plasma ball example. Provide evidence to explain these behaviors in reference to electrical potential energy. Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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P5C Behavior of Charges

WRITING SCIENCE

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High School Physics

P5D

Direct Current Circuits

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P5D Direct Current Circuits

Student Handout Name:

Date:

Circuits 1.

Take two wires, a battery, and a light bulb. Connect these components to make the bulb light up.

Diagram the circuit you built in step 1. Use the key on the next page for the correct symbols.

Take four wires, a battery, and two light bulbs. Connect these components to make the bulb light up.

Diagram the circuit you built in step 3.

If you disconnect one light, does the other light go out?

Using eight wires, a battery, and two light bulbs, create a circuit that lights up both bulbs but does not go out when one bulb is disconnected. Diagram this circuit.

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P5D Direct Current Circuits

Student Handout Circuit Diagram Key

Example Diagram In this circuit, there are two lights and a resistor—all connected to a single battery.

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P5D Direct Current Circuits

Student Journal Name:

Date:

Group:

Background: Around It Goes 1.

What is an electrical circuit?

How are elements connected in series?

_______________________________________________________________________________ _______________________________________________________________________________ 3.

How are elements connected in parallel?

_______________________________________________________________________________ _______________________________________________________________________________ 4.

In the space below, use the information provided to draw each circuit.

a. two light bulbs and one resistor b. one resistor connected in parallel connected in series with two light bulbs in series

What is Ohm’s law? How do you calculate resistance using Ohm’s law?

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P5D Direct Current Circuits

Student Journal Part I: Construct a Circuit 1.

State the purpose of your circuit.

_______________________________________________________________________________ _______________________________________________________________________________

In the space below, design your circuit. Be sure to draw each element large enough so you can write in characteristics next to it.

List your safety precautions.

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P5D Direct Current Circuits

Student Journal Part II: Identify Your Circuit’s Characteristics 1.

After identifying and labeling your circuit diagram in Part I, complete the Ohm’s law calculations to fill in the table below. Use additional paper to show your work, as needed.

Circuit Element

Voltage (V)

Current (A)

Resistance (Ohm)

Power (W)

What careers are involved in designing, building, and/or troubleshooting circuits? Identify and describe some of them.

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P5D Direct Current Circuits

Student Journal Reflections and Conclusions 1.

What is the total power used by your circuit? How did you calculate that value?

A voltmeter is always connected in parallel and an ammeter is connected in series. Explain why this is the case.

Using all of the following terms, develop a graphic organizer. Use additional paper, as needed.

Terms: series circuit, parallel circuit, voltage, current, resistance, volts, amperes, Ohms, power, watts

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P5D Direct Current Circuits

Student Journal Additional Practice 1.

An 11-ohm resistor, a 5-ohm resistor, and a 4-ohm resistor are connected in a series across a 10-volt potential difference. What is the current in the circuit? What is the power in the circuit?

Two resistors, x and y, are connected in series across a 15-volt potential difference. The current of the circuit is 0.25 amperes. What is the equivalent resistance in the circuit? What is the power in the circuit?

Two 10-ohm resistors and one 5-ohm resistor are connected in parallel. What is the equivalent resistance in the circuit?

Four resistors are connected in parallel and the equivalent resistance in the circuit is 5 ohms. What is the resistance in each individual resistor?

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STEMscopedia: DIRECT CURRENT CIRCUITS P5D Reflect Are you on your computer every day, either doing work or playing games? Did you ever stop to think how it runs? It contains an electrical circuit. Is there anything else that is important and you need that contains electrical circuits? If you watch television, cook your food, or even use your mobile phone, then you are using electrical circuits. The circuits used in many devices are very complicated, but we can break them down into simple parts. Knowing a little about circuits can help you every day. Think back to fifth grade where electrical circuits were introduced. You probably made a simple circuit with a switch and a light with connecting wires. Did you really understand circuits and how they work? Conductors and Insulators Electric current is a flow of electrons, ions, or electrons and ions. With electrons, the current flows through a wire. If the flow is carried by ions, the flow is through electrolyte, which can be a liquid or a gel. When the ions and electrons are mixed together in space, they form plasma. You might visualize in your mind that a circuit is like a racetrack. The current flows along the closed track. Some materials allow a current to flow more easily than others. These are called conductors. Materials called insulators do not allow easy current flow. How does a conductor work? The atoms in the material have loosely attached valence electrons. These electrons can move or drift easily between the atoms. Because electrons can flow easily through these materials, electric currents have no problem moving. We say that the material conducts electricity. Metal objects composed of aluminum, copper, and gold are good conductors. Because of this, common circuits are made of copper wire. Silver is an even better conductor, but copper and aluminum are more abundant and cost effective. Look outside at the power lines. These lines are made of copper and aluminum. How does an insulator work? The atoms that make up an insulating material have tightly bound electrons. The electrons do not move easily from one atom to another or between atoms. Because the electrons do not move easily, little or no current flows. Rubber, plastic, glass, and wood are some examples of insulators. Most electrical wires are surrounded by rubber insulators so that we do not get shocked. Take a look at the photograph of power lines. The metal wires, which conduct strong electric currents, are supported by metal towers. Yet, if you were to touch the bottom of the metal tower, you would not get shocked. This is because an electrical insulator—usually ceramic—separates the wires from the tower. © Accelerate Learning Inc. - All Rights Reserved

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STEMscopedia: DIRECT CURRENT CIRCUITS Few Facts About Electricity • A Greek philosopher named Thales of Miletus discovered static electricity in 600 BC. • Benjamin Franklin, an American, named two kinds of charges as positive and negative. • In 1827, Georg Ohm discovered that some materials carry a current better than others. He then did more experiments and used the word resistance to explain the flow of electricity with these different materials. • In 1820, Hans Christian Oersted discovered that by putting an electric cable close to a compass, magnetism can be made by the electric current. • By 1882, Thomas Edison was building electric power plants.

Look Out Electric circuits are made up of electrical components. These components must be joined together without any gap in between to form a closed circuit. There are two ways in which an electric circuit can be arranged: series and parallel. A series circuit is a route for the flow of electricity that has only one path. A series circuit is a closed circuit in which the current follows one path. A series circuit connects the components one after the other. A single loop is formed. A parallel circuit has many paths for current to travel and more than one resistor. If one resistor stops working, current will still travel to other resistors on the same circuit. The voltage across all branches or paths of a parallel circuit is the same. A parallel circuit divides into two or more branches. The current divides and flows through each parallel branch. If a component breaks or is removed, the other components remain on. The flow of any electric current is measured in units of amperes (A).

One specific property about a circuit is that it must be a closed loop. The reason for this is conservation of electric charge; The total number of charges in a circuit remains constant. If current flows in a circuit, the electrons must travel on a loop so the total number of electrons stays constant. If there is a break in a circuit, current will not flow. This is how switches in electrical circuits work.

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STEMscopedia: DIRECT CURRENT CIRCUITS Circuits deliver electrical energy to a load, or device, that will use that energy. Loads change electrical energy into some other form of energy. Light bulbs, fans, and buzzers are common loads. Think about a light bulb. When current passes through the wires inside the bulb, electrical energy changes into heat energy and light energy. Similarly, when current passes through a buzzer, electrical energy changes into sound energy. And when current passes through a fan, electrical energy changes into mechanical energy. Remember, energy is not created in an electric circuit. When the light comes on, the speakers are belting out your favorite song, or the stove element is turned on—energy is simply changing forms. What causes current to flow? Electric current flows in a circuit when there is a potential difference between points in the circuit. A difference in electric potential means that charged particles gain or lose kinetic energy moving between points. A potential difference in a circuit is also called a voltage. Voltage is measured in units of volts (V).

A battery provides a potential difference in a circuit. Inside a battery, chemical reactions take place that separate positive and negative charges. Positive charges (protons) are moved to the positive terminal (end) of the battery. Similarly, negative charges (electrons) are moved to the negative terminal (end). Because positive and negative charges are attracted to each other, the battery must contain materials that make it difficult for the electrons to move back to the protons. This creates a potential difference, or voltage, between the ends of the battery. The voltage rating of a battery, such as nine volts or 1.5 volts, indicates the size of the potential difference.

When wire is connected between the two terminals, electrons at the negative terminal are attracted through the wire to the protons at the positive terminal. Thus, electrons flow around the closed path from one terminal to the other. Eventually, the chemical energy that separates positive and negative charges in the battery runs out. The battery no longer produces voltage, and no current will flow around a circuit. When this happens, we say that the battery is dead.

