STEMscopes Science Florida - Physics 1

OKLAHOMA 3D K-12 SCIENCE HS Physics STEMscopedia ISBN:979-8-88826-232-0 Published by Accelerate Learning Inc. 5177 Richmond Ave, Suite 800, Houston, TX 77056. Copyright © 2024, 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.

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OKLAHOMA 3D K-12 SCIENCE

HS Physics STEMscopedia Table of Contents Lesson

The Four States of Matter

Graphing Motion

Newton’s Three Laws

The Four Fundamental Forces

Universal Gravitation

Coulomb’s Law

Electric Circuits

Work and Power

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1 17 39 57 73 85 101 123 iii

HS Physics STEMscopedia Table of Contents

OKLAHOMA 3D K-12 SCIENCE

Lesson

Page

137

Impulse and Momentum

155

Conservation of Energy

173

Energy in Systems

189

Characteristics of Waves

203

Behavior of Waves

215

Image Formation

229

Electromagnetic Spectrum

241

Speed of Light

Patterns of Matter in the Universe

iv

255

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HS Physics STEMscopedia Table of Contents

OKLAHOMA 3D K-12 SCIENCE

Lesson

Page

Appendix

Glossary

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271

v

The Four States of Matter

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1

STEMscopedia You have already learned that matter is the stuff that everything in the universe is made of. In chemistry, scientists study matter and the changes associated with it. For example, water is matter that can exist in three different states: a solid, a liquid, or a gas. You can freeze liquid water, and it will change into ice (a solid), or you can heat liquid water, and it will evaporate into water vapor (a gas).

What distinguishes these forms of water from one another, and how do they behave differently?

'RHV PDWWHU KDYH D PRUH VSHFL¿ F GH¿ QLWLRQ WKDQ VLPSO\ ³VWXII´" 6FLHQWLVWV GH¿ QH PDWWHU DV DQ\WKLQJ that has mass and takes up space. Mass is a measure of the amount of matter a substance contains; volume is the amount of space a substance takes up. Even gases that you cannot see, such as water vapor, have mass and volume. Like solids and liquids, gases are matter.

All matter is made of atoms, the smallest particles of a substance that still have the properties of that substance. Atoms combine to form molecules; a molecule consists of two or more atoms joined by chemical bonds. A molecule of water always contains two atoms of hydrogen and one atom of oxygen.

This molecule is the same whether it is an ice cube, a drop of liquid water, or a puff of water vapor.

When matter changes state—for example, from solid to liquid or gas—it does not form different kinds of molecules.

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The Four States of Matter | 3

STEMscopedia atom and element. An atom is an individual unit of matter. An element is D VXEVWDQFH WKDW FRQWDLQV RQO\ RQH NLQG RI DWRP 6FLHQWLVWV KDYH GLVFRYHUHG PRUH WKDQ GLIIHUHQW elements. All of the atoms of an element contain the same number of protons, which are a type of subatomic particle. There are other subatomic particles as well. Electrons orbit the nucleus in the electron cloud and have almost no mass while carrying a negative charge. Protons and neutrons are found in an atom’s nucleus and carry 99% of the atom’s mass. Protons are positively charged while neutrons have no charge.

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Also, do not confuse the terms molecule and compound. A molecule consists of two or more atoms joined through chemical bonds. A compound consists of two or more elements joined through chemical bonds. Hydrogen gas (H2) and oxygen gas (O2) are molecules—each consists of multiple atoms of only one type of element. Water (H2O) and carbon dioxide (CO2) are both molecules and compounds.

6FLHQWLVWV XVH WZR W\SHV RI SURSHUWLHV WR LGHQWLI\ PDWWHU SK\VLFDO DQG FKHPLFDO $ physical property FDQ EH REVHUYHG RU PHDVXUHG ZLWKRXW FKDQJLQJ WKH PDWWHU LWVHOI 6RPH H[DPSOHV RI SK\VLFDO SURSHUWLHV of matter include color, smell, melting and boiling points, magnetism, and density. You can observe the color of water by looking at it and the smell of water by smelling it. You can measure the melting and boiling points of water by heating it; you may cause a change of state, but you do not produce new kinds of matter. You can observe whether water is magnetic by holding a magnet beside it. You can calculate the density of water by dividing a sample’s mass (measured using a balance) by its volume (measured using a graduated cylinder). None of these observations or measurements change the water into a different kind of matter.

4 | The Four States of Matter

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STEMscopedia chemical property can be observed only when the matter changes as a result of a chemical reaction. In other words, you observe chemical properties only when one type of matter changes into DQRWKHU 6RPH FKHPLFDO SURSHUWLHV LQFOXGH UHDFWLYLW\ WR GLIIHUHQW FKHPLFDOV DQG À DPPDELOLW\ &RPELQLQJ molecules of two different chemicals—for example, hydrogen and oxygen—creates molecules of a new FKHPLFDO ZDWHU <RX FDQ REVHUYH ZKHWKHU D VXEVWDQFH LV À DPPDEOH E\ EXUQLQJ LW EXUQLQJ LV D FKHPLFDO UHDFWLRQ WKDW SURGXFHV QHZ NLQGV RI VXEVWDQFHV )RU H[DPSOH ZRRG LV YHU\ À DPPDEOH DQG EXUQLQJ wood produces new substances, such as carbon dioxide and ash.

Under different conditions, the properties of a substance can change. During a physical change, the chemical composition or identity of a substance does not change. In other words, only the substance’s physical properties change during a physical change. For example, a physical change occurs when you break ice into many small pieces. Additionally, all state changes are physical changes. For example, a physical change occurs when you freeze water to form an ice cube or when you melt ice to form water.

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The Four States of Matter | 5

STEMscopedia chemical change results from the formation of a new substance. In other words, the substance’s chemical properties change. (These are usually accompanied by physical changes.) If you dissolve an antacid tablet into water, a chemical change occurs. The gas bubbling through the water as the tablet dissolves is a sign of this change. The properties of the gas are different than the properties of the tablet or the water.

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The movement and arrangement of particles is different in solids, liquids, and gases. The atoms and molecules in matter are in constant motion, but some particles move more quickly and farther apart than others. Because of this, solids, liquids, and gases have different properties. Remember that a molecule of a substance (such as water) is the same whether it is in a solid, liquid, or gaseous state.

6WDWH RI PDWWHU GHSHQGV QRW RQ WKH W\SHV RI PROHFXOHV WKDW PDNH XS D VXEVWDQFH EXW RQ KRZ WKHVH molecules move and interact.

6 | The Four States of Matter

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STEMscopedia

Solids: Of the three states of matter, a solid has particles that move the least. The particles that make up a solid have relatively little energy. As a result, they are packed closely together, vibrating slightly DQG LQ D ¿ [HG DUUDQJHPHQW %HFDXVH WKH SDUWLFOHV LQ D VROLG FDQQRW PRYH YHU\ PXFK VROLGV DUH UHODWLYHO\ incompressible. In other words, if you press down on a solid, it does not move as much as a liquid or gas ZRXOG PRYH 7KLV DUUDQJHPHQW RI SDUWLFOHV DOVR JLYHV VROLGV D ¿ [HG VKDSH DQG D VSHFL¿ F YROXPH $Q LFH cube has the same shape and volume whether it is sitting in a square box, in a round pitcher, or upon a À DW WDEOH Liquids: The particles in a liquid are not as closely packed as the particles in a solid. They have more HQHUJ\ DQG PRYH IUHHO\ DURXQG HDFK RWKHU 7KLV LV ZK\ OLTXLGV À RZ DQG WDNH WKH VKDSHV RI WKHLU containers. However, the particles in a liquid have less energy than the particles in a gas. As a result, they are still quite attracted to each other. Liquids are more compressible than solids but less FRPSUHVVLEOH WKDQ JDVHV DQG²OLNH VROLGV²D OLTXLG KDV D ¿ [HG YROXPH ,I \RX SRXU OLTXLG ZDWHU LQWR a round pitcher, the water will take on a round shape. If you pour liquid into a square box, the ZDWHU ZLOO WDNH RQ D VTXDUH VKDSH +RZHYHU WKH ZDWHU ZLOO QRW H[SDQG RXWZDUG WR ¿ OO WKH YROXPH RI either container.

Gases: Of the three states of matter, a gas has particles with the most energy. Gas particles can move IDU DSDUW IURP HDFK RWKHU $V D UHVXOW JDVHV KDYH QHLWKHU ¿ [HG VKDSHV QRU ¿ [HG YROXPHV 7KH\ DUH YHU\ FRPSUHVVLEOH ,I \RX SLSH ZDWHU YDSRU LQWR D FORVHG F\OLQGHU WKH JDV ZLOO VSUHDG RXW WR ¿ OO LWV FRQWDLQHU If you press down on the lid of the container, the gas will decrease in volume as its particles are forced closer together. If you have ever watched steam rising from a boiling pot of water, you might have noticed that the steam diffuses—or spreads out—into the air as the water molecules move as far from each other as possible.

There is a fourth state of matter: plasma. A plasma is similar to a gas, but it is made up of ionized—or FKDUJHG²SDUWLFOHV 6RPH RI WKH SDUWLFOHV LQ D SODVPD KDYH SRVLWLYH FKDUJHV ZKLOH RWKHU SDUWLFOHV DUH free electrons (in other words, electrons that are not attached to a nucleus). Plasmas are important FRPSRQHQWV RI À XRUHVFHQW OLJKW EXOEV QHRQ VLJQV DQG SODVPD WHOHYLVLRQV For most types of matter, the particles are more closely packed in the solid state than in the liquid state. These solids are denser than the liquids they become when they melt. (In other words, a sample of the solid contains more particles than the same volume of liquid.) Water is an important exception.

Molecules of solid water are spaced farther apart than molecules of liquid water. As a result, ice is less GHQVH WKDQ ZDWHU ,FH À RDWV RQ ZDWHU

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The Four States of Matter | 7

STEMscopedia States of Matter

Melting

Solid

Vaporization

Liquid Freezing

Ionization

Gas

Condensation

Plasma Deionization

This phenomenon is caused by hydrogen bonds: weak interactions between the hydrogen and oxygen atoms of neighboring water molecules. Oxygen atoms have slightly negative charges, while hydrogen atoms have slightly positive charges. Recall that opposite charges attract and like charges repel. When water molecules come together to form ice, the hydrogen atoms attract the oxygen atoms and repel the other hydrogen atoms. The result is a crystal, or lattice, structure, with large gaps between neighboring water molecules.

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8 | The Four States of Matter

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STEMscopedia

do the in w o H 3. ehave b s le partic compared a solid gas? to a

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The Four States of Matter | 9

STEMscopedia The heat of your hand quickly causes an ice cube to melt, and your hand begins to feel very cold. You notice the same thing in a glass of ice water. If you leave the glass of water out long enough, the ice will PHOW DQG WKH WHPSHUDWXUH RI WKH ZDWHU ZLOO GHFUHDVH :KDW FDXVHV WKHVH HIIHFWV" 'RHV ³FROG´ PRYH LQWR your hand? What is heat, and how does it affect temperature?

To explain these macroscopic, or large-scale, properties of matter such as heat and temperature, you have to consider matter at the microscopic, or molecular, level. When you describe the kinetic energy (energy of motion) or potential energy (stored energy) of an object such as a ball, you probably mean its macroscopic energy. If the ball is moving, for example, it has kinetic energy. If you lift the ball above the ground, you increase its potential energy. All substances have energy associated with the motion and interactions of their particles. This internal energy is composed of kinetic energy due to the motion of the particles and potential energy due to the forces and interactions among the particles. Another name for internal energy is thermal energy.

Thermodynamics is the study of this internal energy and its effects on macroscopic properties of a substance. Thermal energy is a measure of the total energy—both kinetic and potential—of the particles of a substance. Temperature is a measure of the average kinetic energy of the particles. Heat is transferred thermal energy. For example, when you hold an ice cube in your hand, the heat moves from your hand into the ice. The thermal energy in your hand decreases and the thermal energy of the ice increases. The increase in thermal energy can increase the temperature of the ice to the point where the ice begins to melt. A tiny amount of energy actually transfers back and forth between the ice and your hand, but generally heat moves from a region of higher temperature to a region of a lower temperature. ,I WKHUH LV QR GLIIHUHQFH LQ WHPSHUDWXUH QR KHDW À RZ RFFXUV

e ibe th s r c s e 4. D transfer y energ cur when c that o er is boiled. at liquid w

10 | The Four States of Matter

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STEMscopedia 7KH *UHHNV K\SRWKHVL]HG WKDW PDWWHU LV QRW LQ¿ QLWHO\ GLYLVLEOH /RQJ EHIRUH WKH PLFURVFRSH ZDV LQYHQWHG ancient Greeks debated the divisibility of matter, and Democritus developed the idea that tiny, indivisible particles called atoms could explain the properties and behavior of matter. <HDUV ODWHU -RKQ 'DOWRQ SUHVHQWHG WKH ¿ UVW H[SHULPHQWDO HYLGHQFH WR VXSSRUW WKH FRQFHSW RI DWRPV 7KLV English schoolteacher carried out experiments that provided indirect evidence of atoms. He showed that R[\JHQ FRPELQHG ZLWK DQRWKHU JDV QLWULF R[LGH LQ VSHFL¿ F YROXPH DQG ZHLJKW UDWLRV ,Q RWKHU ZRUGV QR matter how much oxygen and nitric oxide he combined, the two always reacted with one another in a constant weight ratio. $OPRVW \HDUV DIWHU 'DOWRQ SURSRVHG KLV DWRPLF WKHRU\ DQRWKHU (QJOLVK VFLHQWLVW - - 7KRPVRQ made another discovery about the nature of matter. Thomson used a device called a cathode ray tube WR H[SORUH VRPH P\VWHULRXV UD\V WKDW FDXVHG D À XRUHVFHQW JORZ +H DGGHG WZR SODWHV WR WKH LQWHULRU RI the tube—one with a positive charge and the other with a negative charge. These plates were positioned above and below the path of the cathode rays. Thomson found that the cathode rays bent away from the negatively charged plate. Therefore, he concluded that the rays were composed of particles that carried a negative charge. His work established that there were much smaller particles than atoms. He proposed a structure of the atom similar to an English dessert known as plum pudding. He envisioned a model in which the negatively charged particles are embedded in a sphere of positive charge, much like raisins are embedded in a plum pudding.

Changes in the Atomic Model

Democritus 460 BCE and Dalton 1803 CE

Thomson 1897

Rutherford 1911

Bohr 1913

Modern quantum cloud model Post-1930

One of Thomson’s former students, Ernest Rutherford, came up with the nuclear model. Rutherford had ZRUNHG LQ 7KRPVRQ¶V ODE LQ WKH V EHIRUH EHFRPLQJ D SURIHVVRU DW DQRWKHU (QJOLVK XQLYHUVLW\ 7KHUH he worked with his own research students to study the nature of a type of radioactivity known as alpha UDGLDWLRQ ,Q 5XWKHUIRUG GLUHFWHG KLV VWXGHQWV WR FRQGXFW VRPH H[SHULPHQWV LQYROYLQJ WKH HPLVVLRQ of alpha radiation at squares of thin gold foil. His students carried out the experiments and reported that PRVW RI WKH DOSKD SDUWLFOHV SDVVHG WKURXJK WKH IRLO ZKLOH D VPDOO SURSRUWLRQ ZDV GHÀ HFWHG EDFNZDUG

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The Four States of Matter | 11

STEMscopedia nuclei. If an alpha particle collided with an atom’s nucleus, the particle bounced off the gold foil. Because most particles passed through the foil, however, Rutherford concluded that the area around the nucleus LV PRVWO\ HPSW\ VSDFH ZLWK D IHZ QHJDWLYH HOHFWURQV +H SXEOLVKHG WKHVH FRQFOXVLRQV LQ UHIXWLQJ the plum pudding model.

Rutherford’s work shed light on the presence of an atomic nucleus (which has been discussed before), but it did not reveal any new information about the positions of electrons in an atom. Niels Bohr, a student in Rutherford’s lab, worked on extending Rutherford’s model to explain how electrons were arranged in the atom. Bohr built on the idea of different elements emitting patterns of light based on a mathematical relationship. He developed a model of an atom with a central nucleus surrounded by electrons moving in orbits. His model allowed that electrons could move from one orbit to another when WKH\ JDLQHG RU ORVW HQHUJ\ ZKLFK H[SODLQHG WKH OLJKW HPLVVLRQ VSHFWUXP RI D K\GURJHQ DWRP 6FLHQWLVWV now think of electrons as occupying electron clouds rather than atomic orbitals but continue to use WKH LGHD WKDW HDFK HOHFWURQ LQ DQ DWRP KDV D VSHFL¿ F HQHUJ\ 5HFDOO WKDW HOHFWURQ FORXGV KDYH EHHQ previously discussed.

e how iz r a m 5. Sum operties of r the p ere used in w of matter velopment the de omic model. the at

12 | The Four States of Matter

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STEMscopedia (UZLQ 6FKU|GLQJHU ZDV ERUQ LQ LQ 9LHQQD +H VWXGLHG DW WKH 7HFKQLFDO &ROOHJH RI 9LHQQD DQG PDUULHG WKH GDXJKWHU RI KLV FKHPLVWU\ SURIHVVRU 6FKU|GLQJHU VHUYHG DV DQ DUWLOOHU\ RI¿ FHU GXULQJ WKH )LUVW :RUOG :DU EXW WUDQVLWLRQHG WR DQ DFDGHPLF SRVLWLRQ DW WKH 8QLYHUVLW\ RI =XULFK LQ ,W ZDV during this time that he developed much of his work, which led to the quantum model of the atom from a dissatisfaction with the Bohr model. He did not agree with the generally accepted model of both wave and particle behavior for electrons and worked to mathematically interpret the behavior in terms RI ZDYHV DORQH +H PRYHG WR %HUOLQ LQ WR DFFHSW D SRVW DV 3ODQFN¶V VXFFHVVRU DQG KDG HDUQHG D 1REHO 3UL]H E\ IRU KLV ZRUN VKDUHG ZLWK 'LUDF RQ WKH DWRPLF PRGHO +RZHYHU ZLWK WKH ULVH RI +LWOHU that year, he chose to leave Germany for England, where he accepted a post at Oxford and later moved WR 'XEOLQ ZKHUH KH EHFDPH WKH 'LUHFWRU RI WKH 6FKRRO IRU 7KHRUHWLFDO 3K\VLFV (YHQ LQ UHWLUHPHQW 6FKU|GLQJHU FRQWLQXHG KLV UHVHDUFK DQG SXEOLVKHG QXPHURXV SDSHUV RQ YDULRXV WRSLFV HYHQ DEVRUELQJ some of Einstein’s work on electromagnetism and gravitation.

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The Four States of Matter | 13

STEMscopedia Atoms are the building blocks of matter, but matter can take many forms. When heat is applied to matter, the particles move faster, which registers as an increase in temperature or average kinetic HQHUJ\ 7KH FKDQJHV WKDW RFFXU RQ D PROHFXODU OHYHO LQÀ XHQFH WKH REVHUYDWLRQV PDGH DW D SK\VLFDO DQG touchable level. For example, the transfer of energy between particles can transform matter between LWV IRXU VWDWHV RU SKDVHV VROLGV OLTXLGV JDVHV DQG SODVPD 6RPH PDWWHU UHDFWV ZLWK RWKHU W\SHV RI matter, creating chemical changes that rearrange the very atoms. The observations of good scientists can impact the future of science itself through discoveries based on these properties and the changes of matter.

Connect It Everyday Matter We observe many different types of changes in everyday activities. From dicing apples and boiling water to cooking eggs, matter is changing before our eyes. Physical changes can alter the phase of matter without affecting its identity or the internal arrangement of molecules. However, chemical changes always result in a new substance being formed by breaking and forming chemical bonds between the atoms of molecules. These observations can lead to new discoveries in science when built on the solid foundations of notable scientists in our past.

14 | The Four States of Matter

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STEMscopedia 1. What happens to the particles in a gas when it is heated?

A. They break apart.

B. They get smaller.

C. They become more dense.

D. They move faster.

2. Which of the following best describes temperature?

A. Average molecular kinetic energy B. The amount of heat given off C. Atomic structure and arrangement D. Total relative electric charge

3. Which of the following properties of sodium metal is a chemical property?

A. +DV D PHOWLQJ SRLQW RI & B. Readily reacts with water C. 6ROLG DW URRP WHPSHUDWXUH D. Is denser than water

4. 'H¿ QH WKH SK\VLFDO SURSHUWLHV WKDW DUH XVHG WR FRPSDUH VROLGV OLTXLGV DQG JDVHV WR HDFK RWKHU

5. ,Q ZKLFK GLUHFWLRQ GRHV KHDW À RZ"

6. List the names of the following scientists who contributed to the development of atomic theory in chronological order with a note describing the contribution of each scientist next to his name: John Dalton, Ernest Rutherford, Niels Bohr, J.J. Thomson.

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The Four States of Matter | 15

Graphing Motion

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17

STEMscopedia How long can you stand still? Think about every time you stand up, get in the car, or go to sleep at night. Even if you are standing in one spot, are you still moving?

Even if you are to stand perfectly still where you are now, we are constantly moving around the universe at 30 kilometers every second. That’s 67,000 miles per hour! When describing an object’s motion, we also need to think about its position, velocity, and acceleration and for how long it was moving. How can we predict an object’s speed? How are an object’s velocity, acceleration, and position related? Can we tell where an object is with this information?

a car o t n i s ou got riend’ 1.. If y to your f ur yo ent and w , how would and house , velocity, e? position tion chang ra accele

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Grap ing Motion

STEMscopedia Sir Isaac Newton described three laws of motion.

7KH ¿ UVW LV WKH ODZ RI LQHUWLD WKH VHFRQG LV WKH law of force and acceleration, and the third is the law of action and reaction. Each of these three laws describes how forces acting on an object change the motion of that object.

When we describe the motion of something, we might say where the object is, how fast it is moving, whether the object is speeding up or slowing down, and where the object is going.

7R GHVFULEH DQ REMHFW¶V PRWLRQ ZH PLJKW ¿ UVW describe an object’s position and how that changes over time. Consider if you are meeting your friend at their house. You know that the house is 5 km away, and it will take you 20 minutes to walk there, but you do not know how to get there from your house. Knowing just the distance from your house or how long it would take you to reach your friend’s house is the scalar quantity.

However, you also know that your friend’s house is directly north of your house. Now, you can describe the direction as well as your speed and distance when moving. Knowing the velocity, both the speed and direction, of your motion is the vector quantity. The reason why velocity, and not speed, is a vector quantity is because a YHFWRU VKRZV WKH FKDQJH RI DQ REMHFW LQ D VSHFL¿ F direction. When we measure the speed of an object, we only measure the distance that an object travels over time.

A body will remain at rest or moving at constant velocity unless it is acted on by an unbalanced force.

2nd

Acceleration

The force experienced by an object is proportional to its mass times the acceleration it experiences.

If two bodies exert a force on one another, the forces are equal in magnitude but opposite in direction.

scribe e D .

2 city is r o l e v to why a vec d e r e not a consid d n a ty quanti quantity. scalar

Grap ing Motion

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STEMscopedia How do we measure these changes in the velocity and acceleration of an object? Using a stopwatch E\ LWVHOI FDQ EH YHU\ GLI¿ FXOW HVSHFLDOO\ LI WKH REMHFW LV PRYLQJ DW D KLJK YHORFLW\ )RU WKLV ZH FDQ XVH PXOWLSOH WRROV WR KHOS DFFXUDWHO\ PHDVXUH DQ REMHFW¶V SRVLWLRQ YHORFLW\ DQG DFFHOHUDWLRQ 7KH ¿ UVW LV D motion detector. A motion detector uses high-frequency sound waves to track the changing position of a moving object. Based on the object’s change in position over time, motion detectors can then determine the object’s velocity and acceleration.

The second is a photogate. Instead of relying on sound waves to track an object, photogates rely on infrared beams by measuring when the beam is blocked by an object as it passes through. By setting up multiple photogates, one can determine the time that it takes for an object to travel between two SRVLWLRQV )URP WKLV GDWD ZH FDQ GHWHUPLQH WKH REMHFW¶V YHORFLW\ DQG DFFHOHUDWLRQ

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Grap ing Motion

STEMscopedia The position of an object is always in reference to something else. In many cases, the starting position is where we begin measurement over time. How far an object changed position during that time is the object’s distance. When we measure an object’s distance, the number will always be positive or zero.

However, because objects can move backward and forward, position can be either positive or negative.

When graphing the position over time of an object, we need to consider the object on a horizontal axis, moving backward and forward. In the following graph, the object moved from its starting position of 0 m to 0.5 m in 1 second and then to 1 m in 2 seconds. The position of the object at 4 seconds is once again at the starting position of 0 m.

In addition, we can interpret from the graph that the object stayed at the same position (3 m) from 7 seconds to 9 seconds. This means that for 2 seconds, the object did not change positions. We can interpret that the object also remained at rest at 4 m from 10 seconds to 11 seconds on the graph before returning to the starting position at 0 m.

Grap ing Motion

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STEMscopedia distance WR ¿ QG WKH REMHFW¶V ORFDWLRQ DW D JLYHQ WLPH ,I ZH ZHUH WR JDWKHU WKH GLVWDQFH WUDYHOHG IRU WKH ¿ UVW VHFRQGV ZH ZRXOG ¿ QG WKDW WKH REMHFW WUDYHOHG P WRWDO This would be the same as walking forward 1 m and backward 1 m. While the total distance traveled was 2 m, the object is back at the original starting position. The difference between the object’s starting SRVLWLRQ DQG ¿ QDO SRVLWLRQ LV NQRZQ DV WKH REMHFW¶V displacement. In this example, the displacement of the object would be 0 m.

Displa ement s Distan e

Displa ement traight line distance et een start and end siti ns Ve tor Distan e

tal distance traveled Line

In this example, we see that the displacement of the car is the straight-line vector from points A to B, where distance is the path that the car actually drove. This is the addition of the lines from A to X to Y to B.

ph of a r g d aw a 3. Dr ving forwar g o n you m 5 s, pausi for en 5 m nd th ur a , s for 2 back to yo g walkin ing position start 5 s. for

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Grap ing Motion

STEMscopedia

eed

tal distance

eters

eters er sec nd

Both speed and velocity are a measure of distance over time; therefore, the same equation that is used to calculate speed is used to calculate velocity. However, like distance, speed can only have a positive or zero value to tell you how many units of distance were traveled over time. Because velocity is both speed and direction, velocity can be either positive or negative. Pretend that we want to see if we are walking at a constant speed. To do so, we need to measure the distance over a period of time. Consider the two graphs shown.

i e s

i e s

)URP WKH ¿ UVW JUDSK RI WRWDO GLVWDQFH YHUVXV WLPH ZH FDQ LQWHUSUHW WKDW IRU HYHU\ VHFRQG ZH ZDON P and this stays constant for the entire 14 second walk. Therefore, to graph the constant speed or velocity of an object, we graph our speed as 1 m/s for those 14 seconds. If we knew that we were walking forward for 14 seconds, then we could say that the velocity was 1 m/s. Within a one-dimensional graph, ZH FDQ FDOFXODWH WKH YHORFLW\ RI DQ REMHFW E\ ¿ QGLQJ WKH VORSH RI WKH GLVWDQFH DQG WLPH

Grap ing Motion

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STEMscopedia 1. Choose two points on the line, and determine the coordinates.

2. )LQG WKH GLIIHUHQFH LQ WKH \ FRRUGLQDWHV RI WKHVH WZR SRLQWV GLVWDQFH 3. )LQG WKH GLIIHUHQFH LQ WKH [ FRRUGLQDWHV RI WKH WZR SRLQWV WLPH 4. Divide the difference, or change, in the y-coordinates by the change in the x-coordinates. ([DPSOH

)RU SRLQWV V P DQG V P

Because the difference in time measured is small, we consider this the instantaneous speed or velocity of an object. However, because the object is moving at a constant speed or velocity the entire time, the DYHUDJH YHORFLW\ DQG WKH LQVWDQWDQHRXV YHORFLW\ DUH WKH VDPH 8VLQJ WKLV ZH FDQ ¿ QG WKH YHORFLW\ RI DQ REMHFW E\ DOVR NQRZLQJ WKH GLVWDQFH WUDYHOHG RYHU D SHULRG RI WLPH )RU H[DPSOH WDNH D FDU WKDW WUDYHOV P LQ VHFRQGV

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We can assume that the starting velocity (vi) of the car is zero and the starting position (xi) is also zero, so the velocity of the car is the distance traveled over time.

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Grap ing Motion

STEMscopedia Y

Position

speed all the time. Sometimes we might slow down, and sometimes we might speed up. This change in velocity is known as acceleration.

Acceleration is caused by an unbalanced (net) IRUFH <RX ZLOO UHFDOO IURP 1HZWRQ¶V ¿ UVW ODZ of motion that an object at rest will remain at rest, and an object will remain at the same speed and motion unless acted upon by an unbalanced force.

X

Time

Think about driving a car. The car initially is not moving, but as you press the gas pedal, the car starts to move faster. In this case, the car has a positive acceleration and is increasing in velocity. Now, you come to a red light, and you slowly press on the brake. The car begins to slow down (decrease velocity), and the acceleration is now negative. If the car is moving at a constant velocity (if you are driving on the interstate, for example), then the acceleration is zero.

Acceleration is a vector quantity because it describes an object’s change in velocity. Acceleration can also be positive or negative depending on the change in velocity. In the picture, the soccer ball moves up and down. During this time, the force of gravity changes the velocity of the soccer ball at an acceleration of 9.8 m/s2. As an object accelerates at a constant rate, the velocity of the object begins to increase, and position increases exponentially.

The soccer ball is at rest.

Grap ing Motion

The foot acts as the unbalanced force, and the ball moves.

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STEMscopedia

*LYHQ WKLV LQIRUPDWLRQ ZH FDQ ¿ QG ERWK WKH GLVSODFHPHQW DQG WKH DFFHOHUDWLRQ DW FHUWDLQ SRLQWV /HW¶V VD\ ZH ZDQW WR ¿ QG WKH DFFHOHUDWLRQ RI WKH REMHFW IURP VHFRQGV WR VHFRQGV :H FDQ VHH IURP WKH graph that the object is accelerating because the velocity is changing, but by how much?