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STEMscopedia: DIRECT CURRENT CIRCUITS Ohm’s Law Voltage makes current flow. How much current flows in a circuit with a voltage source? The German physicist Georg Ohm discovered that the current in many materials is proportional to the applied voltage. According to Ohm’s law, V=IR. Ohm’s law can also be written as I=V/R. In these equations, V is the voltage of the circuit, I is the current flowing through the circuit, and R is the resistance of the circuit. Resistance is a measurement of how much a conducting material resists the flow of current through it. Resistance is measured in Ohms, written with the symbol Ω (the Greek letter omega). As previously discussed, voltage is measured in volts (V), and current is measured in amperes (A). You may wonder why current is assigned the variable I in Ohm’s law. The answer is that Ohm’s law refers to current intensity. Resistance indicates how easily current can flow in a circuit. A large resistance means current has a harder time flowing. Increasing the resistance in a circuit leads to less current. If the resistance decreases, the current increases. Ohm studied the electrical properties of many different materials. Ohm’s law states that, for many materials, the resistance is constant over a wide range of voltages. For these materials, a graph of applied voltage versus the current shows a straight line. Resistors that stay constant over a wide range of voltages are called Ohmic resistors. For example, if a 60-Ω Ohmic resistor is wired into a circuit, we can increase the voltage through the circuit and the current will decrease, but the resistance will always stay the same. Not all resistors are Ohmic. Materials that do not obey Ohm’s law are said to be non-Ohmic. In a non-Ohmic material or device, the graph of applied voltage versus current does not look like a straight line. The material does not have a fixed value of resistance. In these cases, you cannot use Ohm’s law to relate voltage, current, and resistance. Non-Ohmic devices include LEDs, like those in many television and computer screens. Power of Circuits Electrons flow out of a voltage source, through the rest of the circuit, and back into the voltage source. Conservation of energy means that electrons must lose the energy they gain from the voltage before returning to the voltage source. Where does this energy go? The electrons lose this energy in the rest of the circuit. For instance, in light bulbs, energy from a voltage source turns into light and heat. The electrons moving in a circuit carry energy from one part of a circuit to another. Power is defined as the change in energy over time in a system. Electrical power is the rate at which energy moves through a circuit. The moving current in a circuit provides power that we can use in many devices. This power can appear as light, heat, or mechanical power, as in an automatic door. Power is measured in units of watts (W). Power in an electric circuit is a function of current (I) and voltage. (V): P=IV

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STEMscopedia: DIRECT CURRENT CIRCUITS What Do You Think? Find the power consumed when 5.0 amps flow through a hair dryer plugged into 120 volts. Solution P = 600 W Series Circuits To discuss series circuits, we must understand what circuits are made of. All circuits have a voltage source, such as a battery, and some conducting material, such as a wire. They must also have a circuit element (or many circuit elements) to which power is delivered. A typical circuit element is a resistor, but there are other types of elements, such as capacitors and inductors. A series circuit may have several circuit elements in it, but the elements connect one after another along a single path. That is, the current must flow through each element, one after the other, in a series circuit. As we discussed earlier, electrons lose energy as they move from the beginning to the end of the circuit loop. We call this a voltage drop. We can use an instrument known as a voltmeter to measure the voltage drop through different locations in a circuit. For example, if one end of the voltmeter is placed on the positive terminal of a battery and the other end is placed on the negative terminal, a voltmeter should show a voltage drop equal to the total voltage of the battery. However, there will be a voltage drop as electrons move across each circuit element in the circuit. In a series circuit, the sum of the voltage drop across each element in the circuit equals the total voltage in the circuit. This property is due to the conservation of energy. The total energy lost by electrons moving along the circuit must equal the energy lost along each step. Parallel Circuits The other type of simple circuit is called a parallel circuit. In a parallel circuit, current can flow along multiple paths between two points. The two paths are said to be in parallel. What is the voltage across a parallel pair of resistors? Conservation of energy tells us the voltage changes by the same amount along each parallel path. Therefore, the voltage across parallel resistors is the same for each path and is equal to the applied voltage from a battery or other source. For example, in a parallel circuit with two resistors, the total voltage in the circuit, V, is equal to the voltage drop across each resistor, V1 and V2, such that: V = V1 = V2. Recall that the current through a series circuit is the same through all resistors. In a parallel circuit, however, the current flowing into the parallel resistors divides like a river into two smaller currents. Relationships Between Electric Current, Voltage, and Resistance The relationship between current, voltage, and resistance in an electric circuit is fundamental to the operation of any circuit or device and is expressed in Ohm’s law: Voltage is equal to the product of the electric current that is passing through and the resistance against the current.

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STEMscopedia: DIRECT CURRENT CIRCUITS •

•

Current: Current is the flow of an electric charge through an object or medium. Potential difference is the amount of energy, per unit charge, needed to move a charged particle from one point to another in an electrical field. Current flows from high potential energy to low potential energy. Current is denoted by I and is measured in amperes (A). The I refers to “intensity,” used by French scientist Andre-Marie Ampere to describe the intensity of the electric current. Voltage: Electric potential is the potential energy per unit charge, and it depends only on the location of the charge within the electric field. Voltage is the difference in electric potential between two points. In a resistor in a circuit, the voltage is equal to the product of the current and the resistance. When voltage is referred to as “electric potential,” it must be distinguished from electric potential energy by noting that the “potential” is a “per-unit-charge” quantity. Electric potential (voltage) is denoted by V and is measured in volts. Resistance: Resistance is a measurement of how an object opposes the flow of electric current through it. A resistor is an electrical component that provides electrical resistance in a circuit. When a charge falls through a potential difference, it dissipates energy. Power is the rate at which this energy is transferred and passed through. Resistance is denoted by R and is measured in ohms (Ω). Equivalent resistance is the total resistance in a circuit or part of a circuit, and it is used to simplify the electrical schematic.

Total Resistance in Series Circuits: Voltages are added together in series circuits. Thus, in a series circuit, the resistances of all the components are summed. Total Resistance in Parallel Circuits: Currents are added together in parallel circuits. So in a parallel circuit, the reciprocals of the resistances are summed.

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STEMscopedia: DIRECT CURRENT CIRCUITS What Do You Know? The flow of electricity depends on an energy source and a path, or circuit, through which it can travel. Study the images below. Decide whether or not electricity will completely flow through each circuit. Write “yes” or “no” and explain your reasoning. Then, for each image that includes the answer “yes,” describe the form of energy produced by the electricity.

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STEMscopedia: DIRECT CURRENT CIRCUITS Connecting With Your Child Build Your Own Circuit Help your child design and build circuits. Make your own simple circuit kit, which includes standard household batteries for voltage sources and a string of holiday lights or small LEDs for resistors. If using a string of lights, use wire cutters to cut the string into individual bulbs or short segments of bulbs. You may need to strip back some of the plastic insulation to expose the wires. You may wish to use tape to connect the wires and batteries. Guide your child in putting together different combinations of bulbs and batteries and observing the relative brightness of the lights. Make sure your child understands what the brightness signifies. (The brightness of a bulb is related to the power output of the bulb, which is defined as P = I(∆V.) According to Ohm’s law, adding more resistors to a series circuit will decrease the total current through each bulb. This will decrease the brightness of the bulbs. However, adding more resistors to a parallel circuit will increase the total current through each bulb. This will increase the brightness of the bulbs.) Have your child design a few combinations, then predict the relative brightness of the combinations. Your child should then check and compare the results with his or her predictions. Discuss what your child discovered in these combinations. How can we predict the brightness of a combination? How could we make a more accurate prediction of the combination?

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P5D Direct Current Circuits

Reading Science Name:

Date:

Group:

Designing a Circuit in a Commercial Building 1

Thick smoke wafts through the office building. The fire alarm is flashing and blaring. This is your first day on the job. Where is the stairwell? You look up and see a red exit sign above one of the doors. As you emerge from the building coughing, you see your new boss and coworkers standing in the parking lot. Even though you were unfamiliar with the building, you found your way to safety. Thanks to a whole team of engineers and craftsmen, the exit signs led you in the right direction.

Most internally illuminated exit signs today use LED lamps. One major advantage of LEDs is the life-span of the light. LEDs last 50,000–200,000 hours, while incandescent bulbs last only about 1,000–2,000 hours. A longer life-span means that the lamps must be replaced less often, saving in both material and labor cost. In addition, for the same brightness, LEDs consume 2–5 watts of power versus 30 watts for incandescent lamps. Lower wattage translates into less energy used, which is better for the environment and cheaper to operate over the life-span of the building.

Most commercial buildings receive their electrical supply from a utility company at 480 and 277 volts AC. Each electrical circuit in the building is protected by 20 amp circuit breakers. Electrical codes limit the load on each circuit to 80% of the circuit breaker rating, which is 4,432 watts for each circuit. Since each LED exit sign draws around 5 watts of power, an engineer could design about 800 exit signs on each circuit! In practice, all the exit signs on one floor are usually connected to a single circuit. Sometimes hallway lights are also connected to the same circuit. Since these lights are switched on and off, and exit signs are not, the exit signs are connected to a part of the circuit that is not switched.

What happens if the power goes out? Do exit signs stay illuminated if the power from the utility company to the building is interrupted? Absolutely yes! To ensure that exit signs remain illuminated in the absence of utility power, one of two design approaches is chosen. If the building has an emergency generator, exit signs are connected to an electrical circuit served by the generator. Another option is to install exit signs that have batteries for backup power. The disadvantage of having each exit sign contain its own battery is that the batteries require testing, maintenance, and replacement at regular intervals. Since paying someone to test, maintain, and replace the batteries is expensive, exit signs are usually connected to the emergency generator when available.

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Reading Science 5

Electrical engineers design circuits every day. They have to consider electrical theory, taking into account voltage, current, size of the conductor and circuit breaker, as well as other more advanced factors. In addition, engineers must be aware of the practical and financial consequences of their design choices. They attempt to minimize construction and maintenance costs, while meeting all applicable codes and regulations. For example, the exit signs above were connected directly to the 277 volt circuit. This practice eliminates the need for a transformer. Transformers take one voltage and change it to another. They can be expensive. Next time you look up in a room and see lights or walk down a corridor and see the exit sign above a door, remember that engineering design combined with an electrician’s skill made it all possible!

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Reading Science 1.

Which of the following statements correctly describes an advantage of LEDs over incandescent light bulbs? A.

LEDs have a longer life-span.

LEDs use more watts for the same illumination.

LEDs can be replaced remotely.

LEDs are harder to purchase.

Commercial buildings receive power from the utility company at – A.

120 and 208 volts AC.

120 and 408 volts AC.

208 and 277 volts AC.

277 and 408 volts AC.

Exit signs – A.

are switched on and off every day.

have to stay illuminated even when utility power is lost.

are never connected to a circuit with other lights.

always have their own batteries.

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Reading Science 4.

In paragraph 4, which two pieces of equipment serve the same function? A.

Exit lights and emergency generators

Exit lights and hallway lights

Batteries and emergency generators

Exit lights and batteries

Installing exit lights that run on batteries into a building means that – A.

technicians have to test, maintain, and replace the batteries regularly.

building occupants have to report burned out lights immediately.

the building requires a larger emergency generator than usual.

the exit lights have to be placed closer together because they are not as bright.

Electrical engineers are responsible for – A.

running conduits and wires through the building.

making sure building occupants have enough stairwells.

designing the electrical circuits to applicable codes.

Xhiring utility companies.

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P5D Direct Current Circuits

Math Connections Name:

Date:

Group:

In a series circuit, the electrical current runs through each component, and each component handles the same current. In a parallel circuit, the voltage is equal in each branch of the circuit. The relationship between current, voltage, and resistance in an electrical circuit is fundamental to the operation of any circuit or device and is expressed in Ohm’s law: Voltage is equal to the product of (a) the electrical current passing through and (b) the resistance against the current. The formula for Ohm’s law is V = IR, where V is voltage in volts, I is current in amps, and R is resistance in ohms (Ω). 1. A 52-volt battery powers a pair of 36 Ω resistors connected in a series circuit. What is the current flowing through this connection? (Round your answer to the nearest tenth.) 2. A 52-volt battery powers a pair of 36 Ω resistors connected in a parallel circuit. What is the current flowing through this connection? (Round your answer to the nearest tenth.) 3. Compare your answers to questions 1 and 2. Discuss similarities and differences. 4. Given the diagram shown on the right: a. Compare the brightness of each of the bulbs. b. Which light bulb draws the most current? c. If light bulb B is unscrewed, what happens to the other two light bulbs? d. If light bulb A is unscrewed, what happens to the other two light bulbs?

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Math Connections 15Ω

5. Look at this diagram of a combination of a series circuit and a parallel circuit. a. What is the parallel part of the circuit?

15Ω

b. How could the parallel part of the circuit be replaced without changing the total current from the battery?

15v 25Ω Resistance is a measurement of how an object opposes the flow of electric current through it. A resistor is an electrical component that provides electrical resistance in a circuit. • Total resistance in series circuits: voltages are added together in series circuits. So, in a series circuit, the resistances of all components are summed together:

R total = R1 + R2 + R3 +….. +Rn • Total resistance in parallel circuits: currents are added together in parallel circuits. So, in a parallel circuit, the reciprocals of the resistances are summed together:

1/R total = 1/R1 + 1/R2 + 1/R3 +….. + 1/Rn 6. Given the circuit below, what is the current in the battery? (Hint: what will need to be found before calculating the current?) 15v 40Ω

40Ω

10Ω 7. A heating pad has several strips of heater wire connected in parallel. Consider eight of the wires, each with 4 Ω resistance, connected to 12 V. Given this scenario, answer the following: a. What is the equivalent resistance of the eight wires? (Wires are in 2 groups of 2.)

b. What is the total current?

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WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK Circuits connected in parallel behave differently from circuits connected in series. Strings of lights are used by many people, especially during the holidays. Christmas lights are available in different colors and different styles, such as green lights and twinkling lights. For Halloween, some people use orange lights, or ones with covers shaped like bats or pumpkins. Have you seen the ones that look like red chili peppers? Each string of lights has the same parts: a connector plug at one end followed by one or more lights. Often the string has a connector at the other end, allowing strings to be linked together. However, the outside appearance does not tell you how the lights are actually connected in a circuit. The diagram above shows a single strand of lights with three light bulbs. In addition to the circuit drawn above, you also have access to a multimeter and can apply it to the circuit at the positions indicated by numbers 1–4 on the diagram. WRITE Describe the behavior of the circuit when all bulbs are working and when one is removed.

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WRITING SCIENCE

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High School Physics

P5E

Electric Circuits and Magnetic Fields

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P5E Electric Currents and Magnetic Fields

Student Journal Name:

Date:

Group:

Background: Get Your Gizmo Built and Running 1.

Describe the energy conversion in the gizmo.

How are electric forces and magnetic forces alike?

How are electric forces and magnetic forces different?

Building Your Gizmo Draw a labeled diagram of your gizmo.

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P5E Electric Currents and Magnetic Fields

Student Journal Reflections and Conclusions 1.

What is a force?

What adjustments (if any) did you have to make to get your gizmo to spin?

The gizmo that you built is a simple version of an electric motor. Where might you encounter electric motors in everyday life?

How would you move a load using your motor?

How could you get your motor to rotate faster?

Describe how you are handling reuse, recycling, and/or disposal of your materials.

Using all of the following terms, develop a graphic organizer. Use additional paper, if needed. Terms: electrical force, magnetic force, motor, current, brush, axle, coil

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STEMscopedia: ELECTRIC CURRENTS AND

MAGNETIC FIELDS P5E

Reflect Look around your room. How many things use electricity? How many use magnets? Computers, mobile phones, cars, televisions, coffee makers, microwaves, light bulbs, and hair dryers are just a few electronic devices you might use. In fact, most modern technology relies upon electricity in some way. While it is rather easy to think of devices that use electricity, it may not be so obvious to think of devices that rely on magnetism. However, it turns out that electricity is fundamentally related to magnetism. Many of the electronic devices that you use actually make use of magnetism as well. What exactly are electricity and magnetism, and how are the two related? How are electricity and magnetism applied in the world around us?

We can’t see electricity, so how do we know it’s there? We can see lightning in the sky during a thunderstorm, sparks from an outlet as we pull the plug, or a plasma ball, but these are a result of charged particles. However, these brief flashes of light are not actually electricity. To better understand electricity, we must understand that the fundamental unit of electricity is a charged particle. A charged particle carries an electric charge, and it is much smaller than an atom. An electric charge can be positive (proton +1) or negative (electron -1). Electrons are the most commonly charged particles that you will encounter.

Magnetic fields and electric currents are interrelated. In fact, both magnets and electric currents cause magnetic fields, while electric charges and changing magnetic fields cause electric fields. Both of these concepts can be seen in electromagnets. Electromagnets can be found in motors and generators, which are used in all areas of our lives.

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STEMscopedia: ELECTRIC CURRENTS AND

MAGNETIC FIELDS

Look Out

Electromagnetism is caused by the flow of electrical current. When this happens, a magnetic field occurs. An electric field is a force field surrounding every charged particle. One of the most important scientific discoveries of the last 200 years was the realization that electricity and magnetism are fundamentally related. This relationship is known as electromagnetism. Moving electric charges (electric current) produce a magnetic field. This means that an electric current produces both an electric field and a magnetic field. You can determine the direction of the magnetic field by the right-hand rule. Point the thumb of your right hand in the direction of the current. Then curl your fingers around the wire. Your fingers point in the direction of the magnetic field. An electromagnet is a temporary magnet created by an electric current. An electromagnet typically has a core made from iron. A simple electromagnet can be made by wrapping wire around an iron nail. When the wire is connected to a voltage source, current flows through the wire and a magnetic field is produced. This magnetic field causes the iron nail to become an electromagnet. The greater the current flowing through the wire, the stronger the magnetic field produced. You can also increase the strength of the electromagnet by increasing the number of windings of wire around the iron nail. Increasing the length of the wire, however, would decrease the strength of the magnetic field produced. Just as moving charges produce magnetic fields, a moving magnet produces an electric field. In other words, a changing magnetic field will produce an electric field. This is known as electromagnetic induction because a moving magnet can induce current in a wire, even if no battery or other voltage source exists.

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STEMscopedia: ELECTRIC CURRENTS AND

MAGNETIC FIELDS

Let’s extend these thoughts to electric motors and generators. How are they related to electromagnetic fields? An electric motor has magnets inside it. These magnets create motion inside the motor. A magnetic field is created as the current flows through the coil. (Review how an electromagnet is made above). The magnetic field produces a force that causes the motor to spin. Motors transform electrical energy into mechanical energy. In fact, more electricity is used by motors than by any other technology on Earth. The magnetic field can be regulated by the amount of electric current traveling through the windings around the core. One advantage of electromagnets is that they can be turned on and off as needed. Think about the speakers in your room. When they are not being used, you turn off the speakers and the electromagnets. When the motor in your car is not running, neither are the electromagnets.

While a motor converts electrical energy into mechanical energy, a generator is a device that performs the opposite task. It transforms mechanical energy into electrical energy. In other words, it generates electricity from a moving source of energy. Like a motor, a basic generator consists of a loop of wire and a magnet. However, the assembly is different for a generator. This time, the magnet is placed in the center of the loop of wire, and it can rotate freely. As the magnet rotates, the changing magnetic field induces an electric current in the loop of wire. Thus, the rotating mechanical energy of the magnet is transformed into electric energy.