:KDW DERXW GLVSODFHPHQW GXULQJ WKLV VDPH WLPH" 7R ¿ QG WKH GLVSODFHPHQW ZH QHHG WR ¿ QG WKH area under the graph. Without accounting for the change in velocity, displacement (x) would equal velocity (v) multiplied by time traveled (t). Between time 20 seconds and 30 seconds, the object PRYHG DW D FRQVWDQW YHORFLW\ RI P V )RU WKRVH VHFRQGV WKH REMHFW WUDYHOHG P

are s r a c o nt 4. Tw t a consta ing a travel ed to their VW spe KH Ş U 7

Q R in DWL GHVWLQ vels 30 m d a n car tr d the seco in n 6 s, a vels 50 m a as car tr hich car h 10 s. W er velocity? great car has Which celeration? r ac greate

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Grap ing Motion

STEMscopedia If we are to graph an object’s motion and the relationship between the object’s displacement, velocity, and acceleration versus time–

Displacement (x) x

a. At v = 0

v

Velocity (v)

Acceleration (a) a

x = constant

b. Motion with constant velocity c. Motion with constant acceleration d. Motion with constant deceleration

0 x

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A. where v = 0, the position of the object remains constant and acceleration remains at zero.

B. where the object has no acceleration, the object moves at a constant velocity. Displacement (x) is calculated by adding the object’s starting position (xo) plus the object’s initial velocity (vo) and multiplying by time (t).

C. as the object maintains a constant acceleration, velocity increases at a constant rate. Displacement then increases exponentially.

D. as the object maintains a constant negative acceleration, velocity decreases at a constant rate.

The resulting displacement change of the object begins to decrease until the object is at rest.

Grap ing Motion

raphs g e n ir ami 5. Ex h the t i w D C and e equations relativ ce. Which tan for dis shows the graph traveling a er s object distance ov r ur greate Explain yo time? soning. rea

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STEMscopedia Vectors are able to be represented mathematically by using scaled lines with arrowheads to depict the direction and magnitude of the object’s motion. Until now, we have worked with understanding motion EDVHG RQ DQ REMHFW PRYLQJ HLWKHU XS DQG GRZQ RU KRUL]RQWDOO\ IRUZDUG DQG EDFNZDUG 7R ¿ QG WKH GLUHFWLRQ RI D PRYLQJ REMHFW IRU RQH GLPHQVLRQDO YHFWRUV ZH FDQ ¿ QG WKH VXP RI DOO WKH YHFWRUV LQ HDFK direction to determine the direction in which the object will move.

y

A x

A A x

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x

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/HW¶V UHWXUQ WR WKH ¿ UVW H[DPSOH LQ ZKLFK \RX DUH ZDONLQJ WR \RXU IULHQG¶V KRXVH 7KLV WLPH \RX NQRZ WKDW WKHLU KRXVH LV QRUWKHDVW RI \RXU KRXVH KRZHYHU WR JHW WKHUH \RX ¿ UVW QHHG WR ZDON NP QRUWK RQ one street (y direction) and then east along the second street for 1 km (x direction). Overall, you walk 3 km, but what is the displacement of your travel?

7R ¿ QG WKH WRWDO YHFWRU GLVSODFHPHQW \RX DGG WKH VXP RI WKH ¿ UVW DQG VHFRQG YHFWRU WR ¿ QG WKDW \RX WUDYHOHG NP %XW ZKDW DERXW WKH GLVSODFHPHQW" 7R ¿ QG WKLV ZH FDQ XVH WKH 3\WKDJRUHDQ WKHRUHP WR ¿ QG WKH XQNQRZQ GLVWDQFH RI WKH K\SRWHQXVH

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Grap ing Motion

STEMscopedia direction, magnitude, and angle.

+HUH WR ¿ QG WKH YHORFLW\ RI WKH [ DQG \ FRPSRQHQWV ZH XVH WKH 3\WKDJRUHDQ WKHRUHP WR ¿ QG WKH RSSRVLWH DQG DGMDFHQW VLGH )LUVW WR ¿ QG WKH YHORFLW\ RI WKH [ FRPSRQHQW ZH PXOWLSO\ P V E\ cos(60), which gives us 5.0 m/s. In the y direction, because it is opposite of our angle, we multiply 10 m/s by sin(60) to get 8.66 m/s. However, because the velocity is decreasing, the velocity in the y direction is -8.66 m/s.

Grap ing Motion

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STEMscopedia objects move, we need to think about all the forces that are acting in multiple directions. Imagine that you throw a baseball. Once thrown, the ball moves along the horizontal (x) axis, but it is also falling along the vertical (y) axis.

We know this to be the case because the ball won’t move in a straight line forever, but how can we SUHGLFW KRZ IDU RU KRZ IDVW WKH SLWFK LV WKURZQ" +HUH ZH KDYH PRWLRQ DFWLQJ LQ WZR GLUHFWLRQV WKH KRUL]RQWDO D[LV DQG YHUWLFDO D[LV 7KHVH ' YHFWRUV GHVFULEH REMHFWV WKDW DUH À \LQJ WKURXJK WKH DLU DW angles, like projectiles. As the baseball is thrown, it will eventually start to go down toward the ground.

This is because the acceleration of gravity continues to act in the vertical y-axis direction. However, once the ball leaves your hand, unless another force acts on it, there is no acceleration in the horizontal x-axis direction. While the equation for vertical and horizontal motion remains the same, because there is no acceleration in the horizontal direction, the equation can be abbreviated.

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Grap ing Motion

STEMscopedia Circular Motion

er form of two-dimensional motion is circular motion, which occurs when an object travels around ular path. A special case of circular motion is uniform circular motion. An object that is moving with UP FLUFXODU PRWLRQ WUDYHOV DURXQG D FLUFXODU SDWK DW D FRQVWDQW VSHHG $ )HUULV ZKHHO D y-go-round, and the rotating hands on an analog watch are examples of circular motion. Some WV H[KLELW XQLIRUP FLUFXODU PRWLRQ HYHQ LI WKH\ GR QRW WUDYHO LQ D IXOO FLUFOH )RU H[DPSOH ZKHQ D FDU s a curved exit ramp, it may travel around a portion of a circular path, but it still undergoes circular n during that time.

an calculate the average speed (v) of an object traveling in uniform circular motion around a circle a radius of r. To do this, recall that the average speed of an object in one-dimensional motion is to the total distance traveled divided by the total time of the journey. The equation for this is as V v = d/t an object travels around a circular path, the total distance that it travels in one complete loop is to the circumference of the circle. The equation for the circumference (C) of a circle with a radius DV IROORZV C = 2ૈr

DQ GH¿ QH WKH DPRXQW RI WLPH WKDW LW WDNHV IRU DQ REMHFW WR FRPSOHWH RQH IXOO ORRS DURXQG WKH FLUFOH which is also called the period of the motion. We can plug these variables into the equation for ge speed to determine the equation for average speed in uniform circular motion. The equation for V DV IROORZV v = 2ૈr/t

ugh the object moves with a constant speed, its direction of movement is constantly changing. the object is accelerating. The acceleration of an object in uniform circular motion is called petal acceleration. This vector points inward, toward the center of the circle. The magnitude of petal acceleration (ac FDQ EH FDOFXODWHG XVLQJ WKH IROORZLQJ HTXDWLRQ ac = v2/r

elocity vector of an object that is exhibiting uniform circular motion always points tangent to the of the motion. The centripetal acceleration vector always points inward, toward the center of the as shown in the diagram below.

α

α

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v Grap ing Motion

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STEMscopedia 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 that are 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.

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Grap ing Motion

STEMscopedia All moving objects have momentum (p). This is a measurement of an object’s motion. The more PRPHQWXP LW KDV WKH KDUGHU LW ZLOO EH WR VWRS LW 0RPHQWXP KDV WZR YDULDEOHV PDVV DQG YHORFLW\ )RU OLQHDU RU VWUDLJKW OLQH PRPHQWXP ZH FDQ PHDVXUH PRPHQWXP ZLWK WKLV HTXDWLRQ p = mv This equation shows us that momentum is directly proportional to both the mass of an object and the velocity of an object. The mass and velocity of the object are inversely proportional to each other. This equation also shows us that if an object is at rest, with velocity equaling zero, the object will have no momentum regardless of its mass.

A spinning object, too, has momentum. But because it is a two-dimensional, rotating system, we give it a different name than linear momentum. We call it angular momentum. Angular momentum (L) is a measurement of how much an object in rotational motion will resist having its rotation changed. It is VKRZQ E\ WKH IROORZLQJ HTXDWLRQ L = rmv Here, r is the radius of the rotation, m is the mass, and v is the linear (or tangential) velocity. Again, like for linear momentum, mass and velocity are directly proportional to the momentum, but so, too, is the radius. The bigger the radius for a given mass and velocity, the greater the angular momentum. Again, just like for linear momentum, if velocity drops to zero, angular momentum drops to zero.

Angular momentum is demonstrated by gyroscopes. A gyroscope, like the one in the image below, can spin upright, balanced on its tip, because of its angular momentum. The amount of force that is required to change the gyroscope’s momentum greatly exceeds the force of gravity, enabling the gyroscope to balance seemingly against the force of gravity.

Bicycles, too, are demonstrations of angular momentum. Because they are wheels that are spinning, the bike tires have angular momentum and enable the bike to balance upright as it moves. This also explains why bikes become wobbly and hard to control as they slow down. As the tangential velocity of the bike tire decreases, its angular momentum decreases and it becomes easier for gravity to overcome it and cause the bike wheel to fall over, bringing the bike with it.

Grap ing Motion

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STEMscopedia René Descartes (1596–1650) was a mathematician and natural scientist. Notably, he was recognized as one of the founders of modern philosophy. His best-known statement is, “I think; therefore, I am.” In mathematics, he developed Cartesian (or analytic) geometry, which is how algebra is used to describe geometry. This became the conventional way to represent unknown numbers using x, y, and z and known numbers using a, b, and c. We continue to use Cartesian coordinates when graphing on the x and y axes. In addition, Descartes pioneered a standard notation using superscripts for exponents and powers (for example, 2 being used to represent x2 or x squared). It is this standard notation and Descartes’s work that laid the foundation for calculus, which was developed by Sir Isaac Newton, and HYROYLQJ PDWKHPDWLFV :KLOH ZH FUHGLW RXU ODZV RI PRWLRQ WR 1HZWRQ 'HVFDUWHV ¿ UVW GLVFRYHUHG DQ HDUO\ theory regarding the law of conservation of momentum, in which he thought of motion on a straight line instead of as circular motion, as was previously described by Galileo Galilei. Descartes further described two additional laws of motion, and these became the bases for the laws of motion that we know today.

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Grap ing Motion

STEMscopedia Motion in physics describes the position of any object in relation to time. The distance that an object travels is the position where that object is in relation to time whereas the displacement of an object is the vector quantity that an object traveled. Speed is one way to describe the motion of an object as a scalar quantity. Once we know the speed and direction that an object is traveling, we use the term “velocity” to describe how much distance is traveled per second. Because the direction of the object is known, velocity is a vector quantity. An object maintains a constant velocity if there is no acceleration acting on the object. If an object maintains a constant acceleration, then the object’s velocity will increase or decrease exponentially. Because vectors are graphed using right angles, the Pythagorean WKHRUHP FDQ EH XVHG WR ¿ QG WKH PDJQLWXGH DQG GLVSODFHPHQW RI GLIIHUHQW YHFWRU TXDQWLWLHV ZKHQ WKH\ are unknown.

Connect It Even if you stand still, are you still moving?

When we describe motion, we use our relative position. However, even Earth itself is continuously moving in the universe. The force of gravity from the Sun and surrounding planets also has an impact on Earth’s velocity and motion. So even if we are standing still, we are continuously moving. While many in physics will use this information to determine how planets are moving or how the universe is expanding, when we calculate our displacement, velocity, and acceleration, we use our relative changes in distance here on Earth.

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Grap ing Motion

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STEMscopedia 1.

A car that is traveling for 15 seconds increases its velocity from 2.3 m/s to 4.5 m/s. What is the magnitude of the car’s acceleration while it travels for 15 seconds?

A. 6.8 m/s2 B. 0.68 m/s2 C. 0.44 m/s2 D. 0.15 m/s2

2. Which of the following graphs shows an object decelerating at a constant rate?

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$QVZHU & 3. Which of the following is a scalar quantity and not a vector quantity?

A. Velocity B. Acceleration C. Speed D. Displacement 4. If an object moves south for 10 m and east for 5 m, what is the overall displacement of the object? $% ¥ $%x2 + ABy2 ¥ 2 + 52 ¥ ¥ P 5. A car moves at a constant velocity of 15 m/s for 2 minutes. How far does the car travel?

T = 20 x 60 = 120

X = Xo + Vot = 0 + (15)(120) = 1,800 m

6. Two runners begin a race. Runner 1 is running at 1.5 m/s and accelerating at 0.2 m/s2 while runner 2 is running at 1 m/s and accelerating at 0.6 m/s2. After 10 seconds of sprinting, which runner is farther ahead?

5XQQHU ; ;o + Vot + 1/2at2 = 0 + (1.5)(10) + ½(0.2)(10)2 = 15 + 10 = 25 m 5XQQHU ; ;o + Vot + 1/2at2 = 0 + (1)(10) + ½(0.6)(10)2 = 10 + 30 = 40 m Runner 2 is ahead.

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Grap ing Motion

Newton’s Three Laws

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39

STEMscopedia Objects stay at rest or in motion due to forces acting on them.

A force acting on an object can be calculated if you know the object’s mass and its acceleration.

Forces always come in pairs that are equal in size and opposite in direction.

nd/or a e m 1. Na ll the a e b i descr t work in a . forces n situation ive the g e will th d w o H 2. name u o y s force the motion e chang e car? of th

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STEMscopedia Sir Isaac Newton (1642–1727) was a brilliant mathematician and physicist. His work Mathematical Principles of Natural Philosophy (published in 1687) is considered one of the most important books in modern science. In it, Newton laid out an orderly world that behaved according to a single set of laws.

These laws, known as Newton’s laws of motion, are exact, quantitative descriptions of how objects move. Newton’s three laws of motion demonstrate the relationships between force, motion, acceleration, mass, and inertia.

how e b i r c s 3. De ity in your tiv e an ac ould b w e f i daily l nt if the e d differ bjects coul of o d. motion e predicte not b

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STEMscopedia 1HZWRQ¶V ¿ UVW ODZ RI PRWLRQ states that objects at rest will stay at rest and objects in motion will remain in motion at a constant velocity unless they are acted upon by an unbalanced force 7KH ¿ UVW law is also called the law of inertia because it describes an object’s resistance to change in motion. In VLPSOH WHUPV WKH ¿ UVW ODZ RI PRWLRQ WHOOV XV WKDW REMHFWV ZLOO NHHS GRLQJ ZKDW WKH\ ZHUH DOUHDG\ GRLQJ unless an unbalanced, outside force causes a change.

In order to understand the law of inertia, you need to remember that forces have magnitude (size) and direction. When the forces are equal in size and opposite in direction, the net force is zero, or balanced.

Force of gravity

Table force

Consider an apple sitting on a table. An apple weighs about 1 newton (about 0.22 lbs.), which means that gravity is pulling down on the apple with 1 N of force, but the table is pushing back with the same amount of force. You can think of it as a math problem: 1 + -1 = 0. Therefore, the combined force, or net force, on the apple is zero. When the net force is zero, we say that there is equilibrium.

Because there is equilibrium in this situation, the apple will not move until an RXWVLGH IRUFH FDXVHV DQ LPEDODQFH 7KLV GHPRQVWUDWHV WKH ¿ UVW KDOI RI WKH ODZ RI inertia: objects at rest remain at rest until acted upon by an unbalanced force.

If an object at rest is to be put in motion, an outside force must be used to create an imbalance. In the pictures, you see two people pushing a heavy box from opposite sides. If they are pushing with equal force, the object will not move because the net force on the box is zero. If the two people were not pushing with equal strength, the box would move in the direction of the greater force because the net force would be greater than zero. Likewise, if they combine their forces and push in the same direction, then the net force will be greater than zero and the object will move in the direction that it is being pushed.

An ect at rest sta s at rest.

An ect at rest sta s at rest.

An ect acted n a alanced rce sta s at rest.

An ect acted n an n alanced rce changes s eed and directi n.

An ect acted n an n alanced rce changes s eed and directi n.

An ect in ti n sta s in ti n.

An ect acted n an n alanced rce changes s eed and directi n.

The soccer ball could potentially stay at rest forever unless an outside force—in this case, the kick—put it into motion. Once it is in motion, it does not need to be continually kicked because it will stay in motion until a force causes it to slow down or change direction. In this case, gravity pulls it down and the net stops its motion. © Accelerate Learning Inc. – All Rights Reserved

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STEMscopedia WKH\ DUH DFWHG XSRQ E\ DQ XQEDODQFHG IRUFH 7KLV LV PRUH GLI¿ FXOW WR YLVXDOL]H EHFDXVH LQ RXU HYHU\GD\ experiences, we do not usually witness something remaining in motion at a constant velocity because something is always acting to slow down the motion of objects. That something is friction. On Earth, friction will always be the unbalanced force that causes objects in motion to slow down and eventually stop. However, according to the law of inertia, objects in motion have the potential to stay in motion in a straight line and at a constant speed forever unless an outside force causes a change. One way to visualize this is to think about rockets.

The rocket boosters provide enough force to propel the rocket upward faster than the force of gravity can act to pull it back to Earth. As the boosters use up their stores of fuel and fall back to Earth, the space capsule atop the rocket continues traveling until it escapes the pull of Earth’s gravity. Once the capsule is in space, where it is no longer encountering friction with air, it will continue traveling in a straight line and at a constant speed without needing the engine to continue supplying force. If the DVWURQDXWV RQ ERDUG ZDQW WR FKDQJH WKH GLUHFWLRQ RU VSHHG RI WKHLU À LJKW WKH\ QHHG WR HQJDJH WKH engine to create an unbalanced force.

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STEMscopedia equipped with safety belts, padded dashboards, and airbags. Consider driving along the highway at 60 mph. Your body is not in motion relative to the car. You might be sitting quite still inside the car, but in actuality, your body is traveling at a rate of 60 mph in the same direction your car is heading. But what happens if you slam on the brakes, causing a sudden unbalanced force that stops the car’s motion? Because of inertia (that tendency of objects to resist change in motion), your body wants to continue traveling forward at a rate of 60 mph. A seat belt or an airbag can provide an unbalanced force to slow and stop your forward motion. Without the seat belt or airbag, your body would continue moving forward until it encountered the dashboard. If the dashboard is padded, it might soften the impact somewhat. You might even continue traveling forward through the front windshield.

Theoretically, you would then continue traveling forward through the air forever except that, on Earth, gravity would eventually provide the force to pull you down, and friction would eventually provide the force to stop your motion.

ll ketba s a b a 4. If less in the ion is mot f a moving aisle o s, explain bu school e ball will h how t hen the w move stops. bus

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STEMscopedia The law of inertia explains how and why objects stay at rest or in motion. Even toddlers know intuitively that forces are needed to set objects in motion. When a young child learns to stack blocks, they instinctively knock their tower down for the sheer joy of seeing the blocks scatter. Soon, they learn that if they hit the tower with more force, the blocks scatter even farther. Without even going to a high school physics class, a toddler knows the basic idea of Newton’s second law of motion, which describes the effect of net force on acceleration. Newton’s second law of motion states that a force that is applied to an object is equal to its mass multiplied by its acceleration. The law can be stated as a formula: force = mass x acceleration (F = ma).

net N

kg

m/s2

• Forcenet is measured in newtons (N).

• Mass is measured in kilograms (kg).

• Acceleration is measured in meters per second squared (m/s2).

The second law is also called the law of constant acceleration. As long as a net force is acting on an object, it will experience constant acceleration. When the force is no longer applied, the object will stop accelerating in relation to that force. <RX NQRZ WKDW D IRUFH LV D SXVK RU D SXOO )RUFHV KDYH VSHFL¿ F QDPHV PDQ\ RI ZKLFK DUH IDPLOLDU WR you. Friction, which was mentioned earlier, is the force that resists the relative motion of two objects or substances sliding against one another. There is friction between two solid surfaces that are in contact ZLWK RQH DQRWKHU VXFK DV ZKHQ \RX SXVK DQ DSSOLDQFH DFURVV WKH À RRU %XW WKHUH LV DOVR IULFWLRQ EHWZHHQ VROLG REMHFWV DQG À XLGV %RDWV HQFRXQWHU IULFWLRQ ZLWK WKH ZDWHU $LUSODQHV HQFRXQWHU air resistance, or friction with the air. Friction always works in the opposite direction of an object’s motion, and for this reason, it is the force that keeps objects from staying in motion forever at a constant velocity. Static friction is the friction between two surfaces when there is no relative motion between them. If you have ever tried to push a stalled car, you know how stubborn static friction can be. You pushed and pushed, EXW WKH FDU UHVLVWHG PRYLQJ XQWLO \RX ¿ QDOO\ JDYH WKDW H[WUD SXVK WKDW ZDV ELJ HQRXJK WR JHW WKH FDU WR move. In that moment, you overcame static friction. Once the car was moving, you probably noticed that it was easier to push; that is because static friction is the hardest type of friction to overcome.

Tension LV WKH IRUFH WKDW LV WUDQVPLWWHG WKURXJK D À H[LEOH REMHFW VXFK DV D VWULQJ URSH RU FDEOH when it is pulled taut from opposite ends. Think of pulling on a rope during a game of tug-of-war. While tension is a pulling force, compression is a pushing force that squeezes an object together; think of pushing down on a spring. Gravity is another force with which you are very familiar because gravity is always at work here on Earth. In the earlier example of the apple on the table, you saw the downward arrow representing the pull of gravity. The equal and opposite force in the picture is called the “table force.” Actually, there is a name for that force; we call it the normal force, and it is the force of one surface that pushes back against an object that is pressed upon it. If you have watched clothes spinning in a front-loading dryer, you have seen the effect of another force. Objects can apply forces on each other as well. These forces are called applied forces. Think of a bowling ball hitting pins; the moving ball applies a force to the pins, putting them in motion. e ton s

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STEMscopedia We can calculate the effect of forces on objects by using free-body diagrams. A free-body diagram shows an object and the directions and magnitudes of all the forces acting on it. A force is a vector quantity, meaning that it has magnitude (size) and direction. Because of this, we can represent forces with arrows, showing their direction and relative magnitude. Below are some examples of freebody diagrams.

FT

FG = mg Let’s review these diagrams a little closer and utilize them to calculate different types of forces.

In diagram A, notice that the vertical arrows are equal in size and opposite in direction (note that the force labeled “weight” is the force of gravity).

Because the normal force and the weight (force of gravity) are equal and opposite, their net force is zero, and they have no effect on the object’s motion. If these were the only two forces acting on the object, it would be stationary.

Diagram A

Notice that the arrow labeled “friction” is opposite in direction when compared to the applied force that the person is exerting as they push the crate, but the force of friction is smaller than the applied force. Because the applied force is greater than the force of friction, the object is in motion.

We can calculate the net force that is acting on the crate by adding the two forces.

100 N + -30 N = 70 N The crate will accelerate to the right with a force of 70 N. Using the formula F = ma and the example in diagram A, if we know that the net force that is moving the crate is 70 N, and if the mass of the crate is 14 kg, we can calculate the acceleration of the box by rearranging the formula F = ma to a = F/m. Then, acceleration would be calculated as follows. a = 70 N / 14 kg a = 5 m/s2 The force results in an acceleration of 5 m/s2.

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STEMscopedia Diagram B shows a stationary object suspended by a rope. The FG arrow shows the force due to gravity, and the FT arrow shows the tension force.

Because the object is stationary, we know that the forces that are acting on it must be balanced. If we know the mass of the object, and the only other force that is acting on the object is gravity, we can calculate the tension force that is acting on the object using Newton’s second law (F = ma).

Diagram B

FT

FG = mg Given that the object has a mass of 10 kg, and acceleration due to gravity is 9.8 m/s2, calculate the tension force. First, calculate the force due to gravity using F = ma.

F = (10 kg) x (9.8 m/s2) F = 98 N Because the object is stationary, we know that the tension force is equal to the gravitational force in the opposite direction. Because FG is 98 N, FT must be -98 N. The free-body diagram shows that the forces have the same magnitude but opposite directions.

Analyze diagram C, which shows FG and FT. Based on our knowledge of free-body diagrams, we can make the following observations: There is a force due to gravity acting on the object, and there is a force due to tension acting on the object. Based on the magnitude of the arrows that indicate the forces, the tension force is greater than the force of gravity.

Diagram C

Flift

Fg

The examples in diagrams A-C show us what happens when objects have linear motion (move in a straight line). Imagine instead a mass (m) moving in a circle. Even if it is moving at a constant speed, the object is accelerating. How do we know that the object is accelerating? Remember that acceleration means change of velocity over time. And velocity is a vector quantity, meaning that it has both size and direction.

For an object that is moving around a circle at a constant speed, the size of the vector will remain the same, but the direction constantly changes. Therefore, the object is accelerating. In this case, the acceleration is directed toward the center of the circle. If an object is accelerating, then Newton’s second law of motion tells us that the object is experiencing a net force (F = ma). Because we know that objects accelerate in the direction of the net force, we know that when an object travels in a circular path, there must be an inward force acting on it. This phenomenon is called centripetal force and explains everything from the rotation of bicycle wheels to planetary motion.

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STEMscopedia Diagram D body diagram, which is shown in diagram D. In this diagram, an object (the small blue circle) follows a circular path (the dotted line). The blue arrow indicates the velocity of the object, the black line indicates a force that is acting on WKH REMHFW ZLWK D ¿ [HG SRLQW DQG WKH FHQWULSHWDO force is indicated with the orange arrow. There are several formulas that can be used to calculate centripetal force.

Centripetal For e r it

vํ F=m r ac =

is

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F m

entri etal rce ass the ect g ing in a circle el cit the ect r Radi s the circle the c rve a entri etal accelerati n

7KH ¿ UVW IRUPXOD WKDW LV XVHG WR FDOFXODWH centripetal force is Fc = mv2/r, where m is the object’s mass, v is its speed, and r is the radius of the path that the object is following. This formula can be used when searching for the centripetal force that is acting on an object and the other known variables are mass, velocity, and radius.

Diagram E

Cir ular Motion

The next formula calculates the centripetal acceleration of an object. This formula is ac = v2/r, where ac is the centripetal acceleration, v is the velocity, and r is the radius. The centripetal acceleration is needed when applying Newton’s second law to circular motion.

7KH ¿ QDO IRUPXOD XVHV 1HZWRQ¶V VHFRQG ODZ IRU objects that are moving in a circle. That formula is Fnet = mac, where Fnet is the net force that is acting on the object, m is the mass, and ac is the centripetal acceleration.

Velocity = 2 m/s

Radius = 1 m Mass = 0.1 kg Centripetal force

Center of rotation

Let’s review a couple of examples.

Analyze the free-body diagram in diagram E to calculate the centripetal force of the yo-yo using the formula F = mv2/r. Plug in the values, and you get the following calculation.

F = (0.1 kg) x (2 m/s)2 / 1 m F = 0.4 N Another way to calculate centripetal force is to use Newton’s second law for centripetal force (F = mac).

7R ¿ QG WKH FHQWULSHWDO IRUFH XVLQJ WKLV IRUPXOD \RX PXVW ¿ UVW FDOFXODWH WKH FHQWULSHWDO DFFHOHUDWLRQ Dc) using the formula ac = v2/r. ac = (2 m/s)2 / 1 m ac = 4 m/s2 Using the ac of 4 m/s2, you can calculate the centripetal force.

F = (0.1 kg) x (4 m/s2) F = 0.4 N

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STEMscopedia motion is that they explain things that we have DOUHDG\ REVHUYHG ¿ UVWKDQG )RU H[DPSOH ZH know intuitively that if a soccer ball is kicked with 270 N of force, it will accelerate more than if it were kicked with a force of 100 N. It is important to remember that when a force is applied to an object, it will accelerate for as long as the force is applied. When kicking a ball, for example, the force is applied for only a split second. As soon as the applied force is no longer acting on the object, it will begin to slow down due to friction. With a more forceful kick, creating more acceleration, the ball will travel longer and farther before friction stops it.

Intuition also tells us that if we use the same force on objects with different masses, the object with the smaller mass will accelerate more. A force of 270 N exerted on a soccer ball that weighs 450 g (0.45 kg) will result in an acceleration of 600 m/s/s (270 = 0.45 x 600). A 270 N force exerted on a 5 kg bowling ball will result in an acceleration of only 54 m/s/s (270 = 5 x 54). Among other reasons, this is why soccer is not played with a bowling ball!

shot t n i o p three to shoot a e mak have 5. To etball, you force than k in bas l with more e shot. How id al the b hoot an ins ond law of s c if you ewton’s se is is true? h does N ove that t pr motion ipetal r t n e the c tes in s e i l p sup satelli t a s h p e 6. W that ke rth? a E e d c n for arou orbit

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STEMscopedia Newton’s third law of motion describes what happens when objects exert force on one another. The law states that for every action force there is an equal, opposite reaction force. In other words, when two objects interact, there will always be two forces at work: the action force and the reaction force. We call these forces an action-reaction pair.

Action-reaction pairs can be seen in the free-body diagram below:

+RZ GR IRUFHV WKDW DUH DFWLQJ RQ RQH REMHFW DIIHFW DQRWKHU REMHFW" $W ¿ UVW JODQFH LW ZRXOG VHHP WKDW WKH forces should cancel each other out because they are equal and opposite. But this is a misunderstanding because although the forces are equal and opposite, they operate on objects of different masses, and Newton’s second law of motion tells us that the same force that is acting upon different masses will cause different accelerations. Therefore, action-reaction pairs can cause objects to start moving, stop moving, speed up, slow down, or change direction.

Action-reaction pairs make motion possible.

Think about swimming. In order for a sea turtle WR PRYH IRUZDUG LW PXVW XVH LWV À LSSHUV WR SXVK the water away from itself. This movement RI WKH À LSSHUV SURYLGHV WKH DFWLRQ IRUFH 7KH reaction force is when the water pushes the turtle in the opposite direction (in this case, forward). The same is true of walking. To move forward, you must exert a force on the ground.

Your foot pushes backward while an equal and opposite force—in this case, friction—pushes your foot forward.

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STEMscopedia shuttle produce a force of around 5.5 x 106 N. Exhaust gases are produced in the rocket engine from the combustion of fuel, and the mass of the burning gases is expelled through the engine nozzles. This is the action force. The reaction force, which is equal in magnitude and opposite in direction, propels the space shuttle forward. Because the action force acts on the exhaust gases and the reaction force acts on the space shuttle, both accelerate in opposite directions. The acceleration of the exhaust gases and the space shuttle differ because their masses are very different.