Generators, today, run most of our power grids. Examples of generators that produce power are hydropower and wind power.

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STEMscopedia: ELECTRIC CURRENTS AND

MAGNETIC FIELDS

Importance of Electromagnetism Computers, mobile phones, and mp3 devices all contain hard drives that store data. Engineers are constantly creating new, denser technologies that allow more data to be stored in the same amount of space. This has allowed computers to become increasingly smaller and more powerful. However, no matter how small the hard drive, the basic principles are the same. Magnets are used to store information. An audio speaker also relies on the interaction between electric and magnetic forces. In an audio speaker, a coil of wire is attached to a cone-shaped object. This assembly is called a speaker cone. The speaker cone is suspended from a flexible frame, allowing it to move. A permanent magnet is suspended at the middle of the cone, next to the coil of wire. When a musical electric current is sent to the coil of wire, it produces a changing magnetic field around the coil. In other words, the speaker cone becomes an electromagnet!

What Do You Know? Draw and label the fields you would expect in the image.

Answer the following questions with your study buddy. 1. Magnetic fields and electric fields are identical in that they both ___________. 2. Aside from a permanent magnet, a magnetic field can also be generated directly by what? 3. Two metal spheres, each with a charge, interact through an electric field. The energy of the electric field can be changed. How can you do this? 4. What characteristic of an object results in its being able to generate an electric field?

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STEMscopedia: ELECTRIC CURRENTS AND

MAGNETIC FIELDS

Connecting With Your Child One example of the interaction between electricity and magnetism is a simple electromagnet. An electromagnet is a magnet produced when an electric current flows and produces a magnetic field. With your child, construct an electromagnet and then discuss the questions. You will need the following materials: • Iron nail, 3-4 inches long • Copper wire, 3 feet long • D-cell battery • Electrical tape • Paper clips • Iron filings • Washer • Screws • Rubber gloves Talk with your child about the relationship between the electric current and magnetic fields. How would they arrange the wire in order for the nail to become magnetized? 1. Take the copper wire and leave about five inches on one end. 2. Begin wrapping the copper wire around the nail. Try to make the coil neat and do not overlap the wire. 3. If needed, take wire cutters and cut off any excess wire. Leave about five inches at the other end when finished coiling the wire. 4. Connect each end to a terminal of the battery with electrical tape. You may want to wear rubber gloves when you do this as the wires will become hot. 5. To observe the properties of the electromagnet, move the electromagnet over a pile of paper clips, screws, washers, iron filings, or any other magnetic material. If the setup is assembled correctly, the above items will be attracted to the iron nail. You and your child can change the design by using a different voltage of batteries, a different type of nail, or increased or decreased windings of the copper wire. Try overlapping the copper wire to see if there is a change in the magnetism. Sit with your child and discuss the following questions. 1. Does increasing or decreasing the number of windings change the strength of the nail in picking up the items? 2. What caused the wire to get hot when you attached it to the terminals of the battery? 3. Electromagnets can be controlled. How can you turn off the electromagnet? 4. Do the batteries with different voltage have an effect on the nails magnetism?

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P5E Electric Currents and Magnetic Fields

Reading Science Name:

Date:

Group:

Roller Coasters and Magnets, a Thrilling Combination 1

You and your friends have waited more than an hour for this ride. Everyone has been talking about the new roller coaster, and finally you get to ride it! You sit down in the car, a little apprehensive. The car accelerates out of the station at high speed and climbs straight up. Screams erupt as it reaches the top and then accelerates backward through the station and up another track. With a strong jolt, the car comes to a quick stop back in the station. As you slowly climb down the stairs, you remember the first roller coaster you rode as a kid, where it seemed like every steep climb of the car was accompanied by the metal-on-metal sound of the chain slowly pulling the car up to the top. Ever wonder what's changed?

Magnets have been around for a very long time. The ancient Greek philosopher Plato described lodestone, also known as magnetite. Lodestone comes from a region of Greece called Magnesia, from which our word magnet derives. Navigators used compasses made with needles magnetized by rubbing them repeatedly across a lodestone. While Chinese literature mentions the properties of lodestone as early as 4 BC, clear evidence for the use of a magnetic compass in navigation comes from 1117 AD. These are examples of permanent magnets.

In contrast, electromagnets are temporary magnets. Electromagnets take advantage of the fact that current in a coil of wire can induce a magnetic field that can be turned on and off. Electromagnets are critical components of electrical motors and telegraphs. Telegraphs took advantage of the fact that a moving magnet can produce an electrical current in a wire. The current traveled to the receiving station and moved the magnet there.

In 1996, the first roller coaster using linear induction motors became operational at Kings Dominion in Doswell, Virginia. Linear induction motors are located on the roller coaster tracks. They produce an electric field that induces a current in a conductor mounted on the coaster car. One example of a conductor is the small metal fins protruding from the car. The opposing magnetic fields of the motor and the fins repel each other, thus pushing the car forward. A large number of induction motors are mounted inside the station, so cars can accelerate to about 100 km/hr in three to four seconds. A smaller number of induction motors are mounted before each element in the track, such as a loop. The roller coaster described in the first paragraph relies on computer controls to switch the polarity of the induction motors to propel the cars backward.

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P5E Electric Currents and Magnetic Fields

Reading Science 5

The roller coaster car also has to be brought to a stop. Modern coasters use a combination of permanent magnets and mechanical brakes to stop the car. Rapid deceleration relies on magnets. The brake magnet is attached to the car. It creates a moving magnetic field in the head of the rail. This generates eddy currents, disturbing the magnetic field and creating a horizontal force. Eddy currents are much like eddies in rivers: movement in eddies is disordered and often in a different direction from the main direction. The horizontal force works against the movement of the magnet and therefore the car. Eddy current brakes don't work at low speeds. Permanent magnets don't require power; therefore, power outages don't affect the braking. Additional mechanical braking using friction is also required to bring the car to a complete stop.

So magnets have played a critical role in making roller coasters more fun. Safety for riders has been enhanced through computer modeling of the track resulting in smoother curves. Biomedical engineering models the forces on the riders and also improves safety. Next time you shoot out of the station in a roller coaster, remember: magnets make it possible!

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P5E Electric Currents and Magnetic Fields

Reading Science 1.

Naturally occurring magnetic rock is called – A.

magnesia.

lodestone.

iron ore.

Plato’s rock.

Which of the following items does NOT use a magnet? A.

Compass

Telegraphs

Linear induction motors

Ballpoint pens

What is one of the advantages of electromagnets? A.

They can be switched on and off.

They are usually very small.

They work even during an electrical outage.

They can have more than two poles.

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P5E Electric Currents and Magnetic Fields

Reading Science 4.

Which part of the roller coaster track has the most linear induction motors close together? A.

The top of a loop

The station

The bottom of a loop

A long straightaway

To make a roller coaster go both forward and backward along the same track – A.

permanent magnets are mounted on both the car and the track.

the polarity of an electromagnet is reversed.

the car has fins on both sides.

the track is heated.

Which type of magnet do roller coasters use for braking? A.

An electromagnet

An eddy magnet

A permanent magnet

An energized lodestone magnet

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P5E Electric Currents and Magnetic Fields

Math Connections Name:

Date:

Group:

The magnetic field of a copper wire can be measured with the following formula: B = μI/2R, where B represents the magnetic field, μ is a constant equaling 4 πx10-7 Tesla-meters/amp, I is the current in amps and R is the radius of the wire. 1.

Determine what unit of measurement would be best to measure the radius of the wire. Justify your answer.

Show two ways to calculate the radius of the wire given the following information: B = 18.2 I = 27 amps

Compare and contrast the relationships between the radius and the magnetic field to the current and the magnetic field.

Write an equation to solve for each variable of the equation.

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P5E Electric Currents and Magnetic Fields

Math Connections Daniel is making a model of the solar system and he wants to include the magnetic fields of each planet on his model. He starts with a paper model shown below. He compares the actual radius of a planet and how far the magnetic field extends out to the radius of the model planet (in inches) in order to calculate how far the magnetic field should extend from the planet in the model. Measure the radius of each planet on the model (in inches) and use ratios to calculate the range of the magnetic field on the model. (Round to the third decimal place.) SUN Actual R

Magnetic Field

1,500 miles

3,000 miles

3,760 miles

150 miles

4,000 miles

40,000 miles

2,100 miles

450 miles

43,400 miles

4,300,000 miles

36,200 miles

23,200,000 miles

15,800 miles

7,300 miles

15,300 miles

8,400 miles

Model R

Model’s Field

Mercury

Venus

Earth Mars

Jupiter

Saturn

Uranus

Neptune

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P5E Electric Currents and Magnetic Fields

WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK Finding landmines using a metal detector relies on the presence of metal in the mines. Minimum-metal landmines have been developed to make them harder to find, although they are not frequently used. Landmines have been used in many conflicts. Mined areas are dangerous to anyone who uses the land. Hidden landmines remain deadly for decades after a conflict ends. Civilians are hurt by landmines every day. Portable mine detection started during World War II after Polish engineer and inventor Jozef Kosacki developed his unit. His design had two metal coils. One coil was connected to an oscillator, producing an oscillating current in the audible frequency. The second coil was connected to an amplifier and headphones. When the device would come close to a metal object, current would be induced in the object, which would alter the balance between the coils and produce an audible signal in the headphones. A fictional firm, Landmines Inc., is proposing to use landmines along a disputed border to limit the number of fighters who cross the border illegally. The firm proposes to use minimum metal mines. You are advising the president of one of the nations involved as to whether such mines should be placed. WRITE What do you recommend to the president regarding using minimum metal mines? Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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P5E Electric Currents and Magnetic Fields

WRITING SCIENCE

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High School Physics

P6ABC

Nuclear Processes

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P6ABC Nuclear Processes

Student Journal Name:

Date:

Group:

Part I: Nuclear Education Nuclear Energy: Fact Sheet A 1.