These forces can be shown using a free-body diagram. In this case, the diagram shows that the action and reaction forces are equal in magnitude but act in opposite directions, resulting in the acceleration of the gases and the space shuttle.

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STEMscopedia is to imagine jumping on a trampoline. As the child in the picture exerts a downward force on the trampoline (the action force), the trampoline exerts a reaction force that is equal in size and opposite in direction, causing the child to accelerate upward.

Or you can imagine a basketball bouncing off the À RRU 7KH EDOO KLWV WKH À RRU ZLWK DQ DFWLRQ IRUFH DQG WKH À RRU DFWXDOO\ (DUWK SXVKHV EDFN ZLWK a reaction force that is equal and opposite. We see the ball bounce because the reaction force is strong enough to cause visible acceleration in the ball, which has a relatively small mass compared to Earth. We do not, however, see or feel Earth “bounce” off the ball because while the force is enough to cause visible acceleration of the ball, it is not enough to cause visible acceleration of Earth, which is much more massive.

other t a h 7. W ction pairs rea action- at work in are of the e r u ict the p ball game? t baske

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STEMscopedia 6LU ,VDDF 1HZWRQ ± LV RQH RI WKH PRVW LQÀ XHQWLDO VFLHQWLVWV LQ KLVWRU\ +H GHYHORSHG WKH ODZV of motion when he was only 23 years old. Like all scientists, his work was based on discoveries and theories that were made by earlier scientists, such as Aristotle and Galileo Galilei. Often, we think of scientists as being important because of their discoveries. In a sense, Newton did not discover the laws of motion because they already existed. He did, however, discover the means for expressing the laws using mathematics. Because the laws are founded on mathematics, they allow scientists to correctly predict how objects will behave when they are acted upon by forces. The laws formed the basis for what is known as classical mechanics: the theory that the motion of any observable object can be calculated with mathematical precision. Because of Newton’s laws, we can determine how long it will take for a car to stop if it is traveling at 55 mph. (On dry pavement, it takes about 300 ft., which is why your driver’s education instructor advises you to abide by the “3-second rule” when you are following another vehicle.) Newton’s laws allow us to understand and predict the motion of everything we can observe, whether we want to improve our golf swing or send a probe into deep space.

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STEMscopedia Newton’s three laws of motion are evident all the time in the world around you. If your desk and all the REMHFWV RQ WRS RI LW DUH UHPDLQLQJ VWDWLRQDU\ LW GHPRQVWUDWHV 1HZWRQ¶V ¿ UVW ODZ RI PRWLRQ REMHFWV DW rest remain at rest. Imagine a small earthquake occurring at the exact moment that you are reading WKLV 7KH REMHFWV RQ \RXU GHVN PLJKW EHJLQ WR VKDNH DQG HYHQ IDOO WR WKH À RRU 7KLV GHPRQVWUDWHV WKH second law: when net forces are greater than zero, masses accelerate in relation to the size of the net force. If, during the imaginary earthquake, you took shelter under your desk (which is a wise thing to do during earthquakes), you would be relying on the action-reaction pairs that are described in Newton’s third law. You would hopefully be protected as you hid beneath your desk because if an object fell down on your desk (action force), your desk would exert an equal, opposite reaction force (pushing upward on the fallen object), and that would prevent the object from landing on you.

Connect It

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STEMscopedia Summarize It 1. Which of the following describe(s) the way that a force can affect an object’s motion?

A. It can cause the object to speed up.

B. It can cause the object to stop.

C. It can cause the object to change direction.

D. All of the above 2. If a force of 500 N acts on an object that weighs 0.5 kg, what will the acceleration be?

A. 250 m/s2 B. 100 m/s2 C. 1,000 m/s2 D. 2,500 m/s2 3. If you jump from the back of a small rowboat into the water, how will the boat move relative to your motion?

A. The boat will move away from you.

B. The boat will move toward you.

C. The boat will stay still.

D. The boat will rotate 90°.

4. Using Newton’s second law of motion, explain why an overhand serve in volleyball is harder to return than an underhand serve.

The overhand serve uses more force than the underhand serve, so the volleyball accelerates more (travels faster), making it harder to hit.

5. Explain how diving off a diving board demonstrates all three of Newton’s laws of motion.

Answers may vary. A possible student response could include the following. Law 1: The diver or diving board are at rest until the diver jumps, and the diver stays in motion until gravity pulls them down.

Law 2: If the diver jumps with greater force, they will accelerate more. Law 3: The diver exerts a force on the board that is equal and opposite to the force that the board exerts on the diver.

6. When an insect splatters on your windshield as you are driving, which of Newton’s laws best explains the results? Explain your reasoning.

Answers may vary; all three of the laws can be used to explain the situation. A possible student response could include the following: The insect was in motion until it hit the car (law 1). The force with which the insect hit the car was equal to its mass multiplied by its acceleration (law 2), or the force of the car hitting the insect caused its body to accelerate so much that it burst (law 2). The insect and the car experienced equal and opposite forces, but the reaction force caused the insect to accelerate more because it had a smaller mass than the car (law 3).

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The Four Fundamental Forces

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57

STEMscopedia Imagine It When astronauts went to the Moon, they had to learn to walk differently. They had to take steps that were more of a hopping motion. The reason for this change in walking was the gravity on the Moon. The Moon’s gravity is just χΤΠ of the gravity that we experience on Earth.

However, if we went to Jupiter, the gravity we experience would be much higher.

1. What if we world witho lived in a ut gravity?

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e Four Fundamental For es

STEMscopedia Gravitational force and electromagnetic force were discovered long before the strong and weak nuclear forces that exist between all objects. Each of these forces acts on and governs the universe around us. Gravitational force governs the attraction between two masses whereas electromagnetic force governs the interaction between charged particles. Strong and weak nuclear forces govern the interaction between subatomic particles and particles in the nucleus. Nuclear forces work only over very small distances; gravitational and electromagnetic force can work over any distance but have less HIIHFW RYHU ORQJHU GLVWDQFHV $W ¿ UVW DOO RI WKHVH forces were thought to be separate from each other, but over time, they came to be viewed as parts of one unifying force.

The Standard Model seeks to describe all the interactions of subatomic particles. Force carrier particles PDGH RI EXQGOHV RI HQHUJ\ FDOOHG ERVRQV LQÀ XHQFH DOO RI WKH VXEDWRPLF SDUWLFOHV (DFK RI WKH IRUFHV LV caused by an exchange of these force-carrying bosons and has a boson that is particular to that force.

Electromagnetic force is carried by the photon. Strong force is carried by the gluon, and weak force is carried by the W and Z bosons. Gravitational force’s carrier, the graviton, has been theorized but not FRQ¿ UPHG WR H[LVW \HW

Carriers of the Four Fundamental Forces

Strong

Strong: Gluon

Gravitational: Graviton

Electromagnetic: Photon

Weak: Boson

Electromagnetic

Gravitational Graviton

Gluon (8)

Photon

Quarks

Mesons Baryons

Atoms Light Chemistry Electronics

Nuclei

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Solar system Galaxies Black holes

Weak Boson

Neutron decay Beta radioactivity Neutrino interaction Burning of the Sun

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STEMscopedia

2. How forces do nuclear gravit differ from a and e tional force s lectrom a gnet ic forces ?

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STEMscopedia Nuclear forces were discovered in the 20th century, when we began to work with the atom. Strong nuclear forces are between protons and neutrons. Weak nuclear forces occur between radioactive particles and electrons that do not experience strong nuclear force.

Strong nuclear force is the strongest force of the four. It holds the fundamentals of matter together. Part of the strong nuclear force keeps protons and neutrons, the nucleons, together in the nucleus of the atom even given the strong repellent force of the positively charged protons. This force acts over a very small distance, though particles have to be within the diameter of a proton of each other.

This force differs from the other forces in that it gets weaker as the particles get closer together. This force is actually strongest when the particles are farthest apart. Force-carrying particles called bosons, in WKLV FDVH VSHFL¿ FDOO\ JOXRQV NHHS WKH SDUWLFOHV ³JOXHG´ WRJHWKHU

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e Neutron Proton

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Nucleons: held together by nuclear binding energy

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3. Why do proto stay togeth ns er in the nuc leus even t hou gh they all ha ve a positive ch arge?

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STEMscopedia get close enough to each other, the nuclei fuse with each other. This process causes the nuclei to lose mass and release large amounts of energy and is called fusion. This is different from the process of ¿ VVLRQ ,Q ¿ VVLRQ WKH QXFOHXV RI DQ DWRP EUHDNV LQ WZR EUHDNLQJ WKH KROG RI WKH VWURQJ IRUFH $V WKHVH two new nuclei break apart, they cause other nuclei nearby to break apart, creating a chain reaction.

This releases massive amounts of energy, like what is found in an atomic bomb. The nucleus can be broken apart when it is bombarded with a neutron or gamma rays. These processes take advantage of a mass defect. The mass of the nucleus is less than the mass of the protons and neutrons. The binding energy actually accounts for the extra mass. The idea is that small amounts of mass can be converted into large amounts of energy.

+

+ +

Total mass of particles 7.058 amu

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+ + +

Binding energy 0.042 amu

Total mass of lithium-7 7.016 amu

e Four Fundamental For es

STEMscopedia Weak nuclear force is responsible for particle decay or turning one subatomic particle into another. If a neutrino comes too close to a neutron, the neutron turns into a proton and the neutrino turns into an electron. When subatomic particles come very close to each other, they can exchange bosons, or force-carrying particles. This exchange of W and Z bosons, which are found in weak forces, causes the subatomic particles to decay into new particles. This force is attractive only and is the secondweakest force.

Carbon dating by archaeologists to determine the age of formerly living artifacts measures this decay.

Naturally occurring carbon-14 has six protons and eight neutrons in the nucleus. Over time, one of those neutrons decays into a proton to make nitrogen-14, which is made of seven protons and seven neutrons.

The decay rate of carbon-14 is predictable and can be measured. Weak nuclear force initiates the fusion reactions that power the Sun. Two protons are smashed together, and the strong force binds them into a helium atom that is unstable because the nucleus is missing two neutrons. The weak force caused by the pair of protons initiates beta decay that eventually creates the more stable helium atom with two protons and two neutrons. Weak nuclear force is different from the other forces also. When the distance increases, the force decreases exponentially. There is no inverse proportionality with distance and force, even of the square of the distance.

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STEMscopedia Gravitational force acts between all objects that have mass. This is why pecans fall from trees and why the Moon orbits Earth. Sir Isaac Newton is thought to have come up with the idea of gravity based on an apple falling from a tree. He described this force as the attraction between two objects. Based on the theory of relativity, Albert Einstein had a different theory. He said that as you approach a large object in space, it will bend space and time around it, creating a sort of hole that other objects fall into. Imagine a mattress with a bowling ball in the middle. Anything placed on the mattress that is smaller than the bowling ball will roll toward the bowling ball. Anything with more mass than the bowling ball will create its own indentation that objects will roll toward.

Gravity is only an attractive force. The farther away from an object you get, the less pull it has on you.

Gravitational force is inversely proportional to the square of the distance between two objects. If you double the distance, you quarter the force exerted. The larger the mass of the object, the more pull it has. The closer you get to the bowling ball on the mattress, the more likely you are to fall or slide toward it. Gravitational force is directly proportional to mass. If you double the mass, you double the force. No matter how strong gravity feels, it is the weakest of the four forces. Think about how easy it is to lift your shoe from the ground.

e e som r a t a h 4. W hat gravity t ways ome daily? rc is ove

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e Four Fundamental For es

STEMscopedia Electromagnetic force is the attraction between unlike electric charges and the repulsion between like electric charges. This force is also called the Lorentz force. This is the force that causes positive protons to be attracted to negative electrons. If the positive or negative charge is large, then the attraction will be large. Theoretically, this attraction continues no matter the distance, but the farther away the objects get from each other, the smaller the effect of the attraction.

This force is the interaction of the electrical force and magnetic force, which are now considered components of electromagnetic force. Electrical force is experienced by objects even if they are stationary, but put the objects in motion and they experience the magnetic force. As the objects move, a magnetic force is created around them. This force is carried by the photon, just like the particle component of light. They are the same particle, but one is visible and the other is not.

e Four Fundamental For es

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STEMscopedia get pulled down to the ground due to gravity because of the repulsion between the atoms of the pan and atoms of the stovetop. Friction is the repulsion of two objects rubbing against each other. Solid objects hold their shape because the negative and positive charges of the atoms hold them together. Air resistance between an airplane and the atmosphere helps keep the plane in the air. Elasticity, molecular bonds, tension, air drag, and normal force are all phenomena that are related to electromagnetic force.

5. How d attach o magnets p a ref apers to rigera tor?

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STEMscopedia Physicists are trying to unify all four forces under a unifying theory. They theorize that all four forces DUH DFWXDOO\ PDQLIHVWDWLRQV RI RQH IRUFH 7KH HOHFWURZHDN IRUFH XQL¿ HG WKH ZHDN QXFOHDU IRUFH ZLWK WKH HOHFWURPDJQHWLF IRUFH 6FLHQWLVWV KDYH SUHGLFWHG WKDW WKH VWURQJ QXFOHDU IRUFH FRXOG EH XQL¿ HG ZLWK WKH HOHFWURZHDN IRUFH WR GH¿ QH DQ HOHFWURQXFOHDU IRUFH )LQDOO\ LI JUDYLW\ FDQ EH XQL¿ HG ZLWK WKHP DOO scientists would have a theory of everything. The theory of everything would explain the entire universe.

3UHGLFWLRQV WKDW SK\VLFLVWV KDYH PDGH EDVHG RQ DOO IRXU IRUFHV EHLQJ XQL¿ HG KDYH JHQHUDOO\ WXUQHG RXW to be correct. They are just looking for proof that they are correct. They have been able to unify gravity that acts on a macro level within the universe and quantum mechanics that act on a microscopic level.

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STEMscopedia Stephen Hawking (1942–2018) is generally thought of as one of the most recognized scientists of the current era. In 1963, he was diagnosed with amyotrophic lateral sclerosis (ALS), which is a motor neuron disease. In 1966, he obtained his PhD in applied mathematics and theoretical physics specializing in cosmology and general relativity from Trinity Hall, of the University of Cambridge. Hawking was initially controversial. His idea that black holes emit radiation, generally called Hawking radiation, was PHW ZLWK GHULVLRQ DW ¿ UVW /DWHU DIWHU PDQ\ PRUH SXEOLFDWLRQV WKLV EHFDPH WKH DFFHSWHG WKHRU\ +H ZDV WKH ¿ UVW SHUVRQ LQ FRVPRORJ\ WR XQLI\ WKH WKHRU\ RI UHODWLYLW\ DQG TXDQWXP PHFKDQLFV +LV ERRN A Brief History of Time spent 237 weeks on the bestseller list.

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e Four Fundamental For es

STEMscopedia There are four fundamental forces of nature. Gravitational force, according to Einstein, is a force that bends space and time around objects and is dependent on mass and distance. Electromagnetic force is dependent on the charge that particles carry and the distance. Particles with the same charge repel each other, and particles with opposite charges attract each other. Strong nuclear forces bind protons and neutrons together. Lastly, weak nuclear forces govern the radioactive decay of subatomic particles.

Scientists hope to unify all four forces into one force in the theory of everything to explain the universe.

Connect It How does force impact our universe?

The four fundamental forces—gravitational, electromagnetic, and strong and weak nuclear forces—and their interactions govern the entire universe.

6. How doe s force impa ct our universe?

e Four Fundamental For es

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STEMscopedia 1. Which of these is not a fundamental force?

A. Gravitational force B. Normal force C. Electromagnetic force D. Weak nuclear force 2. Gravity is due to– A. the pull between Earth and the Moon.

B. the pull between an electron and a proton.

C. the pull between objects with mass.

D. the pull between positive and negative charges.

3. What is the ranking of the forces from strongest to weakest?

A. Strong nuclear, gravity, weak nuclear, electromagnetism B. Weak nuclear, electromagnetism, gravity, strong nuclear C. Gravity, electromagnetism, weak nuclear, strong nuclear D. Strong nuclear, electromagnetism, weak nuclear, gravity 4. What is the correlation between gravitational force and distance, and how does it differ from the correlation between gravitational force and mass?

5. How are magnetic force and electric force connected?

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Universal Gravitation

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73

STEMscopedia Have you ever wondered about the forces between objects? Consider a game of billiards. What forces are acting between the balls during the game?

Effect of Mass Stronger

Weaker

Effect of Distance Stronger Weaker

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ni ersal Gra itation

STEMscopedia Newton’s laws of motion discuss the forces experienced by bodies here on Earth but can be applied to celestial bodies. 1HZWRQ¶V ¿ UVW ODZ RI PRWLRQ states that a body must remain at rest or move in a straight line at constant speed unless it is acted upon by an outside force. Neither the object at rest nor the one traveling at constant speed are accelerating; therefore, objects do not accelerate unless acted upon by an external force. 1HZWRQ¶V VHFRQG ODZ RI PRWLRQ states that if such a force acts upon a mass, then acceleration occurs. This relationship is given by the formula F = ma where the force produced is the product of both mass and acceleration. This also explains why a force applied to a more massive object would accelerate less than one with less mass. 1HZWRQ¶V WKLUG ODZ RI PRWLRQ states that when one body exerts a force on a second body, the second body exerts an equal and opposite IRUFH EDFN RQ WKH ¿ UVW ERG\ )RU H[DPSOH LI WZR FDQRHV DUH WLHG WRJHWKHU DQG WKH ¿ UVW FDQRH SXOOV WKH second one, it is exerting a tension force on the second canoe. The second canoe exerts a force back RQ WKH ¿ UVW RQH LQ UHVSRQVH WR WKDW WHQVLRQ IRUFH 7KHVH ODZV PDNH VHQVH IRU PRWLRQ RQ (DUWK EXW ZKDW NHHSV (DUWK PRYLQJ DURXQG WKH 6XQ" 6LU ,VDDF 1HZWRQ ZDV WKH ¿ UVW VFLHQWLVW WR H[SODLQ JUDYLWDWLRQDO force for falling objects and the motion of the planets. Newton made the great discovery of JUDYLW\, or the mutually attractive physical force between any two masses. He then went on to apply this concept to what is known as 1HZWRQ¶V ODZ RI XQLYHUVDO JUDYLWDWLRQ, which states that every object in the universe attracts every other object with a force directed along the centers of the two objects. His universal law of gravitation further states that the amount of gravity that something possesses is proportional to its mass and distance between it and another object. Newton used this law, along with his laws of motion, to explain motion of various types such as falling objects and planets. The universal law of gravitation coupled with circular acceleration keeps objects, such as Earth, in orbit. The law of universal gravitation can be explored mathematically using the following formula where F is the attractive gravitational force between two objects of mass m1 and m2 separated by some distance r; the constant G is called the universal constant of gravitation with a value of 6.67 x 10-11 m3kg-1s-2.

F = force measured in newtons (N) G = gravitational constant (6.67 x 10-11 m3kg-1s-2) m1 PDVV RI ¿ UVW REMHFW LQ NLORJUDPV NJ m2 = mass of second object in kilograms (kg) r = distance between two objects in meters (m)

ni ersal Gra itation

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STEMscopedia ([DPSOH You and your best friend each have a mass of 60 kg. You are standing 20 cm away from each other. Calculate the gravitational attraction force between you.

G = 6.67 x 10-11 m1 = 60 kg m2 = 60 kg r = 20 cm (convert to meters)

would t a h 2. W o Earth’s n t happe if we were ? y gravit o the Sun t closer

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ni ersal Gra itation

STEMscopedia N • m2 G = Universal gravitational constant = 6.67 x 10 kg2 -11

40 kg 20 kg 10 m

G =6.67 x 10-11 m1 = 40 kg m2 = 20 kg r = 10 m

([DPSOH What gravitational force does the Moon produce on Earth if Earth has a mass of 5.98 x 1024 kg, the Moon has a mass of 7.34 x 1022 kg, and their centers are 3.88 x 108 m apart?

G =6.67 x 10-11 m1 = 5.98 x 1024 kg m2 = 7.34 x 1022 kg r = 3.88 x 108 m

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STEMscopedia The JUDYLWDWLRQDO IRUFH between two objects is directly proportional to their masses. More mass means more force. If the mass of one object is doubled, so is the force. The gravitational force between two objects will decrease as you move the objects farther apart and increase as you move them closer together.

Direct and Inverse Relationships in the Law of Universal Gravitation 50 g

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Mass and gravitational force are directly proportional. When the mass is doubled, the force of gravity is doubled.

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Gravitational force is inversely proportional to the square of the distance between objects.

If distance is doubled, the force of gravity is ¼. ld you u o c 5. How e mas s of e th WR chang VW REMHFW U WKH Ş four times ou give y f o r c e ? the

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ni ersal Gra itation

STEMscopedia 1LFRODXV &RSHUQLFXV ¿ UVW GHVFULEHG WKH VRODU V\VWHP DV KHOLRFHQWULF RU 6XQ FHQWHUHG LQ 3ULRU WR this time, Earth was accepted as the center of our solar system. Copernicus further described the orbits of planets around the Sun as traveling in a circular orbit at constant speeds. Johannes Kepler wrote his ¿ UVW WZR ODZV RQ SODQHWDU\ PRWLRQ LQ LQFRUSRUDWLQJ REVHUYDWLRQV JDWKHUHG E\ KLV PHQWRU 7\FKR Brahe. After further observations, he added a third law ten years later. .HSOHU¶V ODZ RI HOOLSVHV was KLV ¿ UVW ODZ ZKLFK VWDWHV WKDW WKH RUELW RI D SODQHW LV DQ HOOLSVH ZLWK WKH 6XQ DW RQH IRFDO SRLQW 7KLV ODZ explains how every planet revolves around the Sun with the Sun as one focal point of its elliptical path.

As the planet follows this path, its distance to the Sun is constantly changing. .HSOHU¶V ODZ RI HTXDO DUHDV, or second law, states that there is a line segment connecting the planet and the Sun that sweeps RXW LQ HTXDO DUHDV GXULQJ HTXDO WLPH SHULRGV 3ODQHWV PRYH IDVWHU ZKHQ WKH\ DUH QHDU WKH 6XQ DQG VORZ down when they are farther away from the Sun along their orbits. Therefore, the orbital speed changes depending on the distance from the Sun. .HSOHU¶V ODZ RI KDUPRQLHV KLV WKLUG DQG ¿ QDO ODZ H[SODLQV that the square of the time it takes a planet to orbit the Sun is proportional to the cube of its average distance to the Sun. This ratio is the same for every planet and is used to estimate orbital periods or the average distance from the Sun for planets in our solar system. Collectively, .HSOHU¶V ODZV describe the motion of planets traveling around the Sun. The law of universal gravitation states that every piece of matter is attracted to every other piece of matter and the force is directly proportional to their masses but inversely proportional to the square of the distance between them. This law applies to all objects with mass, big or small. The law of universal gravitation applies to the planets as much as it does to the falling of an apple to Earth’s surface. Recall Newton’s second law of motion. Forces cause acceleration. Gravity is a force with an acceleration of 9.8 m/s2. The law of universal gravitation is based on the balancing point of the masses of two objects in a straight line. When that line becomes curved, the center of mass does not change, but the distance between the objects may vary, as it does with the planets in our solar system

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STEMscopedia applying uniform circular motion. Objects traveling in a circular path are constantly accelerating toward WKHLU FHQWHU RI PRWLRQ 7KHUHIRUH DFFRUGLQJ WR 1HZWRQ¶V ¿ UVW ODZ RI PRWLRQ WKHUH PXVW EH D IRUFH DFWLQJ on the planet that is directed toward the center of its orbit, the Sun. Newton’s second law allows for determining the magnitude of this force in terms of mass and acceleration of the circular motion (a = v2/r), which is the force required to keep Earth traveling on its circular path. Newton’s third law implies that if Earth is attracted to the Sun, then there must be an equal and opposite force attracting the Sun to Earth. Since the Sun’s movement is so minuscule that it can be neglected, the force of attraction between Earth and the Sun must be dependent upon mass.

Orbitals may be altered due to collisions with or gravitational effects from other objects in the solar system. Asteroids and comets have been observed to change course in response to traveling too close to planets or their moons. In 1994, the Shoemaker-Levy 9 comet was traveling too near Jupiter, which SXOOHG WKH FRPHW LQWR LWV JUDYLWDWLRQDO ¿ HOG 7KH FRPHW EURNH LQWR VHYHUDO SLHFHV EHIRUH ¿ QDOO\ FUDVKLQJ into Jupiter’s atmosphere.

ink you th o d 6. How tary orbits plane clipses? t e impac

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ni ersal Gra itation

STEMscopedia Katherine Johnson (1918–2020) was a female African American PDWKHPDWLFLDQ ZKR FDOFXODWHG DQG DQDO\]HG WKH À LJKW SDWKV RI many spacecrafts. She loved math and studied geometry for the purposes of space travel. The National Aeronautics and Space Administration (NASA) hired Johnson as one of its “human computers” in 1953. In 1962, the United States decided to send humans to the Moon, but there were many mathematical obstacles during their journey.

Johnson was part of a dynamic mathematical team whose calculations helped send astronauts to the Moon and back. The movie Hidden Figures highlights the story of the team of female African American mathematicians who served a vital role in NASA during the early years of the US space program.

The Big Picture Gravitational interactions exist not only between Earth and other objects but between all objects. The amount of gravitational attraction that is present is directly proportional to the product of the objects’ masses. In Newton’s law of gravity, we also notice that mass is a crucial quantity. More mass means more force.

Connect It the e v l o S 7. uation q e n give law of . e h t using gravitation sal univer

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STEMscopedia What variable(s) can change the force between objects using the law of universal gravitation? $ Mass of objects % Distance of objects & Both A and B ' None of the above The gravitational force between two objects will _____________ as you move the objects farther apart. $ increase % decrease & become inverse ' vary Which of the following has an incorrect unit? $ Mass = J % Force = N & Distance = m ' All are correct.

Explain how mass can change the amount of force that is present between two objects using the law of universal gravitation.

The more mass an object has, the more force it will have. The law of universal gravitation has two objects present. The larger the mass(es), the larger the force that will be present.

How can the law of universal gravitation apply to all objects on Earth?

All objects that exist have mass. Objects on Earth are also all experiencing a gravitational pull toward Earth and other objects.

How does the gravitational force change as objects become closer together or farther apart?

The closer together that objects are, the stronger the gravitational force; as the objects get farther apart, the gravitational force becomes weaker.

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ni ersal Gra itation

Coulomb’s Law

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85

STEMscopedia If you rub a balloon on your shirt then hold it near your hair, your hair will be attracted to the balloon, as shown in the picture. Would the balloons still attract your hair if your hair were shorter? How far away will you be able to hold the balloons and still have your hair be attracted?

s factor t a h 1. W think do you e how in determ tracted to s at hair i balloon? a

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Coulom s La

STEMscopedia You have probably heard the phrase “opposites attract.” This is the concept that explains why hair is attracted to balloons in the picture above. But what is opposite about the balloons and the hair?

The balloons and the hair, like all matter, are made of atoms. Atoms are made of positively charged protons, neutral neutrons, and negatively charged electrons. Neutral atoms have no electric charge and are composed of equal numbers of protons and electrons.

However, not all atoms are neutral. While the protons and neutrons are tightly held in the nucleus of the atoms, the negatively charged electrons on the outside of the atoms can be removed, resulting in an imbalance of charges.

Atoms with fewer electrons than protons have a positive charge, but if there are more electrons than protons, they will have a negative charge.

All charges are the result of moving electrons, and the resulting electric charges exert forces.

Electricity cannot be seen directly, but it is a physical phenomenon associated with the movement of charged particles. Therefore, lightning or sparks are the by-product of this movement. Charged particles are tiny particles that carry an electric charge that can be positive or negative, such as protons and electrons.

When you rub a balloon on your shirt, electrons are transferred from your shirt to the surface of the balloon, giving it an overall negative charge. This accumulation of electric charge on the surface of an object is called static electricity. When this negatively charged balloon is brought near a neutral object, like hair or a wall, it will draw the opposite (positive) charge toward it, causing the two objects to be attracted to each other. This is called electrostatic attraction. Eventually, the accumulated charges will dissipate, resulting in the objects returning to their neutral state and no longer being attracted.

Coulom s La

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STEMscopedia You may have experienced this same phenomenon when removing clothes from the dryer. As clothes tumble together, electrons are rubbed from some and onto others, creating an opposite charge and causing them to “stick” together. Sometimes, the charge dissipates quickly. Have you ever felt a small shock when touching something after walking across a carpet? When your shoes rub on the carpet, electrons are rubbed off the carpet and accumulate on the surface of your body. When you touch something conductive, the electrons can be suddenly transferred to the object, resulting in a small shock.

will a y h W 2. tract t a t o n balloon less it has n hair u rubbed on been QJ Ş UVW" KL VRPHW

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Coulom s La

STEMscopedia Like Charges Repel What would happen if two negatively charged balloons came near each other? If opposites attract, what would happen if the charges were the same?

Though opposite charges attract, like charges repel. A Van de Graaff generator is a machine that removes electrons from an inner belt, causing an accumulation of static charge on a metal globe. If you get too close to the metal globe while it is charged, the charge could be suddenly attracted to you and you could get a shock as the charge transfers to you. But if you were to stand on something to insulate you from the ground and touch the globe as it is starting to charge, the charges would accumulate on the globe and on you.

As the static charge accumulates on the hair of the student in the picture, the strands of hair all accumulate the same charge and repel each other, causing the top hairs to move as far apart from each other as they can. This electrostatic repulsion is the principle behind how an electroscope works.

Charges within matter can be altered by separating positive and negative particles or removing electrons from one medium and transferring them to another by means of friction or other methods. However, charges are not created or destroyed through these processes. The total charge remains constant, thus obeying the law of conservation of charge.

Coulom s La

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STEMscopedia

As shown in the top of the diagram, if the two leaves that are hanging near each other are neutral, they neither attract nor repel. When the leaves have the same charge, whether positive or negative, they repel. If the leaves are attached to a metal ball when in the presence of static electricity, the electrostatic charge will be transferred to the leaves and the leaves will repel.

The force of attraction or repulsion between objects with stationary electric charges is called the electrostatic force.

ink you th o d 3. How amount of the would e g r a ch static the leaves affect ectroscope? el of an

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Coulom s La

STEMscopedia Charles-Augustin de Coulomb was a French physicist who studied electrostatic attraction and repulsion in the 1700s. His work resulted in the description of electrostatic force known as Coulomb’s law, which states that the force of interaction between charged particles is based on the strength of the charges and the distance between the particles.

The electric charges we have discussed come from protons and electrons. These particles and their charges are very small. The SI unit used to measure the charge is a coulomb (C). One coulomb is equal to the quantity of electricity conveyed in 1 second by a current of 1 ampere. This is equal to the charge of 6.24 x 1018 protons or electrons. Therefore, the charge of just one proton is 1.6 x 10-19 C, and the charge of an electron is -1.6 x 10-19 C. According to Coulomb’s law, 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.

The accumulated static charge on objects is usually much less than 1 coulomb, so it is measured in microcoulombs (μC = 10-6 C) or nanocoulombs (nC = 10-9 C). If the objects are repelling each other, WKH\ ZLOO KDYH D OLNH FKDUJH DQG WKH ¿ QDO IRUFH ZLOO EH SRVLWLYH ,I WKH REMHFWV DUH DWWUDFWLQJ HDFK RWKHU WKH\ ZLOO KDYH RSSRVLWH FKDUJHV DQG WKH ¿ QDO IRUFH ZLOO EH QHJDWLYH 7KH ³ ´ RU ³ ´ VLJQV RI WKH FKDUJHV are sometimes dropped when they are entered into an equation to avoid confusion, and it is simply noted if the force is one of attraction or repulsion. The distance is measured between the centers of the objects, not their surfaces, and is measured in meters.

Coulom s La

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STEMscopedia /HW¶V XVH WKH WZR QHJDWLYHO\ FKDUJHG EDOORRQV VKRZQ HDUOLHU IRU WKH ¿ UVW H[DPSOH $VVXPH WKDW WKH balloons were both rubbed on the same shirt and accumulated the same charge of -5.20 nC. If the distance between the centers of the balloons is 42.3 cm, what is the electrostatic force of repulsion between them? Note: Convert nC to C and cm to m to use in the equation.

F=

kc q1q2 d2

(8.99 x 109 Nm2/C2) (-5.20 x 10-9 C) (-5.20 x 10-9 C) F=

(0.423 m)2

2.43 x 10-11 Nm2 0.1 9 m2

F=

F = 1.36 x 10-6 N Example 2: :KDW LI WKH WZR EDOORRQV KDG RSSRVLWH FKDUJHV" $ EDOORRQ ZLWK D FKDUJH RI & DWWUDFWV D & charged balloon with a force of 0.0597 newtons. How close are the two balloons? Note: Convert nC to C; the value for force is entered as a negative because it is an attractive force.

F=

.

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10 C

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Coulom s La

STEMscopedia If you are familiar with Newton’s law of universal gravitation, you may notice that Coulomb’s law is very similar.

Both forces act on protons in a nucleus. They are attracted to each other because of their masses (Newton’s law of universal gravitation), but they repel each other due to their like charges (Coulomb’s law). It would seem that the gravitational force must be stronger than the repulsive force because the protons stay together in the nucleus. But this is not the case. The repulsive force between two protons in a nucleus due to their charges is 4.1 × 1042 times stronger than the attractive gravitational force between them due to their masses. Protons staying together in the nucleus despite this strong repulsive force is what led scientists to propose that strong nuclear force binds together protons and neutrons in a nucleus.

Coulom s La

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STEMscopedia hat is 4. W ence iffer the d a positive en betwe e value forc e egativ n a in and value e c r fo s law? ’ b m o l Cou

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Coulom s La

STEMscopedia

he electric ield directi n is al a s directed a a r sitive s rce charges and t ard negative s rce charges.

Charged particles exert forces on each other, and the strength of those forces depends largely on their distance apart, much like Coulomb’s law. When electrons move closer to the region around other electrons, the charges repel. When they move closer to the region around protons, the charges attract.

The repulsion or attraction is greatest when these regions are close together. An HOHFWULF ¿ HOG is the region surrounding each charged particle and is indicated by arrows to signify the amount of force experienced by each particle. Arrows point toward negative charges and away from positive ones. The length of the arrows indicates the relative strength of the electrical force and depends on the distance IURP RWKHU SDUWLFOHV $ SURWRQ¶V LQWHUDFWLRQ ZLWK DQ HOHFWURQ ZRXOG EH VLJQL¿ FDQW ZKHQ WKH\ DUH FORVH together but would diminish when that distance increased.

The potential energy of any object on Earth is a product of its mass, height, and the gravity experienced by the object. Therefore, gravitational potential energy is the energy stored within an object due to its position and useful for doing work. As an object is lifted higher, work is done to the object, and it increases its gravitational potential energy, which can then be transferred to do work by the object. In a very similar way, the electric potential energy of a particle is the product of its charge, distance IURP DQRWKHU SDUWLFOH DQG WKH HOHFWULF ¿ HOG VWUHQJWK 7KLV HQHUJ\ LQFUHDVHV DV WKH SDUWLFOHV PRYH FORVHU together, much like a falling object increases velocity due to gravity. The difference in electric potential energy LV PHDVXUHG LQ YROWDJH DQG VLJQL¿ HV WKH ZRUN UHTXLUHG WR PRYH HOHFWULF FKDUJHV :KHQ VLPLODU charges are brought together, the potential energy increases. However, if two different charges are brought together, then the potential energy decreases. This should make sense, since similar charges repel each other, which produces kinetic energy due to an increase in that potential energy.

2YHUDOO HOHFWULF DQG JUDYLWDWLRQDO ¿ HOGV UHSUHVHQW LQWHUDFWLRQV EHWZHHQ PDWWHU DQG WKH HQHUJ\ FKDQJHV produced by these interactions. Both gravitational and electric potential energy are inversely related to the distance between objects or particles. While gravitational energy depends on the mass of both objects, electric potential energy is contingent on their charges.

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STEMscopedia ravitati nal tential nerg all

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Coulom s La

STEMscopedia Fabiola Gianotti, PhD, and the CERN Particle Accelerator Fabiola Gianotti was born in Italy in 1960. She received her PhD in experimental particle physics from the University of Milan in 1989. Gianotti began working as a research physicist at the European Organization for Nuclear Research (also known as CERN) in Switzerland in 1994. She worked on detector development and construction, software development, and data analysis. In 2009, she was promoted to project leader and spokesperson for the ATLAS Experiment. She played a major role in the discovery of the Higgs boson and presented its discovery to the world in 2012. For her work, Gianotti has received many prestigious honors and awards. She became an honorary professor at the University of Edinburgh LQ ,Q VKH ZDV HOHFWHG DV WKH ¿ UVW IHPDOH GLUHFWRU JHQHUDO RI &(51

Coulom s La

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STEMscopedia Protons and electrons have opposite charges. When objects rub against each other, they accumulate static charges. Charged objects exert an electrostatic force on each other. Like charges will repel while opposite charges will attract. The strength of the electrostatic force depends on the charges of the objects and the distance between them, as described by Coulomb’s law.

Connect It What factors do you think determine how hair is attracted to a balloon?

7KH EDOORRQV LQ WKLV SLFWXUH DUH PXFK VPDOOHU WKDQ WKH EDOORRQV LQ WKH ¿ UVW SLFWXUH EXW WKH\ VWLOO attract hair. Because the balloons and hair are attracting each other, they must have opposite electrostatic charges.

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Coulom s La

STEMscopedia Summarize It 1. When two objects rub together, which atomic particle is being transferred?

A. Protons B. Neutrons C. Electrons D. Nucleus 2. For a Van de Graaff generator to work, which charge(s) must accumulate on the metal globe?

A. Positive only B. Negative only C. Either positive or negative D. Both positive and negative 3. Which charge would create the greatest electrostatic force?

A. & B. -6.42 μC C. Q& D. -9.03 nC 4. Explain why a balloon that is electrostatically attracted to a wall will eventually fall away from the wall.

The balloon is electrostatically attracted only if it has accumulated a static charge. Once in contact with the wall, the static charge will begin to dissipate. When the balloon and wall are no longer oppositely charged, they will no longer be attracted to each other, and the balloon will fall away.

5. Why does an electroscope operate by electrostatic repulsion and not attraction?

The two leaves of an electroscope receive the same electric charge when in the presence of static electricity. Because they both have the same charge, they repel and not attract.

6. What is the electrostatic force of repulsion between two objects with charges of 2.48 μC and 4.31 μC that are located 3.92 cm apart?

Coulom s La

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Electric Circuits

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101

STEMscopedia Think about things you might use in your daily life that contain electric circuits. This list can get long very quickly because circuits are everywhere around us. Circuits light lamps, cook food, open automatic doors, and send and receive calls on mobile phones.

o you d e r e 1.. Wh ric circuits d lect see e room aroun in the ight now? you r

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le tri Cir uits

STEMscopedia A current LV D ÀRZ RI HOHFWULF FKDUJHV WKDW LV UHSUHVHQWHG E\ WKH YDULDEOH , ,Q PRVW VROLG FRQGXFWRUV VXFK DV PHWDO ZLUH FXUUHQW LV WKH ÀRZ RI PRYLQJ FKDUJHV WKURXJK WKH PDWHULDO 7KH ÀRZ RI HOHFWULF current is measured in units of amperes (A), or amps, and can be calculated if you know the amount of charge (measured in coulombs) divided by the amount of time (measured in seconds) it takes for a charge to move a given distance. So, 1 A = 1 C/s.

0DWHULDOV FDQ EH JURXSHG LQWR WKUHH FDWHJRULHV EDVHG RQ KRZ HDVLO\ WKH\ DOORZ D FXUUHQW WR À RZ WKURXJK WKHP FRQGXFWRUV VHPLFRQGXFWRUV DQG LQVXODWRUV 7KH À RZ RI WKH FXUUHQW LV GHSHQGHQW RQ the number of free electrons available in the material. These electrons can move from a valence band into a conduction band when excited. Conductors DOORZ D FXUUHQW WR À RZ HDVLO\ GXH WR WKH QXPEHU RI free electrons within the material. Conductors have a full valence band, a conduction band with free electrons, and many empty energy levels. When energy is added to a conductor, the electrons move easily between energy levels. This means that an electric current can also move easily within the conductor. Common examples of conductors include metals such as copper, aluminum, brass, tin, gold, and silver.

Semiconductors DOORZ DQ HOHFWULF FXUUHQW WR À RZ XQGHU FHUWDLQ FRQGLWLRQV EXW QRW RWKHUV 7KH valence band of semiconductors is full, but they have an empty conduction band at low temperatures.

Electrons can jump from the valence band to the conduction band when thermal energy or light energy is added. The conductivity will increase as temperature increases, since more electrons are jumping bands. Common examples of semiconductors include crystalline solids such as silicon, germanium, and gallium arsenide.

Insulators GR QRW DOORZ DQ HOHFWULF FXUUHQW WR À RZ HDVLO\ $Q LQVXODWRU KDV D IXOO YDOHQFH EDQG EXW WKH JDS EHWZHHQ WKH YDOHQFH EDQG DQG WKH FRQGXFWLRQ EDQG LV YHU\ ODUJH 7KLV PDNHV LW GLI¿ FXOW IRU the electrons to make the jump between the bands. Also, the electrons within an insulator are tightly bound and do not move easily. This means that an electric current cannot move easily with the insulator.

Common examples of insulators include plastic, rubber, glass, and wood.

A circuit provides a path for a current to travel and can be described as either open or closed. )RU D FXUUHQW WR À RZ WKH FLUFXLW PXVW EH FORVHG ,PDJLQH DQ HOOLSWLFDO WUDFN WKDW D UDFH FDU WUDYHOV on. There is a starting line, a lane for the car to WUDYHO RQ DQG D ¿ QLVK OLQH 7KLV LV VLPLODU WR D closed circuit that a current travels on. Circuits can also be described as alternating current (AC) or direct current (DC). An AC circuit has a current WKDW FKDQJHV WKH GLUHFWLRQ WKDW D FXUUHQW À RZV in a given cycle. For example, wall plugs in the United States are AC circuits that have 60 cycles of oscillation per second. AC circuits in Europe and Asia have 50 cycles of oscillation per second.

DC circuits only allow the current to travel in one direction. The remainder of this scope will focus on DC circuits.

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STEMscopedia The only way for an object to move is if an unbalanced force is exerted on it. The same is true of FKDUJHV ,Q WKLV FDVH WKH XQEDODQFHG IRUFH LV DQ HOHFWULFDO IRUFH IURP D SRZHU VRXUFH ,Q WKH LPDJH RQ WKH SUHYLRXV SDJH \RX VHH D VLPSOH FLUFXLW :KDW LV WKH SRZHU VRXUFH LQ WKDW FLUFXLW" $ EDWWHU\ ,I \RX look closely enough, you can see a “+” and a “–” on opposite ends of the battery. These signs indicate the two terminals of that battery. These terminals are the origin of the force that is needed to get charges moving.

The terminals of a battery have an electric potential difference between them as a result of chemical reactions happening in the battery. The terminal with the “+” has a high electric potential while the “–” LQGLFDWHV D ORZ HOHFWULF SRWHQWLDO ,Q WKH FLUFXLW diagram, you see a battery indicated with the symbol below. ,Q DQ\ FLUFXLW WKH GLIIHUHQFH LQ HOHFWULF SRWHQWLDO is referred to as voltage and measured in volts (V).

Voltage is always positive as it measures the difference between high electric potential and low electric potential.

Battery + _

ic electr s i 2. How l important tia poten ushing in p hrough ons t r t c e l e uit? a circ

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STEMscopedia 8S WR WKLV SRLQW ZH KDYH GLVFXVVHG WKH À RZ RI D FKDUJH RU FXUUHQW LQ D FLUFXLW 7KLV LQYROYHV D SRVLWLYH test charge, not an electron. Electrons, however, are the actual carrier of the charge in a circuit. Think back to chemistry and how metals have a sea of electrons that are able to move from place to place.

This is why metal is a good conductor; it allows the electrons the ability to move easily. However, the path an electron has to take as it moves is not so easy. As the electrons move, they collide with the atoms of the wire, resulting in a change in the direction of the motion. This results in resistance, RU RSSRVLWLRQ WR PRWLRQ 5HVLVWDQFH LV PHDVXUHG LQ RKPV ZULWWHQ ZLWK WKH V\PERO ƻ WKH *UHHN letter omega).

Resistance is impacted by several factors. These include the length, thickness, and type of wire. The longer a wire is, the more atoms that an electron will encounter, resulting in higher resistance. Have you ever noticed how some electric cords are really thin while others are much thicker? Which wires have high resistance? The thin wire has much higher resistance because an electron has less space to travel. <RX FDQ WKLQN RI LW WKLV ZD\ :DWHU À RZLQJ WKURXJK D SLSH À RZV PXFK HDVLHU DQG IDVWHU LQ D ODUJH SLSH versus a small pipe. Some metals, such as silver and copper, have much lower resistance while others, such as lead, have higher resistance. This is why most electric wires are composed of copper.

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STEMscopedia So, we know now that voltage provides the energy that is needed for a charge to move from a low– electric-potential terminal in a battery to a high–electric-potential terminal, which, in turn, allows a FXUUHQW WR ÀRZ LQ D FLUFXLW *HUPDQ SK\VLFLVW *HRUJ 2KP GLVFRYHUHG D UHODWLRQVKLS DPRQJ WKH YROWDJH current, and resistance in a circuit. His experiments proved that there was a proportional relationship between the current and resistance and the voltage. Essentially, if you were to increase the resistance and keep the current the same, the voltage would have to increase. This led to the mathematical relationship of voltage, current, and resistance called Ohm’s law.

Voltage = Current x Resistance V = IR ,Q PRVW FDVHV ZH NQRZ WKH YROWDJH JLYHQ WR WKH EDWWHU\ ZH DUH XVLQJ )RU H[DPSOH W\SLFDO DONDOLQH EDWWHULHV $$$ $ & DQG ' DUH 9 DQG D UHFWDQJXODU EDWWHU\ FDOOHG D YROW EDWWHU\ LV 9 2KP¶V law allows us to manipulate the formula so that the current can be determined if the voltage and resistance are given.

Current = Voltage/Resistance I = V/R 5HVLVWDQFH LQGLFDWHV KRZ HDVLO\ D FXUUHQW FDQ ÀRZ LQ D FLUFXLW /DUJH UHVLVWDQFH PHDQV WKDW WKH FXUUHQW KDV D KDUGHU WLPH ÀRZLQJ ,QFUHDVLQJ WKH UHVLVWDQFH LQ D FLUFXLW OHDGV WR OHVV FXUUHQW ,I WKH UHVLVWDQFH GHFUHDVHV WKH FXUUHQW LQFUHDVHV 2KP VWXGLHG WKH HOHFWULF SURSHUWLHV RI PDQ\ GLIIHUHQW PDWHULDOV DQG found that, for many materials, the resistance is constant over a wide range of voltages. For these materials, a graph of applied voltage versus current shows a straight line. Resistors that stay constant RYHU D ZLGH UDQJH RI YROWDJHV DUH FDOOHG RKPLF UHVLVWRUV )RU H[DPSOH LI D ƻ RKPLF UHVLVWRU LV ZLUHG into a circuit, we can increase the voltage through the circuit and the current will increase, but the resistance will always stay the same.

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STEMscopedia 6R IDU ZH KDYH GLVFXVVHG WKH FXUUHQW YROWDJH DQG UHVLVWDQFH LQ D FLUFXLW 7KLV LQYROYHV WKH À RZ RI FKDUJHV GXH WR D SRWHQWLDO GLIIHUHQFH LQ D SRZHU VRXUFH ,Q UHDOLW\ WKH PRYHPHQW RI WKHVH FKDUJHV through a wire provides no use for a household. However, adding components to the wire, such as a light bulb, allows for the transformation of the energy in the current into energy that we can use. This leads to power ,Q WHUPV RI HOHFWULFLW\ SRZHU LV WKH UDWH DW ZKLFK HOHFWULFDO HQHUJ\ LQ D FLUFXLW LV WUDQVIRUPHG into different energy by an element in the circuit. Electric 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, such as in an automatic door.

3RZHU FDQ EH FDOFXODWHG LQ VHYHUDO ZD\V %DVHG RQ WKH GH¿ QLWLRQ ZH QHHG WR NQRZ WKH DPRXQW RI HQHUJ\ consumed by an element in a circuit as well as the amount of time needed for the consumption to KDSSHQ *LYHQ WKDW LQIRUPDWLRQ WKH IRUPXOD LV HQHUJ\ GLYLGHG E\ WLPH DQG LV PHDVXUHG LQ ZDWWV : (1 watt = 1 joule/second).

Power = Energy/time P = E/t Power can also be calculated using current and voltage by multiplying the two measurements.

Power = Current x Voltage P = IV

n the n i a l p x 3. E etwee b e c en differ e, power, voltag istance. es and r

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STEMscopedia Types of Circuits FRQGXFWLYH PDWHULDO WKDW DOORZV HOHFWURQV WR À RZ By adding different elements to the circuit, you have lots of different ways that you can set up those circuits as long as there is a closed path for the electrons to travel. Elements that can be added to circuits can be resistors, capacitors, or LQGXFWRUV *HQHUDOO\ ZH DGG HOHPHQWV VXFK DV light bulbs because they are good indicators of FXUUHQW À RZLQJ /LJKW EXOEV ZRXOG EH FODVVL¿ HG as resistors.

Circuits are drawn using diagrams with symbols.

Here are the symbols you will need to be familiar with to interpret and draw your own diagrams.

Battery

Generator Resistor

Switch

Ammeter

Voltmeter

A

V

Common devices have complicated circuits inside them. We can break many circuits down, though, LQWR WZR EDVLF W\SHV VHULHV DQG SDUDOOHO ,Q D series circuit D FXUUHQW FDQ RQO\ ÀRZ DORQJ D VLQJOH SDWK ,Q D parallel circuit, a current FDQ ÀRZ DORQJ WZR RU PRUH SDWKV EHWZHHQ two points.

Lamp

itch

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 ÀRZ WKURXJK HDFK HOHPHQW RQH DIWHU WKH RWKHU LQ a series circuit.

As discussed earlier, electrons transfer 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 that is equal to the total voltage of the battery. However, there will be a voltage drop as electrons move across each element in the FLUFXLW ,Q D VHULHV FLUFXLW WKH VXP RI WKH YROWDJH drops across each element in the circuit equals the total voltage in the circuit. This property is due to the conservation of energy. Essentially, you can summarize it by saying that the total energy that is transferred from the charges that are traveling in the circuit is equal to the voltage drop at each element. © Accelerate Learning Inc. – All Rights Reserved

atter

Light ire

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STEMscopedia R1 and R2, the voltage drop across each resistor is V1 and V2 UHVSHFWLYHO\ DQG WKH VXP VKRXOG WRWDO WKH WRWDO YROWDJH RI WKDW FLUFXLW ,I WKH WRWDO YROWDJH LQ WKH circuit is V V, then you can calculate with the formula below.

V = V1 + V2 + ... :KLOH WKH YROWDJH GURSV DFURVV GLIIHUHQW HOHPHQWV LQ D VHULHV FLUFXLW WKH FXUUHQW ÀRZLQJ WKURXJK HDFK HOHPHQW LV WKH VDPH ,I \RX PHDVXUHG WKH FXUUHQW DW R1 and R2, the current would be the same. ,1

,2

When we think of the resistance of elements in a circuit, we can think of many resistors combining to act like one big resistor. This idea is known as equivalent resistance. The equivalent resistance, Req, of resistors in a series circuit is the sum of the individual resistances.

Req = R1 + R2 The total resistance increases as you connect more resistors in a series.

To solve problems in series circuits, it may be helpful to follow these steps: •

Calculate the equivalent resistance, Req, of the circuit. This is the sum of each resistor in the circuit.

Req = R1 + R2

•

8VH 2KP¶V ODZ WR GHWHUPLQH WKH WRWDO FXUUHQW LQ WKH FLUFXLW 7KH FXUUHQW I, in the circuit is equal to the voltage, V, of the power source divided by the equivalent resistance, Req, of the series resistors. , 9 5eq

•

$SSO\ 2KP¶V ODZ WR HDFK LQGLYLGXDO UHVLVWRU WR GHWHUPLQH WKH YROWDJH GURS DFURVV LW )RU D FLUFXLW with resistors R1 and R2, the voltage drop across each is calculated individually. Remember that , ,1 ,2 and V = V1 + V2.

V1 ,1R1 V2

•

,2R2

Power (W) equals current multiplied by voltage.

3 ,9

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STEMscopedia multiple paths between two points. The two paths are said to be parallel.

Resistor 12

Resistor 6

+

Battery 6V

What is the voltage across a parallel pair of resistors? Conservation of energy tells us that 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 V, is equal to the voltage drop across each resistor, V1 and V2, such that Vtotall = V1 = V2. /RRNLQJ DW WKH FLUFXLW DERYH \RX FDQ GHWHUPLQH WKH IROORZLQJ YROWDJH 9total = 6V, V1 = 6V, and V2 = 6V. Equivalent resistance in parallel circuits is different than in series circuits. For parallel circuits, adding more resistors on more branches will decrease the equivalent resistance of those resistors. To help you XQGHUVWDQG ZK\ LPDJLQH D EXV\ URDG ZLWK MXVW RQH ODQH IRU WUDI¿ F ,I \RX DGG DGGLWLRQDO ODQHV WR WKH road with the same number of cars traveling on it, the road will not seem as busy because cars have a choice of lanes to drive in. The same is true of parallel circuits. The current has several paths it could travel on while still getting to the same destination.

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STEMscopedia the equivalent resistance equals the sum of the reciprocal of each individual resistor in parallel circuits.

The equation is below.

7R VHH WKLV LQ DSSOLFDWLRQ FRQVLGHU DJDLQ D SDUDOOHO FLUFXLW ZLWK WZR UHVLVWRUV ,Q WKLV FDVH WKH UHFLSURFDO of the equivalent resistance equals the sum of the reciprocals of all the resistances. Consider a parallel circuit containing two resistors: R1 ƻ DQG 52 ƻ 7KH YROWDJH SURYLGHG E\ WKH EDWWHU\ LQ WKLV FLUFXLW is 9V.

1RWLFH WKDW WKH WRWDO UHVLVWDQFH IRU WKH FLUFXLW ƻ LV OHVV WKDQ WKH VPDOOHVW UHVLVWRU LQ WKLV SDUDOOHO FLUFXLW ƻ 7KLV LV RQH ZD\ WKDW \RX FDQ FKHFN WKDW \RXU DQVZHU PDNHV VHQVH

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STEMscopedia LV WKDW LQ SDUDOOHO FLUFXLWV D VKRUW FLUFXLW RFFXUV GXH WR UHVLVWDQFH ,I IRU DQ\ UHDVRQ D SDWK RQ D SDUDOOHO circuit has no resistance, all the current will follow that path and the other elements will not receive any current, meaning that they will not work.

5HFDOO WKDW WKH FXUUHQW WKURXJK D VHULHV FLUFXLW LV WKH VDPH WKURXJK DOO UHVLVWRUV ,Q D SDUDOOHO FLUFXLW KRZHYHU WKH FXUUHQW ÀRZLQJ LQWR WKH SDUDOOHO UHVLVWRUV GLYLGHV OLNH D ULYHU UHVXOWLQJ LQ WZR VPDOOHU FXUUHQWV ,Q WKLV FDVH WKH WRWDO FXUUHQW LQ WKH FLUFXLW Itotal FDQ EH IRXQG XVLQJ 2KP¶V ODZ YROWDJH DQG UHVLVWDQFH ,I \RX DUH FDOFXODWLQJ WRWDO FXUUHQW \RX ZLOO XVH HTXLYDOHQW UHVLVWDQFH ,I \RX DUH FDOFXODWLQJ current on one branch of the circuit, you will use the resistance for that individual branch.

Based on what we have calculated so far, Itotal, I1, and I2 for our 9V circuit would be calculated as shown below.

The total current is also equal to the sum of the current through each branch of the circuit.

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STEMscopedia •

Calculate the equivalent resistance, Req, of the circuit using the reciprocal relationship.

•

8VH 2KP¶V ODZ WR GHWHUPLQH WKH WRWDO FXUUHQW LQ WKH FLUFXLW RU WKH FXUUHQW RQ HDFK EUDQFK RI WKH FLUFXLW 7KH FXUUHQW , LQ WKH FLUFXLW LV HTXDO WR WKH YROWDJH 9 RI WKH YROWDJH VRXUFH GLYLGHG E\ WKH equivalent resistance, Req, of the series resistors.

series e r a s 4. How allel circuit ar and p ent from differ ther? o each

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STEMscopedia Magnets, Magnetic Force, and Magnetic Fields A magnet, or magnetized material, is an object with a north pole and a south pole that produces a PDJQHWLF ¿ HOG DV VKRZQ LQ WKH LPDJH EHORZ &HUWDLQ REMHFWV SDUWLFXODUO\ PHWDOV OLNH LURQ WKDW HQWHU WKH PDJQHWLF ¿ HOG DUH DWWUDFWHG WR WKH PDJQHW 0DJQHWV DOVR KDYH DQ LPSRUWDQW FRQQHFWLRQ WR HOHFWULFLW\ Magnetism results from the movement of electrons in a material. Usually, this movement is in the form RI VSLQQLQJ HOHFWURQV $OO HOHFWURQV VSLQ D VSLQQLQJ HOHFWURQ FUHDWHV D WLQ\ PDJQHWLF ¿ HOG ZLWK D QRUWK SROH DQG D VRXWK SROH ,Q QRQPDJQHWL]HG PDWHULDOV WKHVH HOHFWURQV VSLQ LQ GLIIHUHQW GLUHFWLRQV DQG WKHLU ¿ HOGV FDQFHO RXW +RZHYHU LQ PDJQHWL]HG PDWHULDOV DOO RI WKH HOHFWURQV VSLQ LQ WKH VDPH GLUHFWLRQ 7KH PDJQHWLF ¿ HOGV RI HYHU\ WLQ\ HOHFWURQ FRPELQH WR SURGXFH D PDJQHWLF PDWHULDO

-XVW DV DOO FKDUJHG SDUWLFOHV DUH VXUURXQGHG E\ HOHFWULF ¿ HOGV DOO PDJQHWV DUH VXUURXQGHG E\ PDJQHWLF ¿ HOGV 7KH PDJQHWLF ¿ HOG À RZV RXW RI WKH QRUWK SROH RI D PDJQHW DQG LQWR WKH VRXWK SROH 0DJQHWLF ¿ HOGV exert forces on other magnets. As a rule, like poles repel each other and opposite poles attract each RWKHU 0DJQHWLF ¿ HOGV DOVR H[HUW IRUFHV RQ PRYLQJ FKDUJHG SDUWLFOHV DV \RX ZLOO OHDUQ ODWHU $Q\ PDJQHWV WKDW DUH SODFHG LQ D PDJQHWLF ¿ HOG ZLOO DOLJQ ZLWK WKDW ¿ HOG 7KH DUURZV RI WKH PDJQHWLF ¿ HOG OLQHV VKRZ KRZ WKH QRUWK SROH RI D EDU PDJQHW ZRXOG EHFRPH DOLJQHG LI LW ZHUH SODFHG LQ WKDW ¿ HOG $ FRPSDVV LV D W\SLFDO H[DPSOH RI KRZ D PDJQHWLF IRUFH DFWV LQ D PDJQHWLF ¿ HOG (DUWK LV D JLDQW magnet. As Earth spins, the core generates a magnetic north pole and a magnetic south pole. A compass LV PDGH RI D VPDOO EDU PDJQHW 7KH FRPSDVV PDJQHW DOLJQV ZLWK (DUWK¶V PDJQHWLF ¿ HOG 6R WKH VRXWK SROH RI D FRPSDVV SRLQWV WRZDUG (DUWK¶V PDJQHWLF QRUWK SROH

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STEMscopedia and Magnetic Fields 2QH RI WKH PRVW LPSRUWDQW VFLHQWL¿ F GLVFRYHULHV RI WKH ODVW \HDUV ZDV WKH UHDOL]DWLRQ WKDW electricity and magnetism are fundamentally related to one another. This relationship is known as HOHFWURPDJQHWLVP 0RYLQJ HOHFWULF FKDUJHV RU DQ HOHFWULF FXUUHQW SURGXFH D PDJQHWLF ¿ HOG 7KLV PHDQV WKDW DQ HOHFWULF FXUUHQW SURGXFHV ERWK DQ HOHFWULF ¿ HOG DQG D PDJQHWLF ¿ HOG )RU H[DPSOH D PDJQHWLF ¿ HOG ZLOO IRUP DURXQG D VWUDLJKW ZLUH WKDW LV FDUU\LQJ DQ HOHFWULF FXUUHQW

_ Battery + This principle can be used to create an electromagnet. An electromagnet is a temporary magnet that is created by an electric current. An electromagnet typically has a ferromagnetic core, such as iron. A simple electromagnet can be made by wrapping wire around an iron nail, as shown in the image above. :KHQ WKH ZLUH LV FRQQHFWHG WR D YROWDJH VRXUFH D FXUUHQW À RZV WKURXJK WKH ZLUH DQG D PDJQHWLF ¿ HOG LV SURGXFHG 7KLV PDJQHWLF ¿ HOG FDXVHV WKH LURQ QDLO WR EHFRPH DQ HOHFWURPDJQHW 7KH JUHDWHU WKH FXUUHQW WKDW LV À RZLQJ WKURXJK WKH ZLUH WKH VWURQJHU WKH PDJQHWLF ¿ HOG WKDW LV produced. You can also increase the strength of the electromagnet by increasing the number of windings RI ZLUH DURXQG WKH LURQ QDLO ,QFUHDVLQJ WKH OHQJWK RI WKH ZLUH KRZHYHU ZRXOG GHFUHDVH WKH VWUHQJWK RI WKH PDJQHWLF ¿ HOG WKDW LV SURGXFHG 6RPH HOHFWURPDJQHWV DUH VR VWURQJ WKDW WKH\ FDQ OLIW FDUV \RX FDQ observe these electromagnets on cranes in junkyards.