Identify the number of protons, electrons, and neutrons in the element carbon (C). The atomic

number identifies the number of protons. The atomic mass minus the atomic number can be used to calculate the average number of neutrons. protons ________ electrons ________ neutrons _______ 2.

Identify the number of protons, electrons, and neutrons in the element uranium (U). protons _______ electrons _______ neutrons _______

Create a diagram to show mass defect and binding energy.

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P6ABC Nuclear Processes

Student Journal Part I: Nuclear Education, continued Nuclear Energy: Fact Sheet B 1.

Is nuclear radiation made of matter or energy? Explain your answer.

_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 2. What makes an atom unstable? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 3. How does the release of energy during fusion provide evidence of mass-energy equivalence? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 4. Can we use fusion in nuclear power plants instead of fission? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 5. Is fusion as dangerous as fission? Explain. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

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P6ABC Nuclear Processes

Student Journal Part I: Nuclear Education, continued Nuclear Energy: Fact Sheet C 1.

What happens to radiation exposure over time after a nuclear accident?

Nuclear Energy: Fact Sheet D 1.

What source accounts for most of the average American’s yearly dose of radiation? How much radiation is it?

_______________________________________________________________________________ _______________________________________________________________________________ 2. How many millirems of radiation do Americans get from natural sources? How many millirems come from human-made sources? _______________________________________________________________________________ _______________________________________________________________________________ 3. What percentage of yearly radiation do Americans get from nuclear power plants? _______________________________________________________________________________ _______________________________________________________________________________ 4. Write a statement concerning Misconception # 2. Explain in what way it is a misconception. Use additional paper, if needed. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 5.

Write a statement concerning Misconception #3. Explain in what way it is a misconception. Use additional paper, if needed.

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P6ABC Nuclear Processes

Student Journal Part II: Nuclear Decay The most common radioactive isotopes released in a nuclear accident are the following. iodine-131 caesium-137 strontium-90 plutonium-241 Research the half-life of each. Write them below. half-life of iodine-131 __________________ half-life of cesium-137 __________________ half-life of strontium-90 __________________ half-life of plutonium-241 __________________ If you have 500 g of each isotope, how much would remain after one year? (Note that this may require you to convert time units.)

How much would remain after 10 years?

How much would remain after 100 years?

How much would remain after 1,000 years?

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P6ABC Nuclear Processes

Student Journal Part III: Develop Your Brochure Use the space below to organize information for your brochure.

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P6ABC Nuclear Processes

Student Journal Reflections and Conclusions 1.

How exactly does mass-energy equivalence relate to the article you selected?

Describe one item from another group’s brochure (that was not in your own brochure) that you found interesting. Explain why it was interesting.

How would you vote on a new energy bill that would put a nuclear power plant outside yourtown? Explain your decision.

In this activity, you have been exploring the application of modern science to current events. Why is this important?

Are science and technology the same thing? Explain.

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STEMscopedia: NUCLEAR PROCESSES

P6ABC

Reflect X-rays, MRI machines, weapons, smoke detectors, insect control, and cancer treatments—how are all of these applications related? All of them are radiation applications and are therefore part of the branch of chemistry that deals with the properties and reactions of atomic nuclei. This branch is called nuclear chemistry. Nuclear chemistry is based on the atom’s nucleus, which is composed of protons and neutrons. Fission and Fusion Large amounts of energy can be harnessed from various nuclear reactions. During World War II, scientists harnessed this energy to build Fat Man and Little Boy, the first nuclear bombs used during warfare.

Fat Man.

Model of an atom.

Little Boy.

These nuclear bombs used a process called fission. Fission occurs when a nucleus collides with a smaller particle and splits into two or more nuclei, releasing a large amount of energy. Fat Man used plutonium as its fuel source, while Little Boy used uranium. Both of these bombs relied on the same chain reaction. The fuel source underwent fission, which released large amounts of energy and a small number of neutrons. These neutrons then bombarded more uranium or plutonium atoms, causing more fission reactions to occur. The fission process. Little Boy dropped on Hiroshima, Japan, on August 6, 1945, killing around 140,000 people. Its explosive force was equivalent to roughly 17,000 tons of TNT. Fat Man dropped three days later on Nagasaki, Japan, killing around 70,000 people. This bomb’s explosive force was equivalent to roughly 21,000 tons of TNT. In both instances, half of the deaths were instant; the remainder died from radiation poisoning. These nuclear bombs caused Japan to surrender, leading to the end of World War II. Today, nuclear power plants harness energy released in fission reactions. The typical fuel is uranium-235, which experiences fission when bombarded with neutrons. Essentially, nuclear power plants convert the energy released from the fission reactions into electrical energy.

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STEMscopedia: NUCLEAR PROCESSES While nuclear fission produces a great deal of energy, many people are concerned about the hazards associated with maintaining fission-based nuclear power plants. Fissionable fuel is dangerous because it is highly radioactive, and the fission process leaves behind highly radioactive waste products. These materials must be contained and kept shielded from humans. Under normal circumstances, this is possible to accomplish. However, natural or man-made disasters can potentially compromise any materials’ containment. This makes running a nuclear power plant difficult and potentially hazardous.

A nuclear power plant.

What Do You Think? Do a quick Internet search on nuclear power plant disasters. Think about the advantages and disadvantages of nuclear power. Do you think we should continue to use nuclear power? Fusion occurs when two small nuclei collide and combine to form one larger nucleus. The word fusion means “to combine.” An example of a fusion reaction is shown in the illustration to the right. This example shows the fusion of a deuterium nucleus with a tritium nucleus. Deuterium ( ) and tritium ( ) are both hydrogen isotopes. As you see in the illustration, each isotope has one proton. However, deuterium has one neutron and tritium has two neutrons. Along with the change in nuclear makeup, large amounts of energy are released during fusion. Nuclear fusion involves two In fact, the energy released by stars, including the Sun, comes from small nuclei fusing to form nuclear fusion from inside the star’s core. one larger nucleus. Radioactive Decay and Half-Life Radioactive decay occurs when an atomic nucleus is unstable. To achieve stability, this unstable nucleus decays, or partially disintegrates. A radioactive atom has an unstable nucleus. When the nucleus decays, it releases mass (often in the form of particles) and energy. We call this radiation. The type of decay depends on the makeup of an atom’s nucleus. Every element is deﬁned by the number of protons in its atom’s nucleus. However, atoms of the same element can have different numbers of neutrons in their nuclei. This variation in neutron number gives rise to different isotopes of an element. For example, all helium atoms have two protons in their nuclei, yet they can have one or two neutrons. These two isotopes of helium are illustrated on the left.

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STEMscopedia: NUCLEAR PROCESSES Notice the symbols used to represent the isotopes. The element’s mass number is written at the upper left of the atomic symbol. This indicates the number of protons and neutrons in the atom’s nucleus. The atomic number is written at the lower left of the atomic symbol. This is the number of protons in the nucleus. Isotopes have the same number of protons but differ in the number of neutrons. This diagram shows both isotopes of helium (He). Some elements’ isotopes tend to be more stable than others. Radioisotopes have unstable nuclei that tend to undergo decay. Often the instability results from having too many or too few neutrons. To achieve stability, a radioisotope releases particles, high-energy photons, or a combination of the two. Radiation is the term used to describe these types of emissions. Let’s look at some speciﬁc examples. Alpha radiation. Many radioisotopes emit alpha radiation. One example is plutonium-24 ( ). The nucleus in a plutonium-240 atom contains 94 protons and 146 neutrons. Therefore, its atomic mass is 240 (94 + 146 = 240). This nucleus is unstable and disintegrates by releasing an alpha particle. This particle, often represented by the Greek letter α (alpha), is composed of two protons and two neutrons and carries a +2 charge. This is the composition of a helium-4 nucleus ( ). What is left of the decayed plutonium-240 nucleus? As a result of the decay, it lost two protons and two neutrons. Because it has lost protons, its elemental identity has changed to a uranium atom with 92 protons and 144 neutrons ( ) Beta radiation. Beta emission involves another type of particle emitted by a decaying nucleus. Many beta particles are electrons, which are particles much smaller than alpha particles and carry a -1 charge. They are represented by the Greek letter beta (β). Carbon-14 ( ) is a radioisotope that emits beta particles when it decays. During each decay event, a neutron in the carbon-14 nucleus breaks down to form a proton and a beta particle. The beta particle is released into the environment, while the proton remains in the nucleus. This added proton changes the atom’s identity from carbon, with six protons, to nitrogen, with seven protons (

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STEMscopedia: NUCLEAR PROCESSES Gamma radiation. The nuclear decay that results in the emission of alpha or beta particles can leave a nucleus with excess energy. The nucleus can release this energy as gamma radiation. Gamma rays are represented by the Greek letter gamma (γ). This type of radiation consists of high-energy photons with no mass and no charge. Because these photons have no mass, their emission does not change the balance of protons and neutrons in a nucleus. For example, when cobalt-60 undergoes radioactive decay, both beta particles and gamma rays are released. These three types of radiation are hazardous to humans because they can damage living cells. Each type of radiation is characterized by a different energy and ability to penetrate matter. Alpha radiation is the weakest. It cannot penetrate the thick layer of human skin cells, although it is dangerous if ingested. Beta radiation is energetic enough to pass through human skin cells and damage living tissue. A thin layer of aluminum metal can stop beta radiation. People working with beta emitters need to wear protective clothing to shield themselves from the emissions. Gamma radiation is the most energetic of all. It is extremely hazardous because of its ability to penetrate most types of matter. Thick lead boxes are necessary to contain radioisotopes that emit gamma radiation.