-XVW DV PRYLQJ FKDUJHV SURGXFH PDJQHWLF ¿ HOGV D PRYLQJ PDJQHW SURGXFHV DQ HOHFWULF ¿ HOG ,Q RWKHU ZRUGV D FKDQJLQJ PDJQHWLF ¿ HOG ZLOO SURGXFH DQ HOHFWULF ¿ HOG 7KLV LV NQRZQ DV HOHFWURPDJQHWLF induction because a moving magnet can induce a current in a wire even if no battery or other voltage source exists. The induced voltage in a circuit can be measured with a voltmeter (voltage is measured in volts). The induced current, or amperage, in a circuit can be measured with an ammeter (the current is measured in amperes). As you will learn in the next section, electromagnetic induction plays an important role in the generation of electricity around us.

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STEMscopedia 7KH LQWHUDFWLRQV EHWZHHQ HOHFWULFLW\ DQG PDJQHWLVP DUH DSSOLHG LQ PDQ\ FRPPRQ GHYLFHV 2QH application is a motor. Motors are devices that cause objects to move when electricity is applied. For example, a motor causes the blades of a fan to spin and the wheels of a car to rotate. Motors transform HOHFWULFDO HQHUJ\ LQWR PHFKDQLFDO HQHUJ\ ,Q IDFW PRUH HOHFWULFLW\ LV XVHG E\ PRWRUV WKDQ E\ DQ\ RWKHU technology on Earth.

A basic motor consists of a rotating loop of wire and a magnet. The loop of wire is placed between the SROHV RI D PDJQHW VR WKDW LW LV LQVLGH D PDJQHWLF ¿ HOG 5HFDOO WKDW WKH PDJQHWLF ¿ HOG ZLOO H[HUW D IRUFH RQ PRYLQJ FKDUJHG SDUWLFOHV 6R ZKHQ DQ HOHFWULF FXUUHQW EHJLQV WR À RZ WKURXJK WKH ORRS RI ZLUH WKH PDJQHWLF ¿ HOG H[HUWV D IRUFH RQ WKH ORRS 7KLV PDJQHWLF IRUFH FDXVHV WKH ORRS WR URWDWH ,Q WKLV ZD\ electrical energy is transformed into mechanical energy when the loop begins to rotate. The image below shows an example of this.

While a motor converts electrical energy into mechanical energy, a generator is a device that performs WKH RSSRVLWH WDVN LW WUDQVIRUPV PHFKDQLFDO HQHUJ\ LQWR HOHFWULFDO HQHUJ\ ,Q RWKHU ZRUGV LW JHQHUDWHV electricity from a moving source of energy. /LNH D PRWRU D EDVLF JHQHUDWRU FRQVLVWV RI D ORRS RI ZLUH DQG D PDJQHW +RZHYHU WKH DVVHPEO\ LV different for a generator. This time, the magnet is placed in the center of the loop of wire, and it can URWDWH IUHHO\ $V WKH PDJQHW URWDWHV WKH FKDQJLQJ PDJQHWLF ¿ HOG LQGXFHV DQ HOHFWULF FXUUHQW LQ WKH ORRS of wire. Thus, the rotating mechanical energy of the magnet is transformed into electrical energy. A QXPEHU RI IRUFHV FDQ FDXVH WKH PDJQHW LQ D JHQHUDWRU WR URWDWH ,Q PRVW FDVHV WKH PDJQHW LV DWWDFKHG to a larger, spinning apparatus called a turbine.

Dire t Current DC Motor S

simple DC ele tri motor is used en t e oil is po ered a magneti ield is generated around t e armature e le t side o t e armature is pus ed a a rom t e le t magnet and dra n to ard t e rig t ausing rotation

S

e armature ontinues to rotate

S

en t e armature e omes orizontall aligned t e torque e omes zero t t is point t e ommutator re erses t e dire tion o urrent t roug t e oil re ersing t e magneti ield

S

e pro ess t en repeats

At nuclear power plants, nuclear energy heats water, and the water evaporates into steam. At other power plants, the energy for heating water into steam comes from burning fossil fuels, such as coal or RLO ,Q HDFK FDVH WKH SUHVVXUH IURP WKH VWHDP VSLQV D WXUELQH DQG HOHFWULFLW\ LV SURGXFHG

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STEMscopedia An important application of electromagnetism is a computer hard drive. When a computer stores data to a hard drive, it actually uses the principle of magnetic force. A simple mechanical hard drive, like the one in the image below, is composed of a plate with a thin, ferromagnetic coating. To store data on the plate, a tiny magnet is moved over a region of the plate. The magnetic force of the magnet causes all of the spinning electrons in a tiny region of the plate to become aligned in a particular direction. For example, the electrons may align pointing upward. Then, the tiny magnet moves to another region, causing the electrons in that region to be aligned in another direction. For example, the electrons in the next region may align pointing downward. An electronic signal from the computer tells the magnet how to align the electrons in different regions.

Computers store data in binary code, which is composed of zeros and ones (called bits). So, the upward alignment of electrons in a region may correspond to a one, and the downward alignment of HOHFWURQV PD\ FRUUHVSRQG WR D ]HUR ,Q WKLV ZD\ WKH VHTXHQFH LQ ZKLFK HOHFWURQV DUH DOLJQHG LQ D UHJLRQ corresponds to a binary code of data that can be stored or retrieved by the computer. Computers, mobile phones, and tablets all contain hard drives that store data. However, in many cases, these hard drives are in a solid state, in which there are no moving parts. 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. $Q DXGLR VSHDNHU DOVR UHOLHV RQ WKH LQWHUDFWLRQ EHWZHHQ HOHFWULFDO DQG PDJQHWLF IRUFHV ,Q DQ DXGLR speaker, a coil of wire is attached to a cone-shaped object. This assembly is called a speaker cone. The VSHDNHU FRQH LV VXVSHQGHG IURP D À H[LEOH IUDPH DOORZLQJ LW WR PRYH $ SHUPDQHQW PDJQHW LV VXVSHQGHG at the middle of the cone, next to the coil of wire. When a musical electric signal (alternating current) LV VHQW WR WKH FRLO RI ZLUH LW SURGXFHV D FKDQJLQJ PDJQHWLF ¿ HOG DURXQG WKH FRLO ,Q RWKHU ZRUGV WKH speaker cone becomes an electromagnet! Then, the permanent magnet exerts attractive and repulsive forces on the electromagnet as the musical signal changes. This causes the speaker cone to vibrate according to the signal from the music, producing sound.

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STEMscopedia *HRUJ 2KP ± FDPH IURP KXPEOH EHJLQQLQJV 7KH VRQ RI D ORFNVPLWK KH ZDV ERUQ LQ %DYDULD LQ ZKDW LV QRZ *HUPDQ\ 2KP DWWHQGHG VFKRRO EXW VSHQW PXFK RI KLV WLPH LQ DIWHU VFKRRO DFWLYLWLHV +H ZDV IRUFHG WR GURS RXW E\ KLV IDWKHU DQG À HG WR 6ZLW]HUODQG ZKHUH KH ZRUNHG DV D PDWK WHDFKHU DQG SULYDWH WXWRU (YHQWXDOO\ UHWXUQLQJ WR *HUPDQ\ 2KP UHVXPHG KLV VWXGLHV DW D XQLYHUVLW\ ZKHUH he received a doctorate degree. He accepted a post as a mathematics professor at the University of &RORJQH ZKHUH KH ZDV DEOH WR XVH WKH SK\VLFV ODERUDWRU\ WR VWXG\ HOHFWULFLW\ DQG PDJQHWLVP ,Q 2KP SXEOLVKHG D ERRN FRQWDLQLQJ KLV IDPRXV ODZ 2KP¶V ODZ +LV DSSURDFK WR HOHFWULFLW\ ZDV FRQVLGHUHG unique at the time because he used a mathematical approach to the study of electricity.

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STEMscopedia (OHFWULF FXUUHQW À RZV WKURXJK FLUFXLWV LQ D QXPEHU RI ZD\V ,W FDQ À RZ LQ RQH VLQJOH ORRS FDOOHG D VHULHV FLUFXLW RU LW FDQ À RZ LQ PXOWLSOH ORRSV FDOOHG D SDUDOOHO FLUFXLW &XUUHQW DQG YROWDJH DUH UHODWHG WR HDFK RWKHU WKURXJK 2KP¶V ODZ ZKLFK GHVFULEHV WKH UHODWLRQVKLS EHWZHHQ YROWDJH FXUUHQW DQG UHVLVWDQFH ,W LV only by understanding all of these properties of circuits that we can understand circuits as a whole.

Connect It Circuits are present in our everyday lives and come in one of two categories: series and parallel.

you 5. Can e the riz catego circuits, of r types ries o e s s a either l, that are paralle t in the n prese ound you ar room now? t h g i r

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STEMscopedia 1. What happens to equivalent resistance in a series circuit as you add more resistors?

A. ,W JRHV XS B. ,W JRHV GRZQ C. ,W UHPDLQV WKH VDPH D. None of the above 2. What happens to equivalent resistance in a parallel circuit as you add more resistors?

A. ,W JRHV XS B. ,W JRHV GRZQ C. ,W UHPDLQV WKH VDPH D. None of the above 3. Which of the following would result in a broken circuit?

A. Closed switch B. 2SHQ VZLWFK C. High resistance D. High voltage 4. 'HVFULEH KRZ DOWHULQJ D FXUUHQW FDQ DIIHFW WKH UHVLVWDQFH ¿ HOG $OWHULQJ D FXUUHQW UHVXOWV LQ D FKDQJH LQ WKH RYHUDOO UHVLVWDQFH ,I D FXUUHQW LV LQFUHDVHG WKH UHVLVWDQFH PXVW GHFUHDVH ,I WKH FXUUHQW LV GHFUHDVHG WKH UHVLVWDQFH ZLOO LQFUHDVH 5. Why is equivalent resistance different for series and parallel circuits?

5HVLVWDQFH LPSDFWV WKH À RZ RI WKH FXUUHQW LQ FLUFXLWV $ VHULHV FLUFXLW RQO\ KDV RQH SDWK WKDW WKH FXUUHQW FDQ À RZ WKURXJK WKHUHIRUH PXOWLSOH UHVLVWRUV ZLOO DGG WRJHWKHU WR IRUP WKH HTXLYDOHQW UHVLVWDQFH IRU WKH FLUFXLW ,Q D SDUDOOHO FLUFXLW WKHUH DUH PXOWLSOH SDWKV IRU D FXUUHQW WR À RZ WKURXJK WKLV WUDQVODWHV WR HDFK resistor having a much smaller impact on the equivalent resistance for that circuit.

6. :KDW LV WKH YROWDJH IRU D VHULHV FXUUHQW WKDW KDV UHVLVWRUV RI ƻ DQG ƻ DQG D FXUUHQW RI $" 30 V

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Work and Power

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123

STEMscopedia Work involves using a force to move an object over a distance.

Power is a measure of how much work is done in a certain amount of time.

Both work and power can be calculated using mathematical formulas.

In the picture above, a tractor is attempting to pull a truck out of the mud, but the truck does not seem to be moving.

r tracto e h t the 1. Is k on r o w doing hy or W ? truck ? Would ot why n that the y you sa s powerful r i tracto ation? u t i s s in thi why not? or Why

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STEMscopedia When we think of the word work ZH XVXDOO\ WKLQN RI WKH HYHU\GD\ GH¿ QLWLRQ :H WHQG WR WKLQN RI GRLQJ work in general terms, such as doing a job (like selling cars) or completing a task (such as writing an HVVD\ +RZHYHU WKH VFLHQWL¿ F GH¿ QLWLRQ RI ZRUN LV PXFK PRUH SUHFLVH ,Q VFLHQFH work LV GH¿ QHG as the measure of the energy transfer that occurs when an object is moved over a distance by an external force that is exerted in the direction of the object’s motion. In other words, work means XVLQJ IRUFH WR PRYH DQ REMHFW RYHU D GLVWDQFH 7KH FDU VDOHVSHUVRQ LQ RXU H[DPSOH FRXOG VHOO ¿ YH FDUV in one day and technically do little, if any, real “work” if they did not use a force to move anything.

Now, if the salesperson lifted the hood on any of those cars so that a potential buyer could take a look at the engine, then we can say that work was done because a force was used to move the hood over a distance. You may feel that you worked really hard on an essay for your literature teacher, but VFLHQWL¿ FDOO\ VSHDNLQJ WKH ZRUN ZDV XVLQJ D IRUFH WR PRYH \RXU SHQFLO DFURVV WKH SDSHU DV \RX ZURWH the words. If your pencil had not been sharpened recently and you had to push so hard to make marks on the page that you got writer’s cramp, then your hand was probably tired from the work. Now, if you used the computer to write your essay, you probably did less work because it takes less force to move the keys on your keyboard, and each key does not move very far! ,W LV LPSRUWDQW WR XQGHUVWDQG WKDW WKH VFLHQWL¿ F GH¿ QLWLRQ RI ZRUN GRHV QRW UHTXLUH PRYLQJ DQ entire object from one place to another. For example, work is done when a force is used to compress a stationary spring or rotate a shaft.

A force can sometimes cause motion that we cannot see, such as when magnetic force causes an imperceptible alignment of particles inside a magnetic material.

Alternatively, it is important to remember that, E\ GH¿ QLWLRQ ZRUN LV GRQH RQO\ ZKHQ HQHUJ\ LV transferred to an object. For example, if you pick up your backpack before you go to school, you are doing work because you are using force to move it over a distance. In moving the backpack, you have transferred kinetic energy (the motion of lifting the backpack) to the backpack so that, once lifted, it has potential energy due to gravity. However, if after lifting the backpack you simply stand there holding it, you are no longer doing work because you are no longer transferring energy to it. True, you are exerting a force on the backpack, and if it is full of books, you might be exerting a large force to hold it against the pull of gravity. However, if it does not move, then work is not being done.

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STEMscopedia back and begin walking horizontally, you are not doing work on the backpack. Why? The force you are exerting to keep the backpack on your back is an upward force against the pull of gravity that is perpendicular to the direction that the backpack is moving. In other words, the force you are using to keep the backpack on your back is not the force that is causing it to move over a distance. On the other hand, if you carry your EDFNSDFN XS D À LJKW RI VWDLUV WKHQ ZRUN LV EHLQJ done on the backpack because the backpack is changing position, moving upward, due to the force you are using to move yourself in the same direction.

WLŞ FDOO\ Q H L F 6 g, what in speak nvolved in is i work g a book? readin

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STEMscopedia We can calculate exactly how much work is done if we know how much force is used and how far an object is moved. If we assume that the force that is acting on an object is constant, we can express f and the distance (d) that the object traveled. Thus, the the work (W) as the product of force (f) mathematical formula for work is W = f x d.

When calculating work using the formula W = f x d, the International System of Units (SI) dictates that we use standard metric units for measuring force and distance. Thus, force is measured in newtons (N), distance is measured in meters (m), and the unit for work is the joule (J). ,PDJLQH OLIWLQJ D ER[ RI SDSHU FOLSV DSSUR[LPDWHO\ J ZKLFK LV HTXDO WR 1 D GLVWDQFH RI 1 meter. Using the formula for work, W = f x d ZH ¿ QG WKDW 1 [ P - $V \RX FDQ VHH - RI work is not that much energy! ,PDJLQH WKDW \RXU VLEOLQJ IHOO DVOHHS RQ WKH À RRU DQG \RX ZDQW WR OLIW WKHP LQWR WKHLU EHG RQ WKH WRS EXQN of your bunk bed. If your sibling weighs a little more than 64 lb., it would take 300 N of force to lift them OE 1 ,I WKH GLVWDQFH IURP WKH À RRU WR WKH WRS EXQN LV P KRZ PXFK ZRUN ZRXOG \RX GR" 7R ¿ QG WKH DQVZHU PXOWLSO\ WKH IRUFH 1 E\ WKH GLVWDQFH P DQG WKH UHVXOW LV of work.

ng standi e n i g a 3. Ima ile holding h a still w lock with b w cinder 133 N. Ho of force ou use the d can y = f x W la formu ve that no to pro eing done? is b work

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STEMscopedia 'RHV 0RUH )RUFH 0HDQ 0RUH :RUN" weighing 360 lb. that you need to lift from the ground up to the bed of a pickup truck, which is a distance of 1 m. Converting pounds into newtons OE 1 LW ZRXOG WDNH D IRUFH RI 1 to move the refrigerator. You would probably need a friend to help you lift it! Together, you would do - RI ZRUN - 1 [ P

ork in w e th ulate ation: c l a C 4. situ each f dog o g a 0 lb. b helf that 5 a t s You lif 2 N) to a 22 is food ( ş RRU H K W

I RI with P m e t s sy ulley force p e a h e T s You u ble pulley. t the dog a lif must a mov eeded to u o y n t u s that i ow 111 N, b ope. n r food is ull 6 m of p

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Now, let’s imagine that your friend is not available to help you, so you decide it would be easier to push the refrigerator up a ramp that LV P ORQJ WR JHW LW LQWR \RXU WUXFN EHG %\ pushing the refrigerator up the ramp instead of lifting it straight up, you spread the force over a larger distance, allowing you to use less force.

This is true because when calculating work, force is inversely proportional to distance. That is, iff W = f x d WKHQ : I G ,Q IDFW \RX QHHG half the original force if you spread it out by exerting the force over twice the distance that is actually needed to get the refrigerator from the ground to the bed of the truck. The work would feel easier because you use less force, but you would still be doing the same amount of work as if you lifted the refrigerator straight up. The formula for work proves that this is true. In the ¿ UVW H[DPSOH - RI ZRUN ZDV GRQH WR PRYH the refrigerator. By using the ramp, you cut that force in half but doubled the distance; therefore, \RX XVHG D IRUFH RI 1 EXW \RX PRYHG WKH UHIULJHUDWRU RYHU D GLVWDQFH RI P 7KH ZRUN LV WKH VDPH 1 [ P - This is the principle behind simple machines.

Simple machines spread the force that is needed to move an object over a greater distance, which makes the work feel easier but does not decrease the amount of work that is actually done. In general, we prefer doing work that feels easier (uses less force) even though we are actually exerting the force over a greater distance.

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STEMscopedia We live in an automated world. For much of the work that we need to do, we have machines to do it for us. A food processor uses force to turn a shaft containing blades that chop your vegetables for you. An HOHYDWRU XVHV D V\VWHP RI SXOOH\V WR OLIW \RX WR WKH WRS À RRU RI D VN\VFUDSHU VR WKDW \RX GR QRW KDYH WR take the stairs. Machines are advantageous not only because they do work for us but also because they do the work faster than we could do it. When we discuss how much time is involved in doing work, we are discussing the concept of power. ,Q RXU HYHU\GD\ XQGHUVWDQGLQJ RI SRZHU ZH WHQG WR HTXDWH LW ZLWK VWUHQJWK :H PLJKW GHVFULEH D volleyball player as having a powerful serve if they are able to hit the ball with enough force that it LV GLI¿ FXOW IRU WKH RSSRVLQJ WHDP WR UHWXUQ LW %XW IRUFH DORQH GRHV QRW GHVFULEH SRZHU 6FLHQWL¿ FDOO\ speaking, power is the amount of energy that is transferred or converted per unit of time. In other ZRUGV SRZHU LV D PHDVXUH RI KRZ TXLFNO\ ZRUN LV GRQH

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STEMscopedia How Is Power Calculated? amount of work by the time it took to do the work. The formula for power is SRZHU 3 ZRUN : WLPH W RU P = W/t.

Because we know that the formula for work is W = f x d, we can also express the formula for power as P = f x d/t.

Using the International System of Units, if we measure work in joules and time in seconds, then the unit for power is the watt (W).

What makes one machine more powerful than another? If two machines do the same amount of work, but the second machine can do the work faster, then the second machine is more powerful WKDQ WKH ¿ UVW &RQVLGHU WKH IROORZLQJ H[DPSOH 8VLQJ D VLQJOH ¿ [HG SXOOH\ \RX FRXOG OLIW D ORDG RI 1 XS WR D GLVWDQFH RI P 0RYLQJ WKH ORDG ZRXOG UHVXOW LQ - RI ZRUN 1 [ P %HFDXVH 1 RI IRUFH LV IDLUO\ GLI¿ FXOW WR OLIW LW PLJKW WDNH VHFRQGV WR PRYH WKH ORDG 8VLQJ P = W/tt - V ZH ¿ QG WKDW WKH WDVN ZDV DFFRPSOLVKHG ZLWK : RI SRZHU Now, suppose that you attach a second, PRYHDEOH SXOOH\ WR \RXU 1 ORDG $ PRYDEOH pulley, like other simple machines, allows you to use less force but spreads it out over a greater distance. In fact, a movable pulley will cut the IRUFH LQ KDOI EXW UHTXLUH WKDW \RX SXOO IRU WZLFH the distance. You would still do 1,000 J of work 1 [ P EXW EHFDXVH LW XVHV OHVV IRUFH you could probably lift the load in less time, SHUKDSV VHFRQGV &DOFXODWLQJ SRZHU 3 - V ZH ¿ QG WKDW WKH VHFRQG situation resulted in 66.7 W. Using the movable pulley made the work feel easier, and because it IHOW HDVLHU WKH ZRUN FRXOG EH GRQH PRUH TXLFNO\ resulting in more power.

Likewise, if two machines work for the same amount of time, but one machine does more work, then it is the more powerful machine. For example, imagine that you have two battery-operated cars WKDW DUH LGHQWLFDO LQ HYHU\ ZD\ H[FHSW WKDW WKH EDWWHU\ LQ WKH ¿ UVW RQH LV RQO\ RSHUDWLQJ DW RI LWV capability. If you set both cars in motion and time them for 30 seconds, the car with a fully charged battery would probably travel the greater distance. Because the cars are identical, we know that the IRUFH WKDW LV UHTXLUHG WR PRYH WKHP LV WKH VDPH IRU HDFK EXW EHFDXVH WKH VHFRQG FDU PRYHV D JUHDWHU GLVWDQFH PRUH ZRUN ZDV GRQH %HFDXVH LW GLG PRUH ZRUN LQ WKH VDPH DPRXQW RI WLPH DV WKH ¿ UVW FDU we know that it is more powerful. This makes sense because there was more power available in the fully charged battery.

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STEMscopedia using P= f x d/t. You might remember that distance divided by time (d/t) is the formula for velocity.

7KHUHIRUH ZH FDQ VD\ WKDW SRZHU LV WKH SURGXFW RI IRUFH PXOWLSOLHG E\ YHORFLW\ 8VLQJ WKLV GH¿ QLWLRQ RI power, we can express that a powerful machine is strong and fast. Modern cars have stronger engines than the old Model A’s, which means that they can travel faster. Modern cars are more powerful than their ancestors because they are both stronger and faster.

Horsepower 1 hp = 550 ft.-lb. f/s

t = 1 second

1 foot

When describing powerful machines, we describe their power using the term “horsepower” (hp). One KRUVHSRZHU LV WKH HTXLYDOHQW RI OLIWLQJ D OE ZHLJKW 1 D GLVWDQFH RI IW P LQ VHFRQG 2QH KRUVHSRZHU LV HTXDO WR : $ W\SLFDO FDU KDV D KS HQJLQH $ VWDQGDUG VSRUWV XWLOLW\ YHKLFOH XVHV D KS HQJLQH ZKLOH D VPDOOHU FRPSDFW FDU PLJKW EH SRZHUHG E\ D KS HQJLQH

e is mor e t e l h ch at lculate the i h W 5. ul? Ca each: f r e w po for . power 300 lb e s e i r A car r a distanc e t e l h At hill fo s them p u ) N e (1,334 0 m. It tak . of 10 0 seconds 6 50 lb.

3 s e i e r B car r a distanc e t e l fo Ath uphill es them ) N (1,557 0 m. It tak . of 10 0 seconds 7

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STEMscopedia Scientists in the Spotlight: Leonardo da Vinci whose painting the Mona Lisa is one of the most well-known pieces of art in the world. But da Vinci’s genius went well beyond painting.

Besides being considered a master artist, da Vinci was an amateur scientist and mathematician who did pioneering work in the ¿ HOGV RI ERWDQ\ DQDWRP\ ]RRORJ\ JHRORJ\ geometry, pyrotechnics, optics, hydrodynamics, and mechanical engineering. His boundless imagination, coupled with his fascination with the world around him, led him to design all sorts of theoretical inventions that, when viewed today, demonstrate the depth of his intuitive understanding of physical principles that would not be articulated until centuries later. Most of his designs were sketched in the margins of the notebooks in which he took copious notes describing and analyzing the phenomena he observed in the natural world.

Among his sketches is a design for something that we recognize today as a helicopter. He called it the aerial screw, and it used the power of four people rapidly turning cranks to create the force that is needed to lift it off the ground. Another invention resembles a prototype for the modern tank. Shaped like a turtle shell and made of wood and metal plates, it was powered by four strong people who turned two internal cranks.

Da Vinci was particularly fascinated with K\GUDXOLFV RU WKH VFLHQFH RI PRYLQJ OLTXLGV through pipes or channels as a source of mechanical force. Among his many sketches was one for a hydraulic saw. He imagined a movable cart with a vertical blade that, when connected to a water wheel, would move up and down to cut a log. The machine he envisioned was similar to the bandsaw that we use today, but of course, today’s saw uses electric power to do the work.

Like most of da Vinci’s ideas, the hydraulic saw was never actually invented, but it did demonstrate that he understood the relationship between work and power and the need for machines that could do more work in less time than doing the work by hand.

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or and Po er

STEMscopedia :RUN LV GH¿ QHG DV WKH PHDVXUH RI WKH HQHUJ\ WUDQVIHU WKDW RFFXUV ZKHQ DQ REMHFW LV PRYHG RYHU D distance by an external force that is exerted in the direction of the object’s motion. The formula for work is W = f x d. When force is measured in newtons (N) and distance is measured in meters (m), the unit for work is the joule (J). Simply exerting force on an object does not mean that work has been done.

The object must move over a distance.

Power is the amount of energy that is transferred or converted per unit of time. In other words, power LV D PHDVXUH RI KRZ TXLFNO\ ZRUN LV GRQH 7KH IRUPXOD IRU FDOFXODWLQJ SRZHU LV P = W/t. When work is measured in joules (J) and time is measured in seconds (s), the unit for power is the watt (W). Machines WKDW XVH D ORW RI IRUFH WR GR ZRUN TXLFNO\ DUH FRQVLGHUHG SRZHUIXO PDFKLQHV

Connect It What is the relationship between work and power?

The image shows a tractor trying to pull a truck out of the mud, but the truck does not seem to be moving.

uck is r t e h 6. If t g, is work ovin not m done? How being ow? What kn d do you be change should the truck l t o p u l cessfully? c out su

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STEMscopedia 1. ,I D 1 IRUFH LV XVHG WR PRYH DQ REMHFW P KRZ PXFK ZRUN LV SHUIRUPHG" A. 3,000 J B. C. D. 2. If you push against a wall with 400 N of force for 10 seconds, but the wall does not move, how much work is done?

A. 4,000 J B. C. 40 J D. 0 J 3. What is the standard unit for power?

A. Watt B. Newton C. Joule D. Horsepower 4. ,I D SHUVRQ LV XVLQJ 1 RI IRUFH WR KROG D JDOORQ RI ZDWHU P RII WKH À RRU LV ZRUN EHLQJ GRQH" Why or why not?

No work is being done because the jug is not moving.

5. &DOFXODWH WKH SRZHU LQ WKH IROORZLQJ VLWXDWLRQ $ SXOOH\ V\VWHP XVHV 1 WR OLIW DQ REMHFW P LQ VHFRQGV 400 watts 6. $ W\SLFDO EOHQGHU FDQ GR - RI ZRUN LQ VHFRQGV 7KH W\SLFDO RXWSXW RI D IRRG SURFHVVRU LV 1,000 W. How much more powerful is a food processor than a blender?

7KH IRRG SURFHVVRU LV : PRUH SRZHUIXO WKDQ WKH EOHQGHU

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Impulse and Momentum

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137

STEMscopedia You hear a screech of tires and the crash of a collision.

Two cars have just gotten into a head-on collision.

But neither driver was hurt. How is this possible?

How can physics help us better understand how some car wrecks injure passengers and drivers while other wrecks are completely survivable and everyone walks away without a scratch? The answer lies with momentum.

that a y a s 1. We car has moving um. But t momen omentum? is m what does t a h W cribe? it des

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Impulse and Momentum

STEMscopedia Have you ever heard someone discuss the momentum of a team or maybe the momentum of a program? For example, “The space program gained momentum in the late 1960s . . . ” or, “The football team had momentum going into the last quarter.” In this case, the program or the team is moving forward and making progress. The more momentum there is, the harder it will be to stop progress. This applies to objects as well. An object with great momentum will take more effort to stop; why is that?

Momentum is a quantity that is based on both size and direction. Momentum is a measure of motion WKDW LV GH¿ QHG DV WKH PDVV NJ PXOWLSOLHG E\ WKH YHORFLW\ P V RI DQ REMHFW 0RPHQWXP LV DEEUHYLDWHG ZLWK D ORZHUFDVH OHWWHU S DQG LV PHDVXUHG LQ NJ P V Momentum = mass x velocity p = mv This equation shows that momentum is directly proportional to both the mass of an object and the velocity of an object. The mass and velocity of the object are inversely proportional to each other.

This equation also shows us that if an object is at rest, or velocity equals zero, the object will have no momentum regardless of its size.