What Do You Know? Complete a triple Venn diagram to compare the characteristics and effects of each of the three types of radiation from above.

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STEMscopedia: NUCLEAR PROCESSES Half-Life Half-life is the length of time required for half of any given amount of an element to decay into another element. Carbon-14 has a half-life of 5,730 years. That means that after 5,730 years, half of that sample decays. After another 5,730 years, one-quarter of the original will remain. If we start with 100 grams of a radioactive substance whose half-life is 15 days, then after 15 days, 50 grams of the substance will remain. The age of the solar system was dated by calculating the half-life of meteorites. The half-life of any substance can be calculated, given the rate of decay, which is the initial quantity of the substance and the quantity remaining after a measured period of time. You can use the formula below: A (final amount) = A1 (initial amount) X (½) t/h (t=time, h=half -life) Let’s say a random isotope has a half-life of 1.23 years. If you start with a sample of 45 grams, how much will be left in 6.7 years? A= 45g X (½) 6.7/1.23 A= 1.03 grams Try It! An isotope has a half-life of 240 years. If you start with 200 grams, how much will be left after 100 years?

Look Out Balanced Nuclear Equations You have seen several types of nuclear reactions. In each of these cases, it is possible to identify the reactants from the beginning of the reaction and the products that result from them. You can write equations to represent these reactants that go into the reaction and products. Also, coefﬁcients can be used to indicate the numbers of each reactant and product to show a balanced equation for any nuclear reaction. In this way, nuclear reactions are like chemical reactions. Nuclear reactions follow the same law of conservation of mass and energy as chemical equations. Matter is neither created nor destroyed. It just changes form. These isotopes are changing into new elements. To balance equations for nuclear reactions, you need to know the atomic numbers and mass numbers attached to atomic symbols representing nuclei. The following diagram illustrates a nuclear reaction in which lithium-6 ( ) collides with deuterium ( ), an isotope of hydrogen.

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STEMscopedia: NUCLEAR PROCESSES The result is two alpha particles ( ). The diagram shows a picture of the reactants and products as well as the symbols needed for the balanced equation.

Study the balanced equation for this reaction. Notice the mass numbers in the upper-left spot next to each atomic symbol and the atomic numbers in the lower-left spot next to each atomic symbol. Now observe that if you add the mass numbers on the reactant side (6 + 2 = 8), the value equals the sum of the mass numbers on the product side (4 + 4 = 8). Also, the sum of the atomic numbers on the reactant side (3 + 1 = 4) is equal to the sum of the atomic numbers on the product side (2 + 2 = 4).

Look Out A similar method is used for beta decay. Because a beta particle is an electron, the symbol 0 e is used to represent a beta particle in reaction equations. The superscript zero indicates the electron’s mass, which is negligible compared to the mass of a proton. Because a beta particle is not a nucleon, its subscript (-1) represents its charge instead of its atomic number. Consider the following reaction in which carbon-14 ( ) decays into nitrogen -14 ( )

The subscripts indicate the change in the nucleus’ charge. The carbon nucleus contains six protons, so it has a charge of +6. The nitrogen nucleus contains seven protons, so it has a charge of +7. The electron charge of -1 balances the charges on the reactant side and the product side of the equation: 6 = 7 – 1. The symbol ( ) represents a gamma ray in a nuclear reaction equation. Both the superscript and the subscript are zero because a gamma ray has neither mass nor charge.

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STEMscopedia: NUCLEAR PROCESSES Review Remember that a particle’s atomic number determines its identity. Suppose, for example, a particle must have a subscript of 92 and a superscript of 238 in order for the nuclear reaction equation to be balanced. You can use the periodic table to determine that the particle must be uranium. We can summarize the requirements for a balanced nuclear reaction as follows: • The sum of the mass numbers of the reactants must equal the sum of the mass numbers of the products. • The sum of the atomic numbers or charges of the reactants must equal the sum of the atomic numbers or charges of the products. • Coefﬁcients are placed in front of a reactant or a product to indicate when the reaction involves more than one of the speciﬁed particle. The table below summarizes the symbols used for different types of particles frequently encountered in nuclear reactions: Name of Particle

Symbol

Properties

Alpha

+2 charge; large mass

Beta

-1 charge; very small mass

Gamma

no charge; no mass

Positron*

+1 charge; very small mass

Neutron

no charge; large mass

*Positrons are another kind of beta particle. A positron is like a positively charged electron.

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STEMscopedia: NUCLEAR PROCESSES Try Now Study the partially completed nuclear equations in the following table. Fill in the missing particle for each equation. Then identify whether each nuclear reaction is nuclear decay, ﬁssion, or fusion. Identify if it is nuclear decay, and state whether alpha, beta, or gamma emission occurs. Partial Nuclear Equation

Identity of Missing Particle

Type of Nuclear Reaction

1. Rank the three most common types of radiation in order of increasing penetrating power. 2. Define fission. Where have we harnessed the power of fission reactions? 3. Define fusion. Give an example of where fusion occurs.

Connecting With Your Child Demonstrating Alpha and Beta Decay Help your child build atoms with different colored candies, beads, or any other circular items in your home. Use one color for protons, one color for neutrons, and one color for electrons. (Be sure to reference the chart on page 8 for alpha and beta decay particles). For example, build a helium atom with two protons, two neutrons, and two electrons. The student should choose three colors of items to represent each particle (red candies for the protons, green candies for the neutrons, and yellow candies for the electrons). This helium atom has an atomic number of 2 (because it has two protons) and has a mass number of 4 (because the mass comes from the nucleus, which includes two protons plus two neutrons). You will be performing one alpha decay series and one beta decay series. Alpha decay normally occurs in atoms with a heavier, unstable nuclei. However, in order to limit the amount of items needed, these are theoretical nuclear reactions.

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STEMscopedia: NUCLEAR PROCESSES Alpha Decay: 1. Build a nitrogen atom with seven protons (all protons should be the same color) and eight neutrons (all neutrons should be their own uniform color) in the nucleus. Then place seven electrons (again, electrons should all be the same uniform color) around the atom’s nucleus. Once your atom is built, fill in the chart below. Atom

Protons

Neutrons

Mass Number

Symbol

Nitrogen

2. This nitrogen atom will undergo alpha decay. Using your built atom, demonstrate alpha decay. Fill in the chart below to show the movement of protons and neutrons out of the nucleus. Reactant

Products

Beta Decay: 1. Rebuild your initial nitrogen atom that you used for the alpha decay. 2. This nitrogen atom will now undergo beta decay. Using your built atom, demonstrate beta decay. Fill in the chart below to show the movement of particles. Reactant

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Products

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P6ABC NuclearProcesses

Reading Science Name:

Date:

Group:

Fusion or Fission 1

Nuclear reactions can generate a great amount of energy. However, not all nuclear reactions are the same. There are two very distinct types of nuclear reactions—fusion reactions and fission reactions. What are the differences and similarities between nuclear fission and nuclear fusion? As you have learned, all atoms are made of subatomic particles called protons, neutrons, and electrons. In the simplest terms, nuclear fission occurs when large, unstable atoms split into smaller atoms to achieve a more stable state. Nuclear fusion is the opposite of fission. Fusion occurs when smaller atoms bind together to form a larger, more stable atom. In both cases, the reaction occurs to bring the atom to a more stable state by a reduction of potential energy.

Nuclear fission reactions occur when the nucleus of an atom is split into fragments. When this occurs, smaller fragments are created. Most often, the result is two fragments of relatively equal mass. How is this energy created? You can compare the mass of the starting atom and the masses of the final products. You will find that the mass of the final products is less than the mass of the starting atom. Yes, in this type of nuclear reaction, mass is lost! This means that matter is lost. This loss of matter is known as the mass defect. Remember, the law of conservation of mass is for non-nuclear changes. Nuclear reactions are described by conservation of mass-energy. The small amount of lost mass is converted directly into large amounts of energy. The energy created from this reaction can be used to generate electricity in power plants or for the huge explosions of atomic bombs.

One type of atom used for fission reactions is an unstable isotope of uranium known as uranium-235. The stable isotope is uranium-238. In order for this reaction to occur, a neutron must collide with the uranium-235 nucleus, creating uranium-236. This collision creates enough energy to split the newly formed nucleus into smaller nuclei. A huge amount of energy is released in the process. As the nucleus splits and releases energy, more neutrons are produced. These may collide with another uranium-235 nucleus, causing it to undergo fission. This will create more energy and produce even more neutrons. The reaction will become something called a chain reaction if enough neutrons are produced during collisions to keep it going.

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P6ABC NuclearProcesses

Reading Science 4

The minimum amount of material that is needed for the reaction to keep going is called the critical mass. The trouble with fission reactions is that radiation and nuclear waste products are created in the process. This is a problem, as many nuclear power plants use fission to produce energy, producing a large amount of radioactive byproducts as a result.

Conversely, in fusion reactions, the nuclei from atoms with low atomic weights combine to create heavier nuclei. This reaction does not require neutrons in order to occur. Two light nuclei must collide with a great deal of energy. Fusion reactions require extremely high heat. In fact, the heat required can exceed several million degrees Celsius (yes, several million!) To put these types of temperatures in perspective, the temperature at the surface of the Sun is around 5,600ºC. Meanwhile, the temperature near the core of the Sun is calculated to be around 15 million ºC. This should give you a hint of how hot a nuclear reaction is. In fact, the Sun is a product of an ongoing fusion reaction that has been occurring for billions of years.

Why is such high heat required for these reactions? Remember, the protons of atoms are all positively charged. In order to combine atoms, the repulsion of the positive protons of the combining atoms must first be overcome. Extremely high heat gives the nuclei the kinetic energy needed to overcome the repulsion. As shown with the Sun, fusion reactions are also very exothermic. Therefore, fusion reactions have the capability of producing more energy than is required to initiate the reaction. This creates a self-sustaining reaction that holds great promise for energy production. A fusion reaction will sometimes begin with a fission reaction to get it started. In the right conditions, it can sustain itself once started. One of the benefits of fusion reactions is that there are no radioactive byproducts. On Earth, fusion reactions result in the element helium. Heavier elements, like beryllium or carbon, are produced by fusion in stars. Hydrogen bombs are produced by fusion reactions in which several isotopes of the element hydrogen are combined to produce helium.

How can you remember the difference between these two types of nuclear reactions? Think in terms of vocabulary that you may already know. A fissure is a crack or opening that can appear on the surface of Earth. It is a separation. A fission reaction will therefore “separate” an unstable atom into parts. A fusion reaction will “fuse” two atoms together.

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P6ABC NuclearProcesses

Reading Science 1.

There are two distinct types of nuclear reactions: fusion reactions and fission reactions. In which reaction is the nucleus of an atom split into two or more atoms? A.

Fusion reactions

Fission reactions

Both nuclear reactions

Neither nuclear reaction

In order for fission reactions to be successful, they must be self-perpetuating, meaning they must be able to keep themselves going. What do you call the minimum amount of material that is needed for the reaction to keep going? A.

Isotope

Mass defect

Critical mass

Neutron

Our Sun is a star that is fueled by a specific type of nuclear reaction. Which type of nuclear reaction is this? A.

Fusion

Solar

Fission

Radioactive

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P6ABC NuclearProcesses

Reading Science 4.

Why is the fusion reaction not currently used to produce energy, especially as it is a "clean" form of energy that does not create radioactive or nuclear byproducts? A.

There are currently not enough fuels for fusion reactions.

Fusion reactions are highly endothermic, making them dangerous.

Fusion reactions do not yet produce enough energy.

The heat it takes to start a fusion reaction is too high to contain.

Fission reactions are currently used to provide energy for many different sources. Where does the energy produced during the reaction come from? A.

From the mass lost during the reaction, or the mass defect

From the mass created during the reaction, or the mass increase

From the critical mass of the reaction

From the protons created during the reaction

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PS6ABC Nuclear Processes

Math Connections Name:

Date:

Group:

Radioactivity is the release of energy and matter that results from changes in the nucleus of an atom. An unstable atom does not have enough binding energy to hold the nucleus together permanently and is called a radioactive atom. In an unstable atom, the nucleus changes by giving off a neutron to get back to a balanced state. As the unstable nucleus changes, it gives off energy and matter (radiation) and is said to be radioactive. The graph below shows the relationship between the number of protons (Z) and the number of neutrons (N) in atomic isotopes. The colored scale on the side shows the stability of the isotope based on its half-life. Atomic Isotopes by Half-Life 1. What does the line Z = N represent?

At what atomic number on the graph do the stable isotopes move away from the graph N = Z?

After what atomic number does there appear to be no more stable isotopes? What element does this represent?

Use the chart and a periodic table to figure out how many protons and neutrons Neon-11 has. Is it stable or unstable?

Use the chart and a periodic table to figure out the number of protons and neutrons in Selenium-72. Is it stable or unstable?

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PS6ABC Nuclear Processes

Math Connections Nuclear reactions can be expressed by an equation similar to that of a chemical equation. However, in a nuclear reaction the nucleus is affected rather than the atom’s electrons. When writing a nuclear reaction, the chemical symbol of the element is used.

The upper number (A) represents the sum of the protons and neutrons, and the bottom number (Z) represents the number of protons. In the following equation, Barium-141 is an isotope that undergoes radioactive decay to produce Lanthanum and beta rays. Notice that the atomic numbers and mass numbers must be equal on both sides.

Complete the following equations using data from the periodic table. 6.

10. Create an equation to show Phosphorus-32 undergoing beta decay.

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P6ABC Nuclear Processes

WRITING SCIENCE Name:

Date:

Group:

LOOK

THINK Fission and fusion processes in stars are a driving force in the universe. Fusion occurs in stars converting hydrogen and helium into heavier and heavier elements. Once all the hydrogen and helium are exhausted, the star expels its outer shell gently as a nebula or violently as a supernova. The supernova creates even heavier elements that may be unstable and will undergo fission. Both fusion and fission produce great amounts of energy. This energy can trigger new stars to form from the remaining gas and dust of other dead stars. Eventually, this process will use up all of the material in the universe. WRITE What will happen to the universe when no more energy is created by fusion and fission? Be sure to • clearly state your central idea; • organize your thoughts; • develop your essay in detail; • choose your words carefully; • use correct spelling, capitalization, punctuation, and grammar.

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P6ABC Nuclear Processes

WRITING SCIENCE

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acceleration

GLOSSARY OF TERMS

body

acceleration – the rate of change in velocity; speeding up, slowing down, or changing direction

angular displacement – the angle in radians through which a point or line has been rotated about a specified axis

action-reaction pair – for every action force, there is an equal and opposite reaction force

angular/rotational acceleration – change in an object’s angular or rotational velocity

additive color – color created attractive force – the tendency for one object to pull other by mixing various different light colors with shades of red, objects toward it green and blue (primary colors) average velocity – the total distance traveled in a specific alpha particle – a positivelydirection divided by the amount charged particle identical to of time over which the distance the helium atom nucleus, with two protons and two neutrons, was traveled that is emitted from radioactive beta particle – a negativelydecay of a nucleus charged electron emitted from the radioactive decay of a ammeter – instrument used nucleus to measure electric current in amperes body – identifiable collection of matter, which may be constrained by an identifiable boundary © Accelerate Learning Inc. - All Rights Reserved

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centripital acceleration centripetal acceleration – change in an object’s velocity that will cause it to move in a circular path rather than a straight line centripetal force – net force acting on a object moving in a curved path that accelerates the object toward the center of the path’s curvature charge – an electrical property of matter which can be neutral, positive, or negative; the net difference between the number of protons and electrons in a molecule; a property of matter giving rise to all electric forces and interactions; there are three kinds of charge: negative, positive, and neutral charge transfer – a fraction of electrical charge transferred between molecular entities

conductor

circuit – a closed loop of conductors through which an electrical current can flow closed system – a system which does not exchange matter or energy with its surrounding environment compression – a force that tries to collapse an object concave lens – a lens with a surface that curves inward conduction transfer – charge transfer that occurs between objects that are in direct contact with each other conductor – a substance that allows the flow of electric charge or transfers thermal energy through matter

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constructive interference

GLOSSARY OF TERMS

constructive interference – occurs when the crest of one wave meets the crest of another wave at the same point, increasing the wave’s amplitude

diffraction

Coulomb’s Law – states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them; (F=Kcq1q2/d2)

converging – in optics, it refers to light rays bending toward current – the flow of an each other as they reflect or electrical charge through an refract object or medium

convex lens – a lens having at degree – an angle least one surface that curves measurement; a complete outward like the exterior of a rotation is 360 degrees sphere destructive interference coordinate axis – a fixed – occurs when the crest of reference line in a coordinate one wave meets the trough system of another wave at the same point, decreasing the wave’s coulomb – SI unit of an electric amplitude charge; equal to the quantity of electricity conveyed in one diffraction – the behavior of second by a current of one a wave as it bends around a ampere sharp edge; occurs when a wave passes through a single narrow slit or multiple narrow slits © Accelerate Learning Inc. - All Rights Reserved

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dimension

dimension – the minimum number of coordinates needed to specify any point within a mathematical space direction – a straight path that something could move along displacement – the vector quantity that gives the straight line distance from starting position to ending position distance – a measure of how far apart two objects are

electric motor

elastic collision – an encounter between objects in which the total kinetic energy of the objects before and after the collision is equal electric field – the force field between different electric charges; a region around a charged particle or object within which a force would be exerted on other charged particles or objects

electric generator – a device that changes mechanical diverging – in optics, it refers energy into usable electrical to light rays bending away from energy each other as they reflect or refract electric motor – machine that uses magnets and electricity to Doppler effect – an apparent make things move shift in the frequency of a wave due to the motion of the observer or the source of the wave