Impulse and Momentum

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STEMscopedia The law of conservation of momentum states that if objects collide, the total momentum before the collision must equal the total momentum after the collision. Total momentum refers to the momentum of all the objects involved in the collision. When a tennis racket strikes a tennis ball, an impulse is applied to the ball. The racket puts a force on the ball for a short time period. By the way, according to Newton’s third law of motion, every action has an equal and opposite reaction. So, the ball also puts a force on the racket, and the racket therefore has an impulse applied to it. The key fact is that the share of the momentum between the objects that are involved in a collision may change, but the total value always remains the same. It is important to note that this is only true if there are no other external forces, such as friction, acting on the system. This law also only applies to the momentum values of closed systems.

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Impulse and Momentum

STEMscopedia Within a closed system, the total momentum of the closed system before a collision equals the total PRPHQWXP DIWHU WKH FROOLVLRQ 7DNH D FDU FUDVK EHWZHHQ WZR FDUV IRU H[DPSOH 7KH ¿ UVW FDU PD\ KDYH OHVV PRPHQWXP DIWHU WKH FROOLVLRQ EXW WKH DPRXQW RI PRPHQWXP WKDW WKH ¿ UVW FDU ORVHV ZLOO EH WKH same as the amount of momentum that the second car gains. Each car had a different velocity and WKHUHIRUH GLIIHUHQW PRPHQWXP ERWK EHIRUH DQG DIWHU WKH FROOLVLRQ %XW WKH RYHUDOO WRWDO PRPHQWXP RI the system did not change, so the difference in momentum equals zero and therefore remains constant.

This is because forces act in pairs. Newton’s third law of motion states that for every action, there is an opposite and equal reaction. From the point of view of momentum conservation, there are two types of collisions.

Elastic collisions are collisions in which both momentum and kinetic energy are conserved.

The system’s total kinetic energy before the collision equals the system’s total kinetic energy after the collision. These types of collisions may be characterized by several factors, including large changes in momentum and impulse caused by large forces. Elastic collisions occur when particles rebound against each other with the same kinetic energy and momentum that they had before the collision. If objects bounce off each other, the collision is considered elastic.

lasti Collisions o De ormation ot Momentum and ineti nerg re Conser ed

e t n s cradle s heres trans erring energ

illiard alls c lliding na l ta le

Elastic collisions are not limited to microscopic objects, such as atoms and molecules. Elastic collisions can occur with larger objects. One such example is billiard balls. As a moving billiard ball collides with a resting billiard ball, the moving ball will come to a VWRS DQG WKH UHVWLQJ EDOO ZLOO PRYH DZD\ IURP WKH ¿ UVW EDOO DW D YHORFLW\ WKDW LV HTXDO WR WKH LQLWLDO YHORFLW\ RI WKH ¿ UVW EDOO ,Q RWKHU ZRUGV WKH PRPHQWXP IURP WKH ¿ UVW EDOO LV WUDQVIHUUHG WR WKH VHFRQG EDOO $ collision is said to be perfectly elastic if the total kinetic energy at the end of the collision is exactly the same as the total kinetic energy at the start of the collision. Elastic collisions also occur during collisions EHWZHHQ REMHFWV ZKHQ QR KHDW LV JHQHUDWHG QR WKHUPDO HQHUJ\ LV WUDQVIHUUHG RU ZKHQ QHLWKHU REMHFW LV permanently distorted.

Impulse and Momentum

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STEMscopedia the impact is considered to be an inelastic collision. Inelastic collisions are encounters between objects in which some of the kinetic energy is converted into other forms of energy, such as sound, light, or heat. In the image, two cars collide and one car appears much more damaged than the other; this is an example of an inelastic collision.

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Impulse and Momentum

STEMscopedia is an energy conversion in which heat is produced by the friction between the objects that are involved in a collision. Recall that heat is the transfer of thermal energy between two objects.

Reshaping is a form of conversion in which one or more of the objects involved in a collision are permanently altered from their original shape, especially if those objects become stuck together.

Sound and light energy are forms of conversion LQ ZKLFK VRXQG RU OLJKW HOHFWURPDJQHWLF ZDYHV are produced during the collision.

A car crashing against a tree is an example of an inelastic collision as the kinetic energy is not conserved. The energy from the car is transferred into sound energy when the car stops. Another example of this type of collision would be a bullet that is shot into a piece of wood. The energy from the bullet is transferred in the form of thermal energy.

e hat ar of W .

2 typ es o w t w the nd ho t a , s n n collisio iffere d y e h are t ach other? e from

Impulse and Momentum

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STEMscopedia Force is a very important variable, but time is just as important. There are situations in which it is necessary to know how long the force acts on an object. For example, if you push a stack of books DFURVV WKH À RRU IRU MXVW D IHZ VHFRQGV WKH DPRXQW RI WLPH LV YHU\ VKRUW +RZHYHU LI \RX SXVK WKH VDPH VWDFN DFURVV WKH À RRU ZLWK WKH VDPH IRUFH DV EHIRUH EXW IRU VHYHUDO PLQXWHV \RX¶YH LQFUHDVHG WKH amount of time the force acts. This is called impulse, or a force acting on an object for a given amount of time. Impulse can be calculated using the force applied to the object multiplied by the amount of time WKDW WKH IRUFH LV DSSOLHG ,PSXOVH LV UHSUHVHQWHG DV - DQG PHDVXUHG LQ 1HZWRQ VHFRQGV 1 [ V Impulse = force x time J = Ft Impulse is actually seen in everyday phenomena.

There are several examples in sports. When a baseball bat hits a ball, the amount of time the bat is in contact with the ball is an example of impulse. For instance, if a ball is hit with the top edge of the bat, the amount of time the ball and bat are in contact is shorter than if the ball is hit with the middle of the bat. The result impacts the change in momentum of the baseball and could be the difference between a foul ball and a home run. What about kicking a soccer ball? Would a kick with the tip of the toe or the inside arch of the foot provide greater impulse? The inside arch of the foot allows for more time in contact with the ball and therefore greater impulse.

You have probably experienced impulse in a car. A car traveling at a certain velocity is coming upon WUDI¿ F ,Q VFHQDULR $ WKH EUDNHV DUH DSSOLHG OLJKWO\ DQG VORZO\ RYHU D ORQJ GLVWDQFH DQG LQ VFHQDULR % the brakes are applied hard and quickly over a very short distance. In both scenarios, the car slows down to the desired speed, but what would be different for the passengers in the two scenarios? With scenario A, the passengers would most likely notice very little change as the car is slowing down; however, in scenario B, the passengers probably felt a quick jolt and may have moved a little as the momentum of the car changed quickly.

e e som r a t a 3. Wh xamples of e other at work in e impuls ly life? dai

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Impulse and Momentum

STEMscopedia the impulse and momentum. Impulse and momentum are also impacted when a force acts in the same direction as the object’s motion, such as pushing the gas pedal to accelerate a car that is already moving. In both events, a force changes the velocity of an object. When the velocity of the object is changed, the momentum of the object changes.

1HZWRQ¶V VHFRQG ODZ RI PRWLRQ VWDWHV WKDW D IRUFH ) HTXDOV WKH SURGXFW RI WKH PDVV RI DQ REMHFW DQG the acceleration of the object.

F = ma The acceleration of an object can be calculated using the change in velocity divided by the change in time.

D ƩY ƩW If the formula for acceleration is substituted in Newton’s second law of motion formula, it looks like this. ) PƩY ƩW If the change in time is multiplied on both sides of the equation, the formula becomes this. )ƩW PƩY In other words, because impulse is calculated as force multiplied by change in time, and change in momentum is calculated as mass multiplied by change in velocity, the equation shows that impulse equals a change in momentum.

Impulse = change in momentum Application of this is important for many aspects of science. It is important to understand that an object’s change in momentum is based on mass and change in velocity. Because an object’s mass generally will not change, the change in velocity determines the change in impulse. When you know those two variables, you are able to determine how time and force can be manipulated in the equation.

It is easier to see this in an example.

Impulse and Momentum

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STEMscopedia WKH SHUVRQ LW ERXQFHV EDFN ZLWK D YHORFLW\ RI P V %DVHG RQ D WLPH ODSVH YLGHR LW LV GHWHUPLQHG that the ball was in contact with the person for 0.02 s. Using this information, determine the change in momentum, impulse, and force exerted when the dodgeball made contact with the person’s leg.

Change in momentum = mass x change in velocity ƩS PƩY ƩS NJ

P V P V

ƩS NJ P V 1V Impulse = change in momentum ,PSXOVH 1V Because we calculated the change in momentum and impulse, we can now calculate the force.

Impulse = force x change in time 1V ) V ) 1 To demonstrate how protective equipment in sports helps, the same scenario is used except the person is wearing protective padding. The time-lapse video shows that this time, the ball was in contact with the person for 0.05 s. How does the padding impact this scenario?

Impulse = force x change in time 1V ) V ) 1 $V \RX FDQ VHH ZLWK WKH FDOFXODWLRQ DERYH WKH LPSXOVH VWD\V WKH VDPH DV LQ WKH ¿ UVW VFHQDULR EHFDXVH the mass and change in velocity did not change. The padding allowed for more time for the dodgeball to stay in contact with the person, changing the time; therefore, the force was reduced. This concept is one that engineers use when designing protective equipment.

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Impulse and Momentum

STEMscopedia When a car gets into an accident or when a shipping box is dropped, the objects inside the car or box go from an initial velocity to a different velocity, meaning that there is a change in momentum. In most cases of accidents or drops, the objects involved need to come to rest in such a way as to reduce damage to those objects. One way to do this is to increase the time it takes for those objects to come to rest from their initial velocity. Remember, the longer it takes for momentum to change, the smaller the force that is applied to those objects. It is known that less force causes less damage. Whenever we want to minimize the force, we extend the time. For example, if the time is extended 100 times, the force of impact is reduced 100 times. This has allowed for the development of many different features to reduce damage during collisions, such as padded equipment and helmets in sports, airbags in vehicles, and arrestor beds for semi trucks.

Safety Features in Vehicles During a car crash, everything inside the car, including the passengers, goes through a rapid change in momentum. For example, the passengers in the car that is hitting another car will go through rapid deceleration. The passengers in the car that is being hit may go through rapid acceleration. Either way, the passengers in both cars will be subjected to great force during the change in momentum, and these forces can cause tremendous injury. One way to reduce these forces is by increasing the time it takes for the change in momentum to occur. Some of the most effective ways to increase this time include the use of seat belts, airbags, and crumple zones in the car.

Padded dashboard

Crumple zone

Airbags

Impulse and Momentum

Seat belts

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STEMscopedia body to change from an initial velocity to zero. In this way, seat belts decrease the forces placed on the body during collisions. They also prevent the passenger from moving around inside the car.

Airbags also increase the time it takes for the passenger’s body to change from an initial velocity to zero.

During a car accident, the driver is propelled forward by incredible force, causing the forward velocity of the passenger to increase rapidly. If there were no airbag on the steering wheel of the car, the forward velocity of the passenger would be stopped suddenly by either the steering wheel or the windshield.

This sudden stop would create a huge force over a very short time period. Airbags greatly increase the time it takes for impact, which in turn greatly decreases the force that is felt by the passenger. Airbags also prevent secondary injuries, such as abrasions, as well as cushion the head and upper body of the passenger.

Crumple zones are exterior areas of the car that absorb impact. The greater the amount of time it takes for the car exterior to crumple, the less force is exerted on the occupants. This is why crumple zones work. Because it is the force of the collision that harms passengers, anything that can be done to extend the time of impact will reduce this force. For example, if cars bounced off each other, or rebounded in an elastic collision, there would be a greater change in momentum and therefore a larger impulse. Larger impulses mean greater force. Luckily, most cars are designed to crumple, which means that the change in momentum is reduced, and this greatly reduces impulse.

Padded dashboards are another safety feature that increases the time to impact and thereby reduces force. Dashboards that are made from soft materials and have some type of cushioning may be found in many modern cars. These dashboards are much safer than the older models’ rigid metal or wooden dashboards.

Impact attenuators include setups such as rows of barrels that are full of water or emergency pull-off ramps that are softer than the road. If a runaway truck hits these setups, the amount of time that it WDNHV IRU WKH FKDQJH LQ PRPHQWXP FROOLVLRQ WLPH LV LQFUHDVHG WKHUHE\ GHFUHDVLQJ WKH IRUFH RQ WKH truck. This decrease allows the truck to slow down.

e the r a t a h 4. W eatures in f safety and how do , a car rease the inc they f impact? time o

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Impulse and Momentum

STEMscopedia Padding extends collision time, which impacts impulse. The extra thickness of gymnastic mats extends the time of momentum change and impacts impulse. In some sports, such as football, players use padded helmets and shoulder pads. In other sports, players have padded gloves, shin guards, and batting helmets. The padding in these types of equipment is compressible, which reduces the force experienced from collision with a fast-moving object or person. This is why skydivers land on bent knees. By bending their knees, less impact force results as bent knees provide a longer time to change the person’s momentum.

Follow-through motion extends collision time, which reduces force. In most racket or bat sports, the athlete is trained to “follow through” when making contact with the ball. This follow through increases the time over which the collision between the racket or bat and ball occurs. This increased time on the impulse side of the equation has an effect on the velocity of the ball, which changes the momentum.

This is true, as the mass of the ball or racket does not change. In other words, follow through causes the ball to rebound from the racket or bat faster than if there were no follow through. This is important in many sports that use rackets and bats, as increased velocity of the ball is advantageous.

Netting absorbs forces by extending collision time. Nets are used in tennis, volleyball, and acrobatics, for example.

e e som r a t a h 5. W examples other pulse of im ntum ome and m letics? in ath

Impulse and Momentum

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STEMscopedia 2Q (DUWK \RX PRYH DURXQG E\ SXVKLQJ DJDLQVW WKH À RRU RU JURXQG %XW D URFNHW LQ WKH YDFXXP RI VSDFH KDV QRWKLQJ WR SXVK DJDLQVW ,I \RX ZHUH WR WKURZ D EDVHEDOO LQ VSDFH \RX ZRXOG ¿ QG WKDW DV \RX SXVKHG the ball forward, you would be propelled backward. This is due to the conservation of momentum.

Momentum that is applied to an object going one direction is canceled out by momentum that is reactively applied in the opposite direction.

Rockets utilize conservation of momentum in their engines. They push matter out the back of the engine at high speeds. The rocket’s exhaust has low mass compared to the rest of the rocket but high velocity. This translates to a low velocity for the higher-mass rocket in the opposite direction from the rocket exhaust!

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Impulse and Momentum

STEMscopedia 3HWHU )ORUMDQÏLÏ DQG <DVX]DEXURX .RERUL $Q LQYHQWRU LGHQWL¿ HV D SUREOHP DQG WULHV WR ¿ JXUH RXW KRZ WR ¿ [ LW E\ XQGHUVWDQGLQJ WKH VFLHQFH DQG designing new technology. Two of the inventors of the automobile airbag came from very different EDFNJURXQGV \HW DUULYHG DW VLPLODU LGHDV LQ WKH VDPH GHFDGH 3HWHU )ORUMDQþLþ ZDV ERUQ LQWR D ZHDOWK\ family in what is now Slovenia in 1919 and succeeded at many things early in his life. He was on the Olympic ski jumping team when he was only 16, made a harrowing escape from the Nazi police to avoid ¿ JKWLQJ LQ :RUOG :DU ,, DQG VXFFHVVIXOO\ VROG WKH SDWHQWV IRU VHYHUDO HDUO\ LQYHQWLRQV LQFOXGLQJ D SXUVH sized perfume pump, plastic ice skates, and an industrial plastic injection pump. However, his design and prototype for the automobile airbag was not so successful as it kept exploding, and he moved on to other ideas only to see his idea become standard in nearly every vehicle on the road before his death in 2020.

The other inventor was Yasuzaburou Kobori. Born into a family without privilege in Japan in 1899, Kobori had to go to work after elementary school, but he worked hard to learn from his experiences and worked up to a position developing cutting-edge machinery for coal mining. After many years, Kobori left the coal industry and started his own “Good Ideas Center” for inventing. Along with an automatic sandwich-making machine, he designed a car airbag system that extended not only to occupants but DOVR WR SHGHVWULDQV ,I WKH EXPSHU FRQWDFWHG D SHGHVWULDQ SROH VKDSHG DLUEDJV ZRXOG LQÀ DWH ZLWK D net to prevent them from falling onto the hood or under the car. Unfortunately, the airbags were never GHYHORSHG LQ -DSDQ EHFDXVH WKH XVH RI JXQSRZGHU LQ WKH LQÀ DWLRQ GHYLFH YLRODWHG WKH -DSDQHVH )LUH Service Act at that time. Kobori was awarded patents for his design all over the world, but he died in 1975 before the system was widely used.

Impulse and Momentum

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STEMscopedia $V \RX FDQ VHH PRPHQWXP KDV D YHU\ LPSRUWDQW UROH LQ WKH ¿ HOG RI VFLHQFH VSHFL¿ FDOO\ LQ SK\VLFV Many people do not know the importance of it in everyday life or even recognize it. The truth is that we use momentum in just about every activity that involves motion, from driving a car to participating in various sports or activities. We must remember that momentum is observed when there is any interaction between two objects occurring in an isolated system.

Connect It Now, how could it happen?

The graphic below shows two different collisions right before they happen.

oth of b e s u ollisions c e s the he law t e v o to pr servation of con entum? of mom

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Impulse and Momentum

STEMscopedia 6XPPDUL]H ,W 'HWHUPLQH WKH PRPHQWXP RI D NJ FDU PRYLQJ QRUWKZDUG DW P V $ NJ P V % NJ P V & NJ P V ' NJ P V Which variable is momentum not dependent upon? $ Mass % Velocity & Force ' None of the above Which is not an example of an elastic collision? $ A game of billiards % A tennis match & A game of darts ' A bowling match Explain how kinetic energy is conserved in an elastic collision but not in an inelastic collision.

Inelastic collisions change some of the kinetic energy that is present into other forms of energy or use it to do work on the other object involved in the collision. Elastic collisions do not use kinetic energy and maintain the total amount during the collision.

Explain whether a tennis ball that is dropped from a high distance experiences an elastic collision or inelastic collision.

Because the tennis ball would not return to the original drop height, some of the kinetic energy that was present during the collision must be transferred away from the tennis ball. This means that this collision must be inelastic.

Which has greater momentum, a train at rest or a moving skateboard? Explain.

7KH PRYLQJ VNDWHERDUG KDV JUHDWHU PRPHQWXP EHFDXVH WKH WUDLQ DOWKRXJK LW KDV D ODUJH PDVV LV DW rest and therefore has no momentum.

Impulse and Momentum

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Conservation of Energy

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155

STEMscopedia You just built a toy-brick space station or a toy-brick house made of more than 500 pieces. After a couple of weeks, some friends come over; one accidentally knocks the toy-brick sculpture off its display area, and it explodes into parts. Unfortunately, you threw away the instructions that allow you WR UHEXLOG WKH VWUXFWXUH 1RZ \RX KDYH D ¿ QLWH QXPEHU RI WR\ EULFNV WR EXLOG VRPHWKLQJ QHZ ZLWK +RZHYHU \RX FDQ¶W EX\ DQ\ PRUH 7KRXJK WKH RULJLQDO VWUXFWXUH LV GHVWUR\HG LW FDQ EH WUDQVIRUPHG LQWR VRPHWKLQJ QHZ

1. How is t same his the amoun as the t or en of matter er world gy in the and is utili how it zed?

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STEMscopedia Energy is the ability to do work, and it comes in two main forms, kinetic and potential. Kinetic HQHUJ\ LV WKH HQHUJ\ RI PRWLRQ OLNH ZKDW ZRXOG be found in objects, electrons, atoms, waves, and VXEVWDQFHV 3RWHQWLDO HQHUJ\ LV VWRUHG HQHUJ\ one example of which is gravitational energy, ZKLFK LV VWRUHG LQ DQ REMHFW¶V SRVLWLRQ LQ D JUDYLW\ ¿ HOG OLNH (DUWK¶V (QHUJ\ FDQ EH WUDQVIRUPHG IURP RQH IRUP RI HQHUJ\ WR DQRWKHU $ EDOO VWRSSHG DW WKH WRS RI D UDPS KDV SRWHQWLDO HQHUJ\ :KHQ WKH EDOO LV UHOHDVHG WKDW SRWHQWLDO HQHUJ\ LV WUDQVIRUPHG LQWR NLQHWLF HQHUJ\ DV WKH EDOO VWDUWV PRYLQJ

Potential Energy (stored energy)

Kinetic Energy (moving energy)

The pitcher winds up, ready to throw the ball.

The pitcher throws a fastball toward home plate.

some e r a t ha 2. W examples other ntial and e of pot energy? kinetic

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STEMscopedia :KHQ D UROOHU FRDVWHU LV SXOOHG XS WKH ¿ UVW KLOO WKH GHVLJQHUV PDNH LW KLJK WR WDNH DGYDQWDJH RI SRWHQWLDO HQHUJ\ DW WKH WRS RI WKH KLOO 1RWLFH WKDW WKH RWKHU KLOOV DUH DOO VKRUWHU WKDQ WKH ¿ UVW KLOO :KHUH GRHV DOO WKDW SRWHQWLDO HQHUJ\ JR" ,W LV WUDQVIRUPHG LQWR NLQHWLF HQHUJ\ DQG KHDW IURP friction 1RQH RI WKH HQHUJ\ LV ORVW ,W PHUHO\ FKDQJHV IRUP LQ DQ energy transformation.

7KH ¿ UVW ODZ RI WKHUPRG\QDPLFV LV WKH law of conservation of energy. This law states that HQHUJ\ FDQQRW EH FUHDWHG RU GHVWUR\HG LW FDQ RQO\ FKDQJH IRUP 7KLV PHDQV WKDW WKH DPRXQW RI HQHUJ\ WKH XQLYHUVH VWDUWHG ZLWK LV WKH DPRXQW RI HQHUJ\ LW ZLOO HQG ZLWK (QHUJ\ WUDQVIRUPDWLRQV WDNH SODFH DOO DURXQG us. Someone uses mechanical energy to À LS RQ D OLJKW VZLWFK WKDW FORVHV D FLUFXLW DQG allows electricity WR À RZ WKURXJK D ZLUH WKDW LV FRQQHFWHG WR D OLJKW EXOE DQG WKH ZLUH LQ WKH EXOE JORZV $ FKLOG SXOOV EDFN D VOLQJVKRW ZLWK D URFN LQ LW XVLQJ NLQHWLF HQHUJ\ DQG WKHQ UHOHDVHV WKH UXEEHU EDQG¶V VWRUHG SRWHQWLDO HQHUJ\ ZKHQ WKH VOLQJVKRW LV OHW JR WR VKRRW WKH URFN 6RPHRQH HDWV DQ DSSOH ¿ OOHG ZLWK chemical energy VWRUHG DV VXJDU DQG WKHQ JRHV RXW IRU D UXQ $OO RI WKHVH DUH H[DPSOHV RI HQHUJ\ EHLQJ transformed from one form to another, and heat is lost in every transformation.

3. Wh y import is it under ant to st HQHUJ and that \ when LV Ş QLWH pow electr onics ering and c ars?

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STEMscopedia ,I WKHUH LV QR LQWHUDFWLRQ RI WKH PDVV DQG HQHUJ\ RI WKH V\VWHP ZLWK LWV VXUURXQGLQJV WKHQ WKH system is closed ,I WKH V\VWHP LV RSHQ WR LWV VXUURXQGLQJV DQG H[FKDQJHV HQHUJ\ DQG PDVV with them, then the system is open ,Q WKH UROOHU coaster example, this is an open system. There LV DLU UHVLVWDQFH DFWLQJ RQ WKH UROOHU FRDVWHU DQG WKH ZHLJKW RI YDULRXV ULGHUV WKDW FKDQJHV ZLWK every run of the roller coaster. A cup of coffee WKDW LV RSHQ WR WKH DLU LV ORVLQJ KHDW WR WKH DLU DURXQG LW 3XW D OLG RQ WKH FXS DQG WKH HQHUJ\ RI the coffee is now limited to the cup; no mass is H[FKDQJHG DQG LW KDV EHFRPH D FORVHG V\VWHP $ SDQ RQ WKH VWRYH FRRNLQJ D SLHFH RI FKLFNHQ LV DQ RSHQ V\VWHP EHFDXVH HQHUJ\ LV EHLQJ WUDQVIHUUHG WKURXJK VWHDP DQG KHDW UHOHDVH WR WKH DLU DURXQG the pan, but put a lid on the pan, and the system becomes closed.

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STEMscopedia Heat transfer plays a major role in the WUDQVIRUPDWLRQ RI HQHUJ\ 8QGHUVWDQGLQJ KHDW transfer is also important to many systems, such as weather and homeostasis in animals. Heat always moves from the warmer object to the cooler object. This indicates that cold is just the DEVHQFH RI KHDW ,I \RX SXW D FROG VSRRQ LQ \RXU coffee, the spoon heats up because heat travels from the coffee to the spoon.

What is this thermal (or heat) energy" Molecules in substances are in motion. The colder WKH VXEVWDQFH WKH OHVV HQHUJ\ WKH PROHFXOHV contain, so the slower the molecules move. The PRUH WKHUPDO HQHUJ\ WKH VXEVWDQFH FRQWDLQV RU the warmer it is, the faster the molecules move. +RZ GRHV WKDW WUDQVIHU WR D WHPSHUDWXUH UHDGLQJ" Surely all of the molecules in the substance aren’t PRYLQJ DW WKH VDPH VSHHG ULJKW" Temperature LV WKH DYHUDJH DPRXQW RI PRWLRQ RU HQHUJ\ LQ the molecules.

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4. Ex plain doesn’ why cold t exis t.

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STEMscopedia Heat can be transferred between substances and objects in three ways. Conduction, convection, and radiation DUH WKH WKUHH W\SHV RI KHDW WUDQVIHU (DFK W\SH RI WUDQVIHU PRYHV WKHUPDO HQHUJ\ IURP WKH ZDUPHU REMHFW RU VXEVWDQFH WR WKH FRROHU REMHFW RU VXEVWDQFH (DFK W\SH RI WUDQVIHU FDQ EH KDUQHVVHG WR power systems and do work.

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STEMscopedia and-spoon example from earlier, the heat moves from the coffee to the cooler spoon. The molecules of WKH FRIIHH DUH PRYLQJ PRUH TXLFNO\ WKDQ WKRVH LQ WKH VSRRQ $V WKH IDVW PRYLQJ PROHFXOHV RI WKH FRIIHH EXPS LQWR WKH PROHFXOHV RI WKH VSRRQ WKH\ WUDQVIHU VRPH RI WKHLU HQHUJ\ 7KH FRIIHH PROHFXOHV VORZ down a little, and the spoon molecules speed up a little. This continues until the coffee molecules and WKH VSRRQ PROHFXOHV DUH PRYLQJ DW WKH VDPH VSHHG ,PDJLQH WKDW VRPHRQH EXPSV LQWR \RX (YHQ LI \RX DUH VWDQGLQJ VWLOO WKH\ VORZ GRZQ ZKHQ WKH\ EXPS LQWR \RX DQG \RX EHJLQ PRYLQJ ZKLFK PHDQV \RX speed up. This is how conduction works.

Frying pan

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Pot handle

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STEMscopedia URFN /LTXLG DQG JDV PROHFXOHV DUH PRUH VSUHDG DSDUW PDNLQJ KHDW WUDQVIHU WKURXJK FRQGXFWLRQ LQHI¿ FLHQW VR WUDQVIHU QHHGV WR WDNH SODFH GLIIHUHQWO\ ,PDJLQH D SRW RI ERLOLQJ ZDWHU 7KH ZDWHU PROHFXOHV QHDUHVW WR WKH KHDWLQJ HOHPHQW JHW ZDUPHU DQG PRUH HQHUJHWLF $V WKH ZDWHU ZDUPV XS LW rises. The cold water at the top of the pot sinks because cold water is more dense than warm water.

7KLV SURFHVV DOORZV KHDW WR EH WUDQVIHUUHG ZLWKLQ WKH OLTXLG 7KH VDPH SURFHVV FDQ ZRUN ZLWK JDVHV 7KH VHFRQG À RRU LV ZDUPHU WKDQ WKH ¿ UVW À RRU RI WKH KRXVH EHFDXVH WKH ZDUP DLU ULVHV 7KLV FRQVWDQW PRYHPHQW RI WKH OLTXLG RU WKH JDV FUHDWHV D FXUUHQW FDOOHG D convection current.

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STEMscopedia electromagnetic rays. Think RI WKH 6XQ 7KH HQHUJ\ IURP WKH 6XQ KDV WR WUDYHO WKURXJK WKH YDFXXP RI VSDFH 7KLV LV WKH DGYDQWDJH RI UDGLDWLRQ +HDW WUDQVIHU LQ WKLV ZD\ GRHV QRW QHHG D PHGLXP VXFK DV D VROLG OLTXLG RU JDV WR WUDYHO WKURXJK $V WKH radiant energy IURP WKH 6XQ UHDFKHV D VXUIDFH WKDW HQHUJ\ LV WUDQVIHUUHG WR WKH VXUIDFH DQG WKH VXEVWDQFH EHJLQV WR KHDW XS 7KH GDUNHU WKH REMHFW WKH PRUH HQHUJ\ LV DEVRUEHG 2EMHFWV FDQ DOVR HPLW UDGLDQW HQHUJ\ ,I \RX KDYH HYHU KHOG \RXU IRRW DERYH D KRW VLGHZDON RU VWUHHW \RX have felt the radiant heat from the street before you even put your foot down.

5. How do conve conduction, c radiati tion, and melt c on work to ho a doub colate usin g le double boiler? (A water boiler boils a bow in a pot, an l d above is suspende t d melt t he water to he ch ocolate .)

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STEMscopedia eat to be used to keep our bodies in homeostasis at a constant 98.6°F. When we touch items that are cooler than our bodies, we lose heat to the object. Most of the time, the air around us is cooler than we DUH DQG ZH DUH ORVLQJ KHDW WR WKH URRP DURXQG XV E\ UDGLDWLRQ ,I ZH VLW LQ VXQOLJKW RXU VNLQ LV EHLQJ ZDUPHG E\ UDGLDWLRQ IURP WKH 6XQ ,I ZH DUH LQ D FRRO URRP WKHUH LV D VPDOO FRQYHFWLRQ FXUUHQW EHLQJ JHQHUDWHG DURXQG XV 2XU VNLQ ZDUPV WKH DLU DURXQG XV DQG WKH QRZ ZDUP DLU ULVHV DQG LV UHSODFHG E\ FRROHU DLU FUHDWLQJ D FRQYHFWLRQ FXUUHQW

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STEMscopedia \RXU RYHQ UDGLDWHV KHDW WKURXJKRXW WKH RYHQ 7KHUH LV VRPH FRQYHFWLRQ KHDWLQJ DW WKH EHJLQQLQJ EXW because the oven is a closed system, all of the air in the oven will be the same temperature eventually.