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electric pontential energy

GLOSSARY OF TERMS

electric potential energy – the potential energy per unit of charge that an object would have at a point in space as the result of the object’s charge and the charges of other objects at other points in space electrical charge – physical property of matter that causes it to experience a force when placed in an electromagnetic field; can be positive, negative, or netural electrical force – the interaction between a charged particle and an electromagnetic field or between two charged particles

electromagnetic wave

electromagnet – a temporary magnet in which the magnetic field is produced by electrical current electromagnetic field – a magnetic field created by an electrical current electromagnetic induction – the production of electric potential difference across a conductor as the conductor moves through a magnetic field electromagnetic wave – oscillations of electromagnetic fields that carry energy through a medium or through a vacuum

electrical potential – the potential energy per unit of charge that an object would have at a point in space as the result of the object’s charge and the charges of other objects at other points in space

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electron

force

electron – a negativelycharged subatomic particle of the electron cloud; involved in the formation of chemical bonds; a negatively-charged subatomic particle with no known substructure or constituent parts; electrons orbit the nuclei of atoms and are involved in the formation of chemical bonds

equivalent resistance – the total resistance in a circuit or part of a circuit

electron affinity – a neutral atom’s likelihood of gaining an electron and becoming a negative ion

fission – a nuclear reaction in which a heavy nucleus breaks into two lighter nuclei, releasing energy

energy – the ability to cause change or do work; controls the amount of change that can occur within a system; without enough energy, change cannot occur.

force – a push or pull that can change the motion of an object; a push or pull that causes an object to move, stop, or change direction; an interaction between an object and another object or field that acts to change the motion of the object

equilibrium – a condition in which all competing influences are balanced

exchange/transfer – to convey or cause to pass from one place, person, or thing to another field – a region in space in which a force is experienced

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free-body digram

GLOSSARY OF TERMS

horizontal component

free-body diagram – a diagram showing an object and the directions and magnitudes of all the forces acting on the object

gamma ray – ionizing electromagnetic radiation of very high frequency and energy emitted from the radioactive decay of a nucleus

frequency – the number of wave cycles that pass a given point per unit of time

gravitational field – the region of space surrounding a body in which another body experiences a force of gravitational attraction

friction – a force that resists the relative motion of two objects or substances sliding against one another friction transfer – a force that resists the relative motion of two objects or substances sliding against one another fusion – a nuclear reaction in which two or more atomic nuclei combine and form a single atomic nucleus

gravitational force – a force that causes objects with mass to attract each other gravity – attraction between two objects with a strength that is proportional to the masses of the objects half-life – the time required for half the nuclei in a sample of a specific isotopic species to undergo radioactive decay horizontal component – the vector component in the x-direction

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impulse

kinetic energy

impulse – a force exerted over insulator – material through a brief time interval that acts to which heat or electricity does not easily flow change the momentum of an object interference – the combination induction transfer – a method of two or more waves to form a resulting wave with an of charging an object that amplitude that is determined involves no contact and only by the amplitudes of the polarizes the charges within combining waves a neutral object, causing it to behave as if it were charged; the induction of electric current isotope – any two or more forms of an element with the to flow using the interaction between charges and magnetic same number of protons in the nucleus but a different number fields of neutrons inelastic collision – an joule – a unit used to measure encounter between objects work or energy in which some of the kinetic energy is converted into other kinetic – in motion forms of energy inertia – an object’s tendency to resist changes in its motion

kinetic energy – the energy of the object due to its motion

instantaneous velocity – the rate of motion of an object at a single point in time

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law of universal gravitation

GLOSSARY OF TERMS

law of universal gravitation – the law that says every object in the universe attracts every other object and that the force is affected by mass and distance; the greater the mass of an object, the greater the attraction; the farther apart the objects, the weaker the attraction magnetic field – the area around a magnet or moving electric charge that can exert a magnetic force magnetic force – a force of attraction or repulsion that arises between electrically charged particles because of their motion

momentum

mass – a measure of how much matter is present in a substance mass energy equivalent – states that mass is concentrated energy; the amount of energy in a given amount of mass can be calculated with the formula E = mc2 mass-defect – the difference between the mass of an atomic nucleus and the sum of the masses of the subatomic particles within the atomic nucleus mechanical wave – a wave that propagates as an oscillation of matter, and therefore transfers energy through a medium

magnitude – size or an amount; a property by which the object or an amount can be momentum – the motion of compared to other objects or amounts of objects of the same a moving object, determined by the product of its mass and kind velocity © Accelerate Learning Inc. - All Rights Reserved

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multimeter

multimeter – an instrument used to measure electric current, voltage and resistance over several ranges of value negative acceleration – when an object is slowing down, the acceleration is in the opposite direction as the velocity, thus this object has a negative acceleration neutron – a subatomic particle of the nucleus of an atom that is without charge and contributes to the mass of an atom Newton’s third law – Newton’s law that states that for every action there is an equal and opposite reaction; often referred to as Newton’s third law of motion

periodic motion

nuclear decay – the spontaneous disintegration of a nucleus with the emission of ration/energetic particles such as alpha particles, beta particles, or gamma rays nuclear stability – nuclear stability is based on the neutron to proton ratio; if a nucleus is stable, then it is not spontaneously emitting any kind of radioactivity open system – a system in which matter and/or energy can be exchanged with the environment parallel circuit – a closed circuit in which the current divides into two or more paths before recombining to complete the circuit

periodic motion – motion that normal force – the force repeats its path over and over generated by a surface in opposition to an object pressed again in equal intervals upon it 456

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permanent magnet

GLOSSARY OF TERMS

projectile motion

permanent magnet – a material that retains its magnetism after it is removed from a magnetic field and without an electrical current flowing through it

potential drop – the difference in the voltage readings before and after each component of a circuit that represents the amount of energy used by that component of the circuit

Planck’s constant – the constant that gives the unvarying ratio of the energy of a quantum of radiation to its frequency; has an approximate value of 6.626 × 10−34 joule per second; represented by the symbol h

potential energy – the energy stored in an object that is not moving

polarization – a separation of electric charge between atoms in a molecule, resulting from the unequal sharing of electrons in a covalent bond potential difference – the amount of energy needed to move a charged particle from one point to another in an electrical field

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power – the rate of work or energy transfer per unit of time projectile – an object thrown through space by the exertion of a force projectile motion – the curved path taken by an object as its horizontal motion remains unchanged due to inertia; while its downward motion is accelerated by gravity

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proton

GLOSSARY OF TERMS

proton – a positively-charged subatomic particle of the nucleus of an atom which contributes to the mass of the atom

resultant

ray diagram – a diagram showing the paths of selected rays through an optical system refraction – change in the direction of a wave as it passes through different objects at different speeds

Pythagorean Theorem – the fundamental relationship among the three sides of a right triangle; the theorem states that repulsive force – a force that the square of the hypotenuse is causes two items to repel one equal to the sum of the squares another of the other two sides resistance – the ability of a material to oppose the flow of radian – an angle electric current through it measurement; 1 ¶ radians is equal to 180 degrees. 2 ¶ radians is equal to 360 degrees resistor – a component of an electrical circuit that opposes the flow of electric current radioactivity – the process by which unstable atomic nuclei become more stable by resting position – an object’s default position outside of emitting energy external forces range – the difference between the largest and smallest values resultant – the vector sum of two or more vectors in a set of values

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rotational motion

GLOSSARY OF TERMS

rotational motion – an object moves in a rotational motion if every point of the object moves in a circular path with a common axis rotational/angular velocity – an object’s rate of rotation (i.e. the number of times it rotates per second)

speed of sound

Snell’s Law – a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air

sound wave – the pattern of scalar quantity – a quantity disturbance caused by the that is fully described by the movement of energy traveling magnitude and does not have a through a medium (such as direction air, water, or any other liquid or solid matter) schematic/circuit diagram – a drawing that illustrates speed – the measurement of a system by using abstract the rate of change of position symbols with respect to time series circuit – a closed circuit speed of light – the distance that has a single path for the light can travel through a given current running from and to the substance in a unit of time power source speed of sound – the distance traveled per unit of time by a sound wave traveling through an elastic medium © Accelerate Learning Inc. - All Rights Reserved

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spring constant

GLOSSARY OF TERMS

vertical component

spring constant – the ratio of a force affecting a spring to the displacement caused by it

tension – a force that tries to stretch an object

460

thin lens equation – relates standing waves – the vibration object distance, image distance, and focal length of a system in which some particular points remain fixed time – measurements used to while others between them quantify intervals, durations, vibrate with the maximum and sequences such as amplitude minutes, hours, etc. static – not moving vector – a quantity with both a magnitude and direction static electricity – an electric charge produced by friction vector quantity – a quantity with both a magnitude and surroundings – the area direction around a given physical or geographical point velocity – the rate of change system – a group of interacting of position; the measurement of speed and direction of an or interdependent elements forming a complex whole, as in object all the factors or variables in an environment or all the variables vertical component – the vector component in the that might affect a science y-direction experiment

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volt

GLOSSARY OF TERMS

work

volt – SI symbol: V; derived unit for electric potential and voltage; named in honor of the italian physicist Alessandro Volta voltage – the difference in electrical potential between two points voltmeter – instrument used to measure electric potential in volts wavelength – the distance between any two corresponding points on successive oscillations of a wave, such as from peak to peak work – the change in the energy of an object as a force is applied to it; the use of force to move an object through a distance; calculated as force times distance

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Physics STEMscopes Georgia Student Notebook

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