7KLV HYHQ WHPSHUDWXUH WKURXJKRXW WKH RYHQ LV ZK\ WKH RYHQ VKRXOGQ¶W EH RSHQHG GXULQJ FRRNLQJ 6RPH ovens, called convection ovens, actually use forced convection currents via a fan to circulate heated air, EULQJ LW LQ FRQWDFW ZLWK WKH IRRG LQ WKH RYHQ DQG GHFUHDVH FRRNLQJ WLPH

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STEMscopedia Dr. Douglas Casa and the Korey Stringer Institute :KHQ 'RXJODV &DVD ZDV KH ZDV UXQQLQJ D NP UDFH DQG KH FROODSVHG IURP H[HUWLRQDO KHDW VWURNH +H ZDV LQ D FRPD IRU VL[ KRXUV 6LQFH WKHQ KH KDV GHYRWHG KLPVHOI WR VWXG\LQJ H[HUWLRQDO KHDW VWURNH DQG KDV EHFRPH RQH RI WKH OHDGLQJ H[SHUWV +H KDV D GRFWRUDWH LQ H[HUFLVH SK\VLRORJ\ IURP WKH 8QLYHUVLW\ RI &RQQHFWLFXW +H IRXQGHG WKH .RUH\ 6WULQJHU ,QVWLWXWH ZLWK WKH 1DWLRQDO )RRWEDOO /HDJXH DQG .RUH\ 6WULQJHU¶V ZLGRZ .HOFL WR DVVLVW LQ KLV VWXGLHV DQG SURYLGH HGXFDWLRQ DQG UHVRXUFHV IRU GHDOLQJ ZLWK H[HUWLRQDO KHDW VWURNH DQG DYRLGLQJ LW 7R GDWH KH KDV VXFFHVVIXOO\ WUHDWHG SHRSOH VXIIHULQJ from exertional heat stroke (zero fatalities).

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STEMscopedia (QHUJ\ FDQQRW EH FUHDWHG RU GHVWUR\HG LW FDQ RQO\ EH WUDQVIRUPHG IURP RQH IRUP WR DQRWKHU +HDW WUDQVIHU PHDQV WKDW KHDW HQHUJ\ PRYHV IURP D ZDUPHU REMHFW RU VXEVWDQFH WR D FRROHU REMHFW RU substance. Heat can be transferred by conduction, convection, and radiation. Conduction happens ZKHQ REMHFWV DUH WRXFKLQJ &RQYHFWLRQ KDSSHQV LQ OLTXLGV DQG JDVHV YLD WKH PRYHPHQW RI KHDW LQ WKH VXEVWDQFH 5DGLDWLRQ LV KHDW WKDW WUDYHOV IURP DQ REMHFW E\ HOHFWURPDJQHWLF ZDYHV $OO WKHVH W\SHV RI KHDW WUDQVIHU SRZHU VRPH RI WKH ODUJHVW V\VWHPV LQFOXGLQJ ZHDWKHU KRPHRVWDVLV RI KXPDQ ERG\ WHPSHUDWXUH DQG KHDWLQJ DQG FRROLQJ RI KRPHV

Connect It How is energy conserved in every energy transformation and heat transfer?

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7. How is conse energy r every ved in transf energy ormati on heat transf and er?

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STEMscopedia

1. :KDW W\SH RI KHDW WUDQVIHU IURP WKH ¿ UH LV EHLQJ H[SHULHQFHG E\ WKH SHRSOH" A. Radiation B. Convection C. Conduction D. Thermal 2. :KLFK LV DQ H[DPSOH RI NLQHWLF HQHUJ\" A. Ball at the top of a hill B. Pear C. &DU UROOLQJ GRZQ D KLOO D. Rubber band stretched out 3. Heat always moves from an object of ______________ temperature to an object of ________________ temperature.

A. cooler, warmer B. zero, warmer C. cooler, zero D. warmer, cooler

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Energy in Systems

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173

STEMscopedia Energy is always conserved in a system, but how is this done? How does energy transform from one type to another?

Energy Energy is the ability of a system to do work or produce heat. The law of conservation of energy states that energy cannot be created or destroyed, but it can change forms. There are many forms of energy, as shown in the diagram above.

• • • • • • •

Mechanical energy is the sum of the potential energy and kinetic energy of an object.

Radiant energy involves the electromagnetic waves that are given off by a source into the surrounding environment.

Chemical energy is the energy that is stored in chemical bonds.

Electrical energy is the energy that is produced as a result of moving electric charges.

Thermal energy is the internal energy of a system, including the kinetic energy and potential energy of its particles.

Sound energy is energy that is made by vibrations traveling as waves and requires a medium (air, water, or solids) to travel.

Nuclear energy is energy that is released by fusing or splitting the nucleus of an atom.

There are many ways in which these forms of energy can be transformed from one to another, but the energy itself is not destroyed and no new energy is created during these transformations.

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STEMscopedia

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Some energy transformations are direct. Radiant energy from the Sun is transformed into thermal energy to heat our planet. Solar panels transform radiant energy from the Sun directly into electrical energy. Plants transform the Sun’s radiant energy into chemical energy through photosynthesis.

Some transformations take several steps. The chemical energy from batteries is transformed into electrical energy and can then be used for several different transformations. It can be transformed LQWR VRXQG HQHUJ\ LQ D UDGLR PHFKDQLFDO HQHUJ\ LQ D WR\ FDU DQG UDGLDQW HQHUJ\ LQ D À DVKOLJKW 7KH chemical energy that is stored in food is transformed by different body processes to provide mechanical energy for you to move, thermal energy to maintain your body temperature, and chemical energy for cellular functions.

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STEMscopedia and then into electrical energy for homes and businesses. There are different ways that a turbine gets its energy. It can come directly from moving wind or water (mechanical energy) or from thermal energy that is created by burning fossil fuels (chemical energy) or from splitting atoms (nuclear energy). This thermal energy is used to heat water and create steam to turn a turbine. The electrical energy that is produced is further transformed into radiant and thermal energy when you turn on a light and into mechanical, sound, and thermal energy to run appliances and machinery.

Mechanical Energy Transformations in Systems One of the easiest energy transformations to observe and calculate is that of potential energy and kinetic energy in different systems, like a swinging pendulum or a roller-coaster car. In these examples, friction and air resistance are ignored to simplify the calculations. The mechanical energy (ME) of a pendulum at any point along its swing is the sum of the potential energy (PE) and kinetic energy (KE) of the pendulum at each location.

Gravitational potential energy is the energy that is stored in an object due to its position. The higher an object is above a surface, like the ground, the more potential energy the object possesses because it has the potential to fall a greater distance.

Kinetic energy is the energy of motion. As the pendulum swings downward, it transforms its potential energy into kinetic energy. As it swings upward, the kinetic energy is transformed into potential energy.

While the potential and kinetic energies are continuously changing, the total mechanical energy is the same, demonstrating the law of conservation of energy.

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STEMscopedia he e is t r e h 2. W l energy ia potent t for the s greate pendulum? g swingin ? Where Why kinetic is the reatest y g i g energ swingin e h t for Why? ? m lu u pend

Advanced Topics Potential Energy Diagrams Potential energy diagrams are used to show the measure of potential energy and changes throughout a situation. This helps us better understand the trends. Potential energy diagrams can be used to show chemical reactions, orbital motions, or pendulum swings.

Chemical Reactions: A potential energy diagram, also called a reaction curve, shows how potential energy changes during a chemical reaction. The diagram shows how potential energy changes as reactants are converted into products. Note that there are two kinds of reaction curves: endothermic and exothermic. In an endothermic reaction, energy is absorbed by the reaction or system, resulting in products that are at a higher energy level than the reactants. In an exothermic reaction, energy is released by the reaction or system, resulting in products that are at a lower energy level than the reactants. It is important to not confuse the two reaction types. All chemical reactions fall into one of the two categories.

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STEMscopedia Consider a satellite orbiting Earth. Most satellites orbit in a circular motion. These VDWHOOLWHV UHPDLQ DW WKH VDPH GLVWDQFH IURP (DUWK DW DOO WLPHV WKH UDGLXV LV ¿ [HG 7KH VSHHG LV DOVR constant. Because the kinetic energy (KE) depends on the speed of an object, the KE will also be constant throughout the motion. The potential energy (PE) is dependent on the height of an object, so the PE will also remain constant. The total amount of mechanical energy remains the same.

Like with circular motion, the total amount of mechanical energy of a satellite remains the same in elliptical motion. Unlike with circular motion, the energy of a satellite changes form in elliptical motion.

The force of gravity is constantly doing work on a satellite and slowing it down as it moves. The gravity pulls the satellite toward Earth. The motion of the satellite keeps it moving in a forward path. As the speed changes, the KE also changes. When the satellite is closest to Earth, the speed is the greatest.

When the satellite is farthest, the speed is the least. As the satellite gets farther from Earth, it loses KE and gains PE. Conversely, as the satellite gets closer to Earth, it gains speed and loses height.

This causes a gain in KE and a loss of PE. Throughout this process, the mechanical energy still remains constant.

Pendulums: The kinetic energy of an object is the energy that it possesses due to its motion. Recall that KE depends on mass and speed, where KE = (½)mv2. The faster an object moves, the more KE it has. The KE of a pendulum increases until the ball is in equilibrium position. The KE decreases as it moves farther away from equilibrium. The potential energy of the object is the stored energy based on the position of the ball. This PE is a gravitational potential energy because gravity is the force that causes the movement. The amount of PE is dependent on the mass and height of the ball’s swing, where PE = mgh.

The equilibrium position is where the pendulum would rest—its lowest position (location 3). At this point, the height would be zero and the PE would be zero as well. As the pendulum swings back and forth, there are times when it moves away from the equilibrium. As it does this, and height increases, PE increases. As it moves toward the equilibrium position and height decreases, the PE decreases.

However, the total mechanical energy of the pendulum will remain the same at all times. Therefore, if the PE is increasing, the KE is decreasing and vice versa. When PE is lost, it appears as KE. There is a transformation of PE and KE as the ball of the pendulum moves.

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nerg in S stems

STEMscopedia Energy is measured in joules. A joule (J) is the SI unit (in the international system of units) for energy, and it is equal to one newton of force applied over one meter of distance. Mechanical energy is the sum of potential energy and kinetic energy.

Mechanical Energy (J) = Potential Energy (J) + Kinetic Energy (J) ME = EP + EK Potential energy is the energy that an object has stored due to its position.

Potential energy (J) = mass (kg) x gravity (9.8 m/s2) x height (m) PE = mgh Kinetic energy is the energy of motion.

Kinetic energy (J) = ½ x mass (kg) x velocity (m/s)2 KE = ½ mv2 Example Problem 1 'HWHUPLQH WKH PHFKDQLFDO HQHUJ\ RI D NJ UROOHU FRDVWHU PRYLQJ DW P V DW WKH ERWWRP RI WKH ¿ UVW dip, which is 15 m above the ground.

PE = mgh PE = (450 kg) (9.8 m/s2) (15 m) PE = 66,150 J KE = ½ mv2KE = ½ (450 kg) (30 m/s)2 KE = 202,500 J ME = PE + KE ME = 66,150 J + 202,500 J ME = 268,650 J Note: A large amount of energy makes sense with a roller coaster.

Example Problem 2 A 5 kg object is moving downward at a speed of 12 m/s. It is currently 2.6 m above the ground. a. What is its kinetic energy?

KE = ½ mv2 KE = ½ (5 kg) (12 m/s)2 KE = 360 J b. What is its potential energy?

PE = mgh PE = (5 kg) (9.8 m/s2) (2.6 m) PE = 127.4 J c. What is its mechanical energy?

ME = PE + KE ME = 127.4 N + 360 N ME = 487.4 J Note: A small amount of energy makes sense with a smaller mass. nerg in S stems

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STEMscopedia

Systems A system is a group of interacting, interrelated, or interdependent elements forming a complex whole.

A system is something that we identify or prepare in order to do experiments and make observations.

It is a part of the universe that we wish to study. Anything that is not part of the system is considered the surroundings. The system and surroundings together make up the universe. The solar system is comprised of all the celestial bodies that are revolving around the Sun or are held by its gravitational attraction. An ecosystem is characterized by the interactions of the biotic and abiotic factors in a given DUHD $ PDVV KDQJLQJ E\ D VWULQJ IURP D ¿ [HG SRLQW FRPSULVHV D SHQGXOXP V\VWHP Isolated Systems: Nothing is perfectly isolated from its surroundings, but we can get quite close— even though, eventually, all barriers break down. An isolated system does not exchange matter or energy with its surrounding environment; nothing can enter or leave. The energy and matter remain the same. Any changes that occur happen inside the system. Examples of isolated systems include a closed WKHUPDO À DVN DQ DLU WLJKW FRQWDLQHU DQG D VHDOHG YDFXXP FKDPEHU

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STEMscopedia negligible and can be ignored. This allows us to use conservation laws in problems, and it helps us DQDO\]H SUREOHPV LQ D PRUH VLPSOL¿ HG ZD\ 6RPH H[DPSOHV LQFOXGH D VZLQJLQJ SHQGXOXP DQG REMHFWV gliding on an air table.

Closed Systems: A closed system will not exchange matter but does exchange energy with its surrounding environment. A closed system has a constant amount of mass, but energy can cross the border in the form of heat or work. Therefore, the volume of the system does not necessarily remain the same if the system expands or contracts with the energy changes. Examples of closed systems include a balloon being heated or cooled, a pot boiling with a lid to trap the steam, and a pressure cooker being heated.

Open Systems: An open system will exchange matter and energy with its surrounding environment.

Examples of open systems include boiling soup on a stove where both heat and steam can leave the system while ingredients can be added. A pond, where water can be added by rain or removed by evaporation and animals can come and go, is also an example of an open system.

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STEMscopedia

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STEMscopedia Entropy +DYH \RX HYHU GURSSHG D JODVV RQ WKH À RRU that then shattered into pieces? A solid piece of material may break into smaller pieces, but you rarely observe small pieces of material form back into a whole piece. Similarly, you may have noticed that cream will dissolve into coffee and a fragrance will diffuse (or spread) into the air of a room. However, the reverse never happens; dissolved cream does not spontaneously separate back into its original form, and a diffused fragrance does not return to an isolated region of the room.

The explanation for these phenomena is entropy. Entropy is a measure of the disorder in a system, and it is a key part of the laws of thermodynamics. What is the law of entropy?

The Second Law of Thermodynamics and Entropy As discussed earlier, cream dissolves into coffee and a fragrance diffuses into a room, but we never observe the reverse process. In both cases, a system becomes less ordered. That is, the particles always spread out and exchange energy until they come to equilibrium.

We observe this whenever one substance is at a greater temperature than another. A hot substance has more thermal energy than a cool substance. The two substances are said to be ordered because one has more energy than the other. When these substances interact with each other, we always observe the hotter substance transfer thermal energy to the cooler substance. After they come to equilibrium, they have the same energy and are more disordered. The measure of disorder in a system is called entropy.

More disorder equals greater entropy.

For example, when a block of ice melts, the molecules of water spread out and become more disordered. The entropy increases.

Consider many gas particles moving at high speed on one side of a chamber. If there is a barrier between the two sides of the chamber, the system is closed. In this case, the entropy of the system will remain constant. However, if a door is opened to the other side of the chamber, the particles will spread out until there are equal quantities of particles in both chambers. In this case, the energy of the particles spreads out and the entropy of the particles increases. nerg in S stems

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STEMscopedia likely to evolve into more disordered states than into more ordered states. For example, a system in an ordered state, like a solid block of ice, is more likely to evolve into a disordered state, like liquid water.

Because states of a system with greater disorder are more probable, the entropy of a closed system always stays the same or increases. That is, the entropy of a closed system does not decrease. This is the second law of thermodynamics, also known as the law of entropy. This law is a statement about the direction of thermodynamic processes. It is one of the few laws in physics that indicates an asymmetry in nature.

Note that the entropy in a system will decrease if we remove energy from it. For example, freezing a cup of water lowers the entropy of the water. The solid ice has less disorder and less entropy than the liquid water. However, the fact that we can add energy to or remove energy from the water means that it interacts with the environment, so it is not a closed system. We never encounter a truly closed system on Earth.

The entropy of individual systems increases or decreases as energy is added to or removed from them.

But the entropy of the universe as a whole cannot decrease because it is a closed system. There is no place outside the universe from which energy may be added to the universe. The entropy of the universe always increases.

Summary of Energy Flow and the Second Law )RU KHDW WR À RZ IURP D ³VRXUFH´ WR D ³VLQN ´ D WHPSHUDWXUH GLIIHUHQFH LV UHTXLUHG :KHQ KHDW LV transferred, the temperature eventually equalizes by a heat source’s temperature falling and a heat sink’s temperature rising. When temperatures are equalized, no more heat is transferred even though objects still contain heat. When heat is converted into work, the heat source’s temperature falls, approaching that of the heat sink. If there is no temperature difference, no heat can be converted into work. But if there is a temperature difference, some of the heat will be used to raise the temperature of the sink. If some of the heat goes into raising the sink, it cannot all be converted to work. Therefore, it LV QRW SRVVLEOH WR FRQYHUW RQH IRUP RI HQHUJ\ WR DQRWKHU ZLWK HI¿ FLHQF\

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STEMscopedia g James Prescott Joule, Physicist In the mid-1800s, James Prescott Joule (1818–1889) proposed that mechanical energy, electricity, and heat were all forms of energy and FRXOG EH FKDQJHG LQWR RQH DQRWKHU +H ZDV WKH ¿ UVW WR SURSRVH WKDW such energy transformations could occur. Joule conducted experiments to determine the amount of heat that was generated by an electric wire, resulting in Joule’s law, which states that the heat that is generated in an electric wire is proportional to the current squared multiplied by the resistance. He did further experiments to determine the amount of mechanical work that is needed to generate a unit of heat. The SI unit RI HQHUJ\ DQG ZRUN WKH MRXOH ZDV QDPHG LQ KRQRU RI KLV VLJQL¿ FDQW VFLHQWL¿ F FRQWULEXWLRQV +LV ODWHU FROODERUDWLRQ ZLWK :LOOLDP 7KRPVRQ (also known as Lord Kelvin) resulted in the discovery that when a gas expands freely, it changes temperature; this is known as the Joule-Thomson effect. This discovery was a basis for refrigeration.

The Big Picture Energy exists in several different forms. Forms of energy can be transformed into other forms of energy by different processes. Some transformations are simple while others are more complex. During these transformations, no energy is destroyed and no new energy is created; all energy is conserved.

Connect It There are several energy transformations in the picture below.

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STEMscopedia 1. Which choice below is not a form of energy?

A. Chemical B. Mechanical C. Fossil fuel D. Thermal 2. What does the law of conservation of energy state?

A. Energy comes from the Sun. B. Energy cannot be created or destroyed.

C. Energy transformations can be simple or complex.

D. There are several different forms of energy.

3. What type of energy is stored in batteries?

A. Electrical energy B. Radiant energy C. Mechanical energy D. Chemical energy

4. Describe the energy transformations that are needed to be able to watch a TV.

5. How does a roller coaster demonstrate the conservation of energy?

6. How do the three types of systems differ? Explain.

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Characteristics of Waves

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189

STEMscopedia You perceive the world around you with your senses. Two of those senses rely on waves. The image below shows the different types of waves that are needed for your senses of hearing and sight.

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STEMscopedia What is a wave" $ ZDYH LV D GLVWXUEDQFH LQ SDUWLFOHV RU D ¿ HOG WKDW WUDQVIHUV HQHUJ\ SURJUHVVLYHO\ IURP SRLQW WR SRLQW ZLWKRXW WKH ¿ HOG RU SDUWLFOHV KDYLQJ DQ\ QHW PRYHPHQW WKHPVHOYHV :KDW GRHV WKLV PHDQ" It means that waves move energy through something. There are two main types of waves. One type is a transverse wave.

A transverse wave is a wave that is propagated in a direction that is perpendicular to the displacement RI WKH WUDQVPLWWLQJ ¿ HOG RU medium. This means that the wave energy moves in one direction while the particles that are disturbed by the wave move at a right angle to that direction. In the image, the wave energy moves from left to right while the particles that are disturbed by the wave move up and down.

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The highest point of the wave is called the crest, and the lowest point is the trough. The midpoint between the crest and trough is the equilibrium point, also called the resting position. The distance from the resting position to the crest or the trough is the amplitude. This can be considered the height of the wave. The amplitude is determined by the amount of energy that created the wave. A wave with greater energy will have a larger amplitude.

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STEMscopedia The image below shows waves with the same frequency but different amplitudes. A higher amplitude is caused by greater energy.

wavelength. The symbol for wavelength is WKH *UHHN OHWWHU ODPEGD NJ 7KH QXPEHU RI ZDYHV WKDW SDVV D SRLQW LQ D VSHFL¿ F DPRXQW RI WLPH LV WKH frequency of the wave and is measured in hertz. One hertz is one wave per second. Because each wave propagates energy, the more waves there are, the more energy that is transferred. Therefore, a higherfrequency wave carries more energy than a lower-frequency wave of the same amplitude.

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STEMscopedia Examples of Transverse Waves: If you wiggle a rope up and down or side to side, it will produce a transverse wave, as shown in the picture.

But there are transverse waves that cannot be seen. These are the waves of the electromagnetic spectrum, which is shown in the diagram below. These electromagnetic waves, or light, do not need a medium to travel through, so they can be transmitted through space. They include the radio waves that are needed for TV and cell phone signals, medical X-rays, and the waves of visible light that are needed for you to see. Indeed, light is a wave that is generated by the oscillation of ERWK DQ HOHFWULF DQG D PDJQHWLF ¿ HOG &KDUJHG particles, such as electrons and protons, create HOHFWURPDJQHWLF ¿ HOGV ZKHQ WKH\ PRYH 7KHVH ¿ HOGV WUDQVSRUW HQHUJ\ DV HOHFWURPDJQHWLF UDGLDWLRQ $V ORQJ DV ERWK ¿ HOGV DUH SUHVHQW the light wave can be transmitted. This is why light can travel through the vacuum of space.

(OHFWURPDJQHWLF (0 ZDYHV RI WKH VSHFL¿ F wavelengths and frequencies of visible light stimulate cells in your eye, allowing you to detect the colors of the visible spectrum.

Different types of EM waves are characterized by their wavelengths and frequencies in the electromagnetic spectrum image.

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STEMscopedia The second main type of wave is a longitudinal wave. A longitudinal wave is a wave that is propagated LQ WKH VDPH GLUHFWLRQ DV WKH GLVSODFHPHQW RI WKH WUDQVPLWWLQJ ¿ HOG RU PHGLXP 7KDW PHDQV WKDW WKH particles that are disturbed by the wave move in the same direction that the wave energy moves. In the diagram below, the coils of the spring that is disturbed by the wave are compressed forward as the wave energy moves forward. Longitudinal waves are also called compression waves.

There is no crest or trough in a longitudinal wave as there is no high or low point. Instead, the characteristics of a longitudinal wave are compression and rarefaction. The compression is the part of the wave where the particles are pushed closer together by the energy of the wave. This is also how amplitude is measured. The amplitude is how close together the particles are in the compression.

The closer together the particles are in the compression, the greater the amplitude of the wave. The rarefaction is the less dense, more spread-out region of a longitudinal wave. The wavelength of a longitudinal wave is the distance between equal parts of the wave that includes one compression and one rarefaction. Like a transverse wave, the frequency of a longitudinal wave is the number of waves that pass a point in a given amount of time.

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STEMscopedia The coiled spring toy is one common example of a longitudinal wave as the compressions are easy to observe. There are longitudinal waves that cannot be seen, such as sound waves.

Vibrations from the speaker in the image above create a disturbance in the air particles that transmits sound energy.

Sound is produced by vibration. The energy of the vibration causes the air particles at the sound source to be compressed. Those particles bump into the particles next to them, passing the energy through the air particles to your ear. The energy is then passed to your eardrum, causing it to vibrate and allowing \RX WR KHDU $ ORW RI HQHUJ\ FDXVHV FORVHU FRPSUHVVLRQ DPSOLWXGH ZKLFK FUHDWHV D ORXGHU VRXQG Quicker vibrations cause a greater frequency of compressions and create a higher-pitched sound.

The same process occurs through liquids and allows you to hear underwater. It also happens through solids. Put your ear on your desk and tap on the desk. The sound wave will propagate through the desk to your ear. Because longitudinal waves require particles to be compressed, they require a medium and cannot propagate in space, where there are no particles or the particles are too far apart to be compressed.

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STEMscopedia Wave speed, also called wave velocity, is a measure of how fast a wave is moving. It is calculated using the wavelength and frequency of a wave.

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Example 1: Determine the speed of the wave in the box below.

1 cm

---------------- 1 second ------------Wavelength: The distance from crest to crest is 4.0 cm = 0.40 m. )UHTXHQF\ 7KH ER[ UHSUHVHQWV VHFRQG 7KHUH DUH ZDYHV VHFRQG +] :DYH VSHHG P [ +] P V Example 2: Determine the speed of the wave in the box below.

1 cm

----1sec----1sec----1sec----1sec---Wavelength: The distance from crest to crest is 4.0 cm = 0.40 m. )UHTXHQF\ ZDYHV VHFRQG +] :DYH VSHHG P [ +] P V

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STEMscopedia The speed of most waves depends on the medium through which they are traveling. Waves of different frequencies traveling through the same medium will have different wavelengths.

All three waves above are traveling at 1.0 m/s through the same medium.

Example 1: &DOFXODWH WKH ZDYHOHQJWK RI WKH ZDYH LQ %R[ $ Rearrange the wave speed equation: wave speed = frequency x wavelength wavelength = wave speed/frequency ZDYHOHQJWK P V +] wavelength = 0.11 m Example 2: &DOFXODWH WKH IUHTXHQF\ RI WKH ZDYH LQ %R[ & Rearrange the wave speed equation: wave speed = frequency x wavelength frequency

= wave speed/wavelength

IUHTXHQF\ P V P frequency

= 3.0 Hz

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STEMscopedia LIGO Scientists and Gravitational Waves

This is a photo of the LIGO facility in Livingston, Louisiana.

7KH /DVHU ,QWHUIHURPHWHU *UDYLWDWLRQDO :DYH 2EVHUYDWRU\ /,*2 FRQVLVWV RI WZR IDFLOLWLHV RQH LQ Washington state and the other in Louisiana, working in unison to detect gravitational waves that are created by cosmic events such as black holes or colliding neutron stars. The LIGO facilities use laser interferometry and multikilometer-scale detectors to measure minute ripples in space-time that DUH FUHDWHG E\ WKH HQHUJ\ RI SDVVLQJ JUDYLWDWLRQDO ZDYHV ,Q /,*2 PDGH LWV ¿ UVW GHWHFWLRQ RI gravitational waves that were created when two black holes collided 1.3 billion light-years away. Many REVHUYDWLRQV RI JUDYLWDWLRQDO ZDYHV KDYH VLQFH EHHQ PDGH ,Q WKUHH RI /,*2¶V FRIRXQGHUV ZHUH awarded the Nobel Prize in Physics.

LIGO scientists are a diverse group working not only at the facilities in Washington and Louisiana but DOVR DW WKH &DOLIRUQLD ,QVWLWXWH RI 7HFKQRORJ\ DQG WKH 0DVVDFKXVHWWV ,QVWLWXWH RI 7HFKQRORJ\ /,*2 SURYLGHV RSSRUWXQLWLHV IRU WKH EURDGHU VFLHQWL¿ F FRPPXQLW\ WR SDUWLFLSDWH LQ GHWHFWRU GHYHORSPHQW observation, and data analysis.

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STEMscopedia Waves transfer energy through substances and space. Different types of waves transfer different types of energy. Not all waves can be seen, but all waves can be described by their characteristic properties.

Connect It How do waves allow you to hear and see?

Your ears detect the sound waves of a music system. Your eyes detect the light and colors from a TV. Both sound energy and light energy are transmitted by waves.

r do you y h 5. W detect ears waves l a n i d longitu e your whil etect ? d s e ey waves e s r e transv

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STEMscopedia 1. What is represented by the letter G in the diagram?

A. &UHVW B. Trough C. Wavelength D. Amplitude 2. What does the frequency of a sound wave determine?

A. Loudness B. Pitch C. &ODULW\ D. Speed 3. What wave characteristics are needed to calculate wave speed?

A. Direction and frequency B. Frequency and wavelength C. Wavelength and velocity D. Direction and wavelength 4. How are both amplitude and frequency related to the energy of a wave?

The amount of energy determines the amplitude of the wave. Because each wave carries the energy, the PRUH ZDYHV WKHUH DUH RI WKH VDPH DPSOLWXGH IUHTXHQF\ WKH PRUH HQHUJ\ ZLOO EH WUDQVPLWWHG 5. Why is light transmitted through space, but sound is not?

Light waves are electromagnetic waves and do not require particles to transmit energy, so they can travel through space. Sound waves are longitudinal waves and require particles to compress to transmit energy. Space does not have particles that are close enough to be compressed, so energy cannot be transmitted by longitudinal waves.

6. Why is amplitude not required to calculate the speed of a wave?

Speed/velocity is a ratio of distance over time. The distance of a wave is the wavelength, and frequency is a measure of waves and time. Amplitude is a measure of the energy that is carried by a wave independent of its speed.

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Behavior of Waves

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203

STEMscopedia How many times per day do you look in a mirror?

Why are you able to see yourself in a mirror?

Waves transmit energy from point to point without transmitting matter. Waves travel through a medium and continue traveling until they encounter an object. When a wave reaches that object, it can behave in different ways depending on the wavelength of the wave and the object it is encountering. Some light waves will hit the object and bounce back in the same direction they traveled from. This is known as UHÀ HFWLRQ DQG LW LV WKH UHDVRQ ZK\ ZH FDQ VHH RXUVHOYHV LQ D PLUURU

some e r a t a 1. Wh xamples of e

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waves travel through different media, they eventually run into various objects in the environment. When waves hit different objects, they don’t just stop; they are actually encountering a new medium, and they change their direction of travel depending on the type of wave, the wavelength, and the composition of the new medium. 5HÀ HFWLRQ occurs when a wave hits the surface of a new medium and is sent back to the medium it traveled from. In other words, the wave bounces back toward the original direction and medium after it encounters the new object. The ray of light that strikes the surface is known as the incident ray, and the ray WKDW LV UHÀ HFWHG RII WKH VXUIDFH LV NQRZQ DV WKH UHÀ HFWHG UD\ $W WKH SRLQW ZKHUH WKH LQFLGHQW UD\ strikes the surface, we can draw a line that is perpendicular to the surface, known as the normal line. This angle, formed between the incident ray and the normal line, is the angle of incidence, and the angle formed between the normal line and UHÀ HFWHG UD\ LV WKH DQJOH RI UHÀ HFWLRQ ,I D ZDYH UHÀ HFWV RII D VPRRWK VXUIDFH OLNH JODVV RU D PLUURU WKH UHÀ HFWHG UD\V ERXQFH RII WKH surface at the same angle at which the incident rays hit the surface, and the waves travel in the VDPH GLUHFWLRQ ,I D ZDYH UHÀ HFWV RII D URXJK VXUIDFH WKH UHÀ HFWHG ZDYH ERXQFHV RII DQG LV scattered in all different directions and angles.

5HÀ HFWLRQ RI OLJKW ZDYHV LV UHDOO\ FRPPRQ DQG \RX SUREDEO\ VHH H[DPSOHV RI UHÀ HFWLRQ HYHU\ GD\ <RX FDQ VHH OLJKW UHÀ HFWLRQ IURP \RXU PLUURU WKH JODUH IURP D ZLQGRZ RU VFUHHQ RU UHÀ HFWLRQ RII WKH VXUIDFH RI ZDWHU 6RXQG ZDYHV DOVR UHÀ HFW Echoes occur because sound waves hit a surface DQG UHÀ HFW EDFN WRZDUG WKH OLVWHQHU 6FLHQWLVWV FDQ measure the depth of underwater objects using sonar technology by sending out sound waves and PHDVXULQJ WKHP DIWHU WKH\¶YH EHHQ UHÀ HFWHG

1RW DOO ZDYHV ZLOO UHÀ HFW RII WKH QHZ PHGLXP WKH\ HQFRXQWHU LQVWHDG WKH\ ZLOO SDVV WKURXJK WKH new medium and continue traveling at a different angle and in a different direction. This is known as UHIUDFWLRQ. Refraction occurs because light travels at different speeds in different media. Light travels the quickest in a gas medium, like air, and the slowest in a solid medium. Sound waves are just the opposite and travel fastest through solid and slowest through gas media. As waves pass through different media, they change their speed of travel, which changes the direction and angle of their travel. The angle at which the wave hits the surface of the new medium is called the angle of incidence. Once the wave passes through the surface of the new medium and changes direction, the angle of change is known as the angle of refraction. Waves with shorter wavelengths are refracted at greater angles than waves with longer wavelengths. e a ior o

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STEMscopedia through a new medium, waves can travel around objects or through gaps and holes. This is known as GLIIUDFWLRQ. Diffraction occurs because the wave has encountered an object, gap, or hole that is similar in size to the size of its wavelength. This is why we can hear people around corners or through open doors. Have you ever seen rainbow light shining off a CD? This happens because a CD consists of a grooved track in a spiral pattern, known as diffraction grating. This diffraction grating allows the light waves to diffract, which shows up as a rainbow.

Di ra tion

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STEMscopedia Wave LQWHUIHUHQFH occurs when two or more waves interact and combine with each other while traveling along the same medium. There are two types of wave interference that can occur. During FRQVWUXFWLYH LQWHUIHUHQFH, the crests of the two waves are displaced in the same direction. The crests of the two waves meet when they reach the same point and combine. This results in one wave with a large amplitude that is equal to the sum of the amplitudes of the individual waves. Let’s take two waves: Wave A and Wave B. They are both traveling along a medium in opposite directions, with their crests facing the same direction. Wave A has an amplitude of 3, and Wave B has an amplitude of 2; when they meet along the medium, Wave A and Wave B will combine to form one wave with an amplitude of 5. 'HVWUXFWLYH LQWHUIHUHQFH occurs when the crests of the waves are facing opposite directions.

When these waves meet, the resulting wave is smaller than the individual waves, and sometimes the wave gets cancelled out completely. Let’s look at Wave A and Wave B again. They are still traveling in opposite directions, but this time their crests are facing opposite directions. Wave A has an amplitude of 2, with its crest facing up, and Wave B has an amplitude of -1, with its crest facing down. When these two waves meet and combine, the resulting wave has an amplitude of 1. If Wave A had an amplitude of 2, and Wave B had an amplitude of -2, the two waves would completely cancel each other out, and no wave would occur at that point along the medium. The process of waves traveling along the same medium and interacting is known as VXSHUSRVLWLRQ.

is the Q t a h 3. W EHWZHH HQFH GLIIHU VWUXFWLYH FRQ HQFH U H I U

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STEMscopedia 6WDQGLQJ :DYHV When two or more waves with the sample amplitude and frequency interfere while traveling in the same medium in opposite directions, VWDQGLQJ ZDYHV are formed. Standing waves appear to be vibrating but not moving horizontally. Let’s look at Wave A and Wave B again. They are moving at the exact same frequency in opposite directions. Wave A has a crest with an amplitude of 2 and a trough with an amplitude of -2. Wave B also has a crest with an amplitude of 2 and a trough with an amplitude of -2.

When the two waves meet, they will undergo destructive interference at their midpoints. This creates a point of no displacement and forms a node. As the midpoints meet, the crest of Wave A and the trough of Wave B are traveling through the same location. The trough of Wave A and the crest of Wave B also travel through the same location. This creates points of vibration called antinodes. Because the two waves are traveling at the same frequency in opposite directions, this continues to happen, and the wave appears to vibrate in place. A standing wave can easily be seen on a plucked guitar string. As the guitar string is plucked, pulses form and the string appears to vibrate vertically.

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V L

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STEMscopedia If you were to take a rope, tie one end to a pole, and stretch it out as far as it could go, you would form a straight line with the rope. If you started to move the rope up and down, you would start to create waves in the rope. If you looked directly at the waves, it would appear that they were traveling toward you in one plane. This is common for many different types of waves, and when light waves travel in one plane, it is known as polarized light. However, light waves do not normally travel in one plane; instead, light vibrates in numerous planes, which is known as unpolarized light. We can transform unpolarized light into polarized light through a process called SRODUL]DWLRQ. You may have heard of polarized VXQJODVVHV 7KH OHQV RI WKH VXQJODVVHV KDYH D VSHFLDO YHUWLFDO ¿ OWHU WKDW LV GHVLJQHG WR UHGXFH JODUH FDXVHG E\ OLJKW PRYLQJ DORQJ WKH KRUL]RQWDO SODQH 7KH YHUWLFDO ¿ OWHUV RQ SRODUL]HG OHQVHV RQO\ DOORZ OLJKW moving along the vertical plane while the light moving on the horizontal plane is blocked.

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STEMscopedia Have you ever been riding in a car on the highway when you heard an ambulance approach and speed by? As the ambulance approaches, the siren sounds very high pitched, and as it passes by and travels away, the siren sounds much lower pitched. This change in the frequency of the pitch is due to the 'RSSOHU HIIHFW. Due to the Doppler effect, there is an apparent shift in the frequency of the wave.

As the source of the sound moves closer to the observer, there is an upward shift in frequency. This is because the sound waves enter the observer’s ear at a shorter wavelength and increased frequency, causing the sound to be more high pitched. As the source of the sound moves farther away, there is a downward shift in frequency as the wavelengths increase, which causes a lower-pitched sound to the observer. The Doppler effect is also apparent with light waves. As an object moves away from us, the light is shifted toward the red end of the visible-light spectrum as the wavelength increases.

When objects move toward us, light is shifted toward the blue end of the visible-light spectrum as the wavelength decreases. This is known as UHGVKLIW DQG EOXHVKLIW, and it allows us to determine if objects are moving toward us or away from us.

some e r a hat 5. W examples other 'RSSOHU

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STEMscopedia Dr. William L. Wilson, PhD, is the executive director of the Center for Nanoscale Systems at Harvard 8QLYHUVLW\ :LOVRQ KDV DQ H[WHQVLYH KLVWRU\ LQ WKH ¿ HOG RI RSWLFV ZKLFK IRFXVHV RQ WKH VFLHQWL¿ F VWXG\ of the behavior of light. He is the chief scientist and founder of InPhase Technologies, which is focused on using holographic storage. Holographic storage allows for millions of bits of storage on a very small disc rather than smaller amounts of storage on a larger disc, like a CD. In holographic storage, rather than using one laser (like with CDs or Blu-ray), there are two intersecting lasers that scan the hologram, allowing for retrieval of data from the storage medium.

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STEMscopedia As waves move through media, they can behave in different ways as they encounter objects, new PHGLD DQG RWKHU ZDYHV 5HÀ HFWLRQ RFFXUV ZKHQ D ZDYH KLWV D VXUIDFH DQG ERXQFHV EDFN WRZDUG WKH original direction and medium from which it was traveling. Refraction occurs when a wave passes through to a new medium and changes the direction and angle of travel because light and sound travel at different rates in different media. Refraction is what causes pencils placed in water to appear broken; light travels faster in air than in water. Diffraction occurs when waves travel through gaps or holes and around objects. Superposition occurs when two or more waves are traveling along the same medium and interact with each other, causing interference. When the two waves combine, there is a resultant wave that is either larger or smaller than the two individual waves. If the resultant wave is larger, constructive interference is occurring, and if the resultant wave is smaller or nonexistent, this is due to destructive interference. Standing waves are waves that appear to be vibrating vertically but not moving horizontally. This is due to destructive interference of two waves that form nodes, which appear to have no displacement, and antinodes, which are areas of maximum amplitude. Light waves vibrate in more WKDQ RQH SODQH NQRZQ DV XQSRODUL]HG OLJKW 6SHFLDO ¿ OWHUV DQG OHQVHV FDQ IRUFH OLJKW WR WUDYHO LQ RQO\ RQH plane and become polarized. This process is known as polarization. The Doppler effect occurs as sources of sound or light move closer to or farther from an observer. As a source of sound or light moves closer to an observer, the wavelengths increase in frequency and decrease in wavelength. As the source moves farther away from an observer, the frequency decreases and wavelength increases. This is the reason why a siren sounds high pitched as it approaches you and lower pitched as it is moving away from you.

&RQQHFW ,W Why can we see ourselves in the mirror? $ PLUURU LV D UHÀ HFWLYH VXUIDFH ZKLFK KHOSV XV VHH RXU RZQ LPDJH /LJKW ZDYHV WUDYHO WKURXJK WKH DLU KLW WKH UHÀ HFWLYH VXUIDFH RI WKH PLUURU DQG ERXQFH EDFN WRZDUG WKH DLU $V WKH OLJKW ZDYHV WUDYHO EDFN from the same direction and medium that they initially came from, those light waves hit the portions of our eyes that allow us to see. We see our image clearly because mirrors are smooth and shiny, and the UHÀ HFWHG UD\V FUHDWH DQ DQJOH RI UHÀ HFWLRQ WKDW LV WKH VDPH DV WKH DQJOH RI LQFLGHQFH )XQKRXVH PLUURUV are a common attraction at carnivals and fairs. If you were to stand in front of a funhouse mirror, you ZRXOG VWLOO VHH \RXU UHÀ HFWLRQ EXW WKH LPDJH ZRXOG EH GLVWRUWHG <RX PLJKW DSSHDU PXFK WDOOHU WKDQ \RXU normal height, or your head might be large and wavy. This occurs because the surface of the funhouse mirror is not smooth and shiny like the mirrors at home. Instead, these mirrors often have a concave or FRQYH[ VKDSH LQ VRPH SODFHV DQG D GXOOHU DSSHDUDQFH 7KLV FDXVHV WKH UHÀ HFWHG UD\V WR EH ERXQFHG EDFN DW GLIIHUHQW DQJOHV RI UHÀ HFWLRQ ZKLFK FDXVHV D GLVWRUWHG LPDJH

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STEMscopedia Summarize It A light wave is traveling through air when it hits a new medium and changes its angle and direction of travel. This is known as– $ UHÀ HFWLRQ % refraction. & diffraction. ' interference.

Two waves are traveling along the same medium in opposite directions. Wave A has an amplitude of 2, and Wave B has an amplitude of 2. What will the resultant wave look like? $ Constructive interference will occur with an amplitude of 4. % Destructive interference will occur with an amplitude of 4. & Constructive interference will occur with an amplitude of 0. ' Destructive interference will occur with an amplitude of 0.

You are standing in the hallway, and you hear two teachers talking around the corner. This is possible because of the _______________ of sound waves. $ UHÀ HFWLRQ % refraction & diffraction ' interference What are standing waves, and how do they form?

Standing waves are waves that appear to be vibrating but not moving horizontally. It is when two or more waves with the sample amplitude and frequency interfere while traveling in the same medium in opposite directions. When the two waves meet, they undergo destructive interference at their midpoints, creating a node of no displacement. Their crests and troughs combine to form areas of maximum amplitude called antinodes.

Explain why a racecar driving on a track sounds high pitched as it travels in front of you but low pitched as it drives on the opposite side of the track.

This is due to the Doppler effect. As the racecar drives close by, the sound waves from the racecar vibrate in the observer’s ear with a higher frequency, which causes a higher-pitched sound. As the racecar drives on the opposite side of the track, the vibrations reach the observer’s ear at a lower frequency, causing a lower-pitched sound.

What is the process of polarization?

Polarization is the process of turning unpolarized light into polarized light. Unpolarized light waves vibrate in more than one plane of motion while polarized light travels in only one plane of motion.

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Image Formation

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215

STEMscopedia When you look at yourself in a mirror, you are looking at an image. The image produced by the mirror is a result of the shape of the surface of the mirror and how light waves interact with it.

ng a i e b ine a 1.. Imag ild seeing ch Q small ŎV UHş HFWLR W H SDUHQ URU IRU WK LU UH LQ D P H :KDW D LP Ş UVW W WKLQNLQJ" \RX

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Image Formation

STEMscopedia :KDW ,V DQ ,PDJH" you are not literally inside or behind the mirror.

What you are seeing is an image of yourself. But what is an image? How is an image formed? Why does it look like you are behind the mirror?

This picture shows several images of the same toy dog. The images produced are virtual images. How do you think the multiple images were achieved?

An optical image is the apparent reproduction of an object. It is formed when light rays interact with mirrors or lenses. The images in the mirrors are virtual images; they appear to be in the mirror but are not really there. Optical images can also be real images, which, as the name suggests, are really formed.

The type of image produced is determined by the shape of the surface of a mirror or lens. A ray diagram is used to illustrate how light rays interact with a mirror or lens to produce an image and show if the image is virtual or real.

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Image Formation

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STEMscopedia 3ODQH 0LUURU ,PDJHV A plane mirror is the most common type of mirror that people use to look at themselves. ,W KDV D À DW VXUIDFH ZKLFK GRHV QRW GLVWRUW WKH image that is formed. The image appears to be behind the mirror, but if you look behind the mirror, the image is not there. The image does not really exist; it is a virtual image. So how can you see it? A ray diagram will help explain this.

In the diagram of a plane mirror to the right, the lines show two light rays coming from the top RI WKH REMHFW %RWK UD\V UHÀ HFW EDFN WRZDUG WKH eye, but at slightly different angles. 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.

Similar rays are drawn from the bottom of the object, and their extensions would intersect at the bottom of the image.

In order for your eye to see an object, light rays must bounce off the object to your eye. If you look directly at an object, the light rays from the object enter directly into your eye.

When you look at a mirror, you are not seeing the light rays directly from the object. The light rays from the object encounter the mirror at an angle, called the angle of incidence. The light UD\V DUH WKHQ UHÀ HFWHG WR \RXU H\H DW WKH VDPH angle, called the DQJOH RI UHÀ HFWLRQ. Your brain interprets the UHÀ HFWLRQ as if the light had traveled in a straight line to your eye and creates an image in the mirror. Notice in the diagram that no light rays are actually creating the virtual image. Because no light rays are used to create it, the image is not real.

The virtual image that is produced by the plane mirror is very similar to the object that produced it. The image is upright, the same size, and the same distance from the mirror as the object. But there is a difference; the image is reversed from left to right.

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Image Formation by Reflection in a Plane Mirror •The virtual image is located behind the mirror.

Observer Reflecting surface

•The image is reversed left to right.

In front of the mirror

Behind the mirror

•The image and object are the same distance from the mirror.

•The image is the same size as the object.

Real object

Virtual image

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Image Formation

STEMscopedia /LJKW UD\V UHÀ HFW RII PLUURUV EXW WKH\ SDVV WKURXJK OHQVHV $V OLJKW UD\V HQFRXQWHU D OHQV WKH\ FKDQJH direction in a process called refraction. Exactly how the light rays change direction depends on the shape and thickness of the lens as well as the material from which the lens is made.

A convex lens is thicker in the middle than it is at the edges. As light rays pass through the curved lens, they are refracted at different angles. This causes the light rays to converge into a single point.

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int

Light rays refract through a convex lens and converge to a single point.

When light rays converge, they form a real image. The lens of your eye is a convex lens. It produces a real image on the retina of your eye, enabling you to see. The location of the object in relation to the lens determines whether the light rays from the object will converge once they are refracted by the lens.

Image Formation

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STEMscopedia For the light rays from an object to converge and produce a real image on the other side of the lens, the object must be located outside the focal point of the lens, as shown in the ray diagram.

Notice that the light rays from the top of the object are refracted to the bottom of the image that is produced. As a result, the image is inverted. If the object is placed at twice the focal length (2F) of the lens, the image will be the same size and same distance from the lens as the object (as shown). If the object is moved farther from the lens, the image will still be inverted but will be smaller than the object and move closer to the lens, as shown.

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Image Formation

STEMscopedia thin lens equation can be used to calculate where the image will appear.

1 f

1

1 di

d

o

f = focal length do = object distance di = image distance In the image on the previous page, assume that the focal length is 4.0 cm and the object is located at 10.0 cm from the center of the lens. Calculate the image distance.

1 f

1

do

1 di

1 o 1 10.0 4.0

1 di

0.15 0.15

1 di

di

1 0.15

di

6.7

The image is 6.7 cm from the lens.

How do you think the image would appear if the object were between F and 2F? Telescopes use convex lenses to produce real images of distant objects. Cameras use convex lenses to SURGXFH UHDO LPDJHV WKDW FDQ EH VWRUHG GLJLWDOO\ RU RQ ¿ OP 3URMHFWRUV XVH FRQYH[ OHQVHV WR SURGXFH UHDO images that can be projected on screens, like the image of the cat at the beginning of this lesson.

Image Formation

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STEMscopedia For objects that are located between the focal point and the lens, the image that is formed is very different.

Refraction of Object inside F

Front

F

Object

F

Back

Image: magnified virtual image on the same side of the lens as the object Applications: magnifying glass, binoculars, telescopes When an object is located inside the focal length of the lens, the light rays that are refracted by the lens do not converge, so no real image is formed. However, to an observer looking through the lens, a virtual image is formed. This virtual image is upright and larger than the object and on the same side of the lens. This is how a magnifying glass is able to make an object appear larger. The farther the object is from the lens, the larger the virtual image will appear until the object reaches the focal point of the lens.

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Image Formation

STEMscopedia So what happens if an object is located at the focal point of the lens? Does it produce a real image or a virtual image?

The answer is—neither. For an object that is placed at the focal point, the light rays do not converge to form a real image, nor is a virtual image produced.

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Image Formation

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STEMscopedia 6SKHULFDO 0LUURU ,PDJHV ,PDJHV IRUPHG E\ D SODQH PLUURU DUH DFFXUDWH UHÀ HFWLRQV RI DQ REMHFW WKH\ DUH WKH VDPH VL]H DQG DSSHDU WKH VDPH GLVWDQFH DZD\ DV WKH REMHFW EHLQJ UHÀ HFWHG 6SKHULFDO PLUURUV DUH FXUYHG DQG SUHVHQW DQ LPDJH WKDW GRHV QRW UHÀ HFW UHDOLW\ $ convex mirror is a type of spherical mirror where the surface of the mirror curves outward. Since they produce wide-angle, upright images, they are perfect as side-view mirrors on cars, allowing drivers to get a better view of what’s happening around them.

A concave mirror is a type of spherical mirror where the surface of the mirror curves inward. Concave mirrors can produce images that are larger or smaller than reality; their images can also be upright or inverted.

The mirror formula is the same as the thin lens formula and shows the relationship between the focal length, object distance, and image distance. f = focal length

1 f

1

do

1 di

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For a convex mirror, the focal length will always be a negative number because the focal point of these mirrors is on the opposite side of the mirror from the object. For a concave mirror, the focal length will always be positive because the focal point is on the same side as the object. The image distance for spherical mirrors can be positive or negative depending on whether the image is real or virtual. A convex mirror always produces virtual images, so the image distance is always negative.

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Image Formation

STEMscopedia J $OYDQ &ODUN DQG 6RQV 7HOHVFRSH 0DNHUV Alvan Clark (1804–1887) was an accomplished artist who created hundreds of oil portraits and miniatures. Following the appearance of the Great Comet of 1843, Alvan taught himself to grind and polish a glass lens to help his son George (1827–1891) construct a small telescope. In 1846, he and *HRUJH IRXQGHG WKH ¿ UP $OYDQ &ODUN 6RQV $OYDQ¶V VHFRQG VRQ $OYDQ *UDKDP ± MRLQHG WKH ¿ UP LQ WKH HDUO\ V DQG WKH IDPLO\ EHFDPH IDPRXV IRU PDNLQJ OHQVHV IRU VRPH RI WKH ODUJHVW refracting telescopes in the world. They ground the lens for the 91 cm telescope at the Lick Observatory, which is still the third largest refracting telescope, and the 100 cm telescope at Yerkes Observatory, ZKLFK LV WKH ODUJHVW VXFFHVVIXO UHIUDFWLQJ WHOHVFRSH LQ WKH ZRUOG ,Q WKH ODWH V $OYDQ WKH IDWKHU discovered two double stars using refracting telescopes. In 1862, while testing a lens he had made, Alvan Graham (the son) discovered the star Sirius B, the predicted companion star of Sirius. It was the ¿ UVW HYHU REVHUYDWLRQ RI D ZKLWH GZDUI VWDU 'XULQJ KLV OLIHWLPH $OYDQ *UDKDP GLVFRYHUHG GRXEOH stars.

Image Formation

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STEMscopedia Light rays interact with mirrors and lenses in different ways to produce images. If the light rays converge, a real image is produced and can be projected. If the light rays do not converge, a virtual image is created.

&RQQHFW ,W How did your parent get in the mirror? :KHQ D FKLOG VHHV D SDUHQW LQ WKH PLUURU IRU WKH ¿ UVW WLPH ZKDW GR WKH\ WKLQN" ,V WKHLU SDUHQW UHDOO\ LQ the mirror? Fortunately, children do not seem to be confused about this for long.

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Image Formation

STEMscopedia 6XPPDUL]H ,W 1. What type of image is produced where light rays converge?

A. Virtual image B. Real image C. 5HÀ HFWHG LPDJH D. Refracted image 2. What type of image is produced by a plane mirror?

A. Upright, virtual image B. Inverted, real image C. ,QYHUWHG UHÀ HFWHG LPDJH D. Upright, refracted image 3. What determines the type of image that is produced by a thin convex lens?

A. The thickness at the center of the lens B. The size of the object C. The amount of light rays being refracted D. The distance of the object from the lens 4. Compare and contrast a virtual image that is produced by a plane mirror and one that is produced by a thin convex lens.

Both virtual images are produced by light rays that do not converge and are upright. The image that is produced by the mirror is the same size as the object and is left-right reversed. The image that is produced by the lens is larger than the object and not left-right reversed.

5. Why can a real image be projected, but a virtual image cannot?

A real image is produced by converging light rays, so it exists and can be projected. A virtual image does not really exist. It only appears to exist. Because it is not made of real light rays, it cannot be projected.

6. How do light rays behave differently when encountering a plane mirror and convex lens? /LJKW UD\V DUH UHÀ HFWHG E\ D SODQH PLUURU VR WKH\ ERXQFH RII LW DQG GR QRW SDVV WKURXJK 7KH\ DUH UHÀ HFWHG DW WKH VDPH DQJOH WKDW WKH\ HQFRXQWHU WKH PLUURU /LJKW ZDYHV DUH UHIUDFWHG E\ WKH FRQYH[ OHQV bending at different angles as they pass through the different thicknesses of the lens.

Image Formation

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Electromagnetic Spectrum

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229

STEMscopedia Televisions are very common and are used by many people. You probably have one or more of them in your home. The radio waves that transmit signals to your television are the same type of energy as the deadly gamma rays in radioactive materials. Both are forms of electromagnetic waves.

Radio Waves

Gamma Rays

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le tromagneti Spe trum

STEMscopedia Electromagnetic Waves are disturbances that transfer energy.

Electromagnetic waves are transverse waves. They are characterized by their amplitude (how tall they are) and their wavelength (how long they are).

The amplitude of the wave is determined by the energy of the disturbance that created it. Think about dropping a stone in a pond. The heavier the stone that is dropped, the more energy that disturbs the water and the higher the waves that are created.

Wavelength Crest Amplitude

Trough

The wave’s length is determined by how many of them are created at a time, also known as wave frequency. The frequency of the wave is determined by the frequency of the vibrations that cause the wave.

If a lot of waves are created, the frequency is high, so the waves are closer together. If fewer waves are created, the frequency is low, and the waves are farther apart.

Each wave transfers energy by mass-less particles called photons. The more waves that pass by, the more energy that is transferred.

This means that waves of the same amplitude with higher frequency transfer more energy than waves with lower frequency.

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le tromagneti Spe trum

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STEMscopedia The range of frequency and wavelength for electromagnetic waves is represented on the electromagnetic (EM) spectrum.

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Wavelengths can be kilometers long or shorter than the distance across an atomic nucleus. This wide range of wavelengths means that there is a correspondingly wide range of frequencies. With increasing IUHTXHQF\ FRPHV KLJKHU HQHUJ\ 7KH HOHFWURPDJQHWLF VSHFWUXP FODVVL¿ HV GLIIHUHQW W\SHV RI ZDYHV EDVHG on their wavelength and frequency. Because it is a continuous spectrum, there is some overlap in WKH FODVVL¿ FDWLRQV 7KH ORQJHVW ZDYHOHQJWKV DUH FODVVL¿ HG DV radio waves. Radio waves range from about 1 millimeter to 100 kilometers long. Their long wavelength and low frequency mean that they are the lowest-energy electromagnetic waves. Radio waves are emitted in nature by lightning and celestial objects.

Microwaves range from 1 millimeter to about 1 meter long and are sometimes considered part of the radio wave category. They are generated naturally by stars and comprise the cosmic microwave background radiation that is left over from the formation of the universe. They can also be produced by atoms and molecules.

Infrared rays (IRs) are next on the EM spectrum. Their name indicates their location, which is immediately next to the wavelengths of red visible light. Infrared rays range from a few millimeters long to microscopic lengths of about 0.7 micrometers. Infrared waves are emitted by hot objects and are sometimes referred to as heat radiation.

Visible light LV WKH QH[W FODVVL¿ FDWLRQ RI (0 ZDYHV DQG LV WKH VPDOOHVW UDQJH RQ WKH VSHFWUXP Wavelengths of visible light are measured in nanometers. As indicated by the name, these waves have enough energy to stimulate cells in your eyes and allow you to see. The colors of visible light are determined by their wavelengths within this part of the spectrum. In order from longest to shortest, they are red, orange, yellow, green, blue, indigo, and violet. Visible light is emitted naturally by celestial objects and can be emitted by atoms and molecules.

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le tromagneti Spe trum

STEMscopedia ultraviolet (UV) waves. UV waves are also measured in nanometers. The energy of ultraviolet waves from the Sun causes skin to tan but can EH KDUPIXO FDXVLQJ VXQEXUQ VNLQ GDPDJH DQG VRPH IRUPV RI FDQFHU 7KH 6XQ¶V 89 UD\V DUH EHQH¿ FLDO in stimulating skin to produce vitamin D. Ultraviolet waves are emitted naturally by celestial objects.

As frequency increases, waves become more harmful. Next to ultraviolet waves are X-rays. These highenergy waves are not much longer than an atom, measuring from about 10 to 0.01 nanometers. They are able to penetrate skin and body tissue and cause damage. Long-term exposure can cause many health problems, including radiation sickness and cancer. X-rays are emitted naturally by some celestial objects and some atoms.

The highest-frequency electromagnetic waves are gamma rays. Gamma waves are measured on the subatomic level. Due to their high energy, gamma rays can destroy living cells. This makes them extremely dangerous to living organisms.

Gamma rays are emitted naturally by some celestial objects and by radioactive atoms. They can also be formed by atmospheric interaction with cosmic rays.

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le tromagneti Spe trum

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STEMscopedia Electromagnetic waves carry energy, and that energy can be put to use. Because of their unique properties, the different types of electromagnetic waves have different applications.

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Heat lamps, IR remote controls, infrared telescopes, infrared cameras, night-vision goggles

Visible Light

Optical devices, cameras, telescopes, light bulbs

Ultraviolet Waves

Space telescopes, blacklights, tanning beds, medical and food sterilization

X-rays

Space telescopes, medical imaging, industrial imaging, security screening

Gamma Rays

Space telescopes, medical screening, radiotherapy, medical and industrial sterilization, nuclear power

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le tromagneti Spe trum

STEMscopedia Observational Tools for Electromagnetic Waves The tools that scientists have used to observe electromagnetic waves have changed over time. The earliest observations were done with just the human eye. The ancient Greeks did this more than 2,000 years ago. As time progressed, new tools were invented to help people study electromagnetic waves.

These include the following: • • •

Lenses Mirrors Prisms

Lenses bend light by the process of refraction. Lenses allow scientists to focus light and project images.

0LUURUV XVH WKH SURFHVV RI UHÀ HFWLRQ WR ERXQFH OLJKW FKDQJLQJ LWV WUDMHFWRU\ 3ULVPV DUH D VSHFLDO NLQG RI lens that breaks up visible light into its component colors, allowing each to be studied.

Sir Isaac Newton famously used prisms and lenses to study the various colors of light. Our modern conception of the colors of light, which are well known as “ROY G BIV,” comes from Newton’s studies.

But technology does not rest, and progress always continues. Building on what Newton found, in 1814, Joseph von Fraunhofer invented the spectroscope to capture light and disperse it. Light from different sources can be analyzed to determine the chemical compositions of objects that emit light.

Interferometer perpendicular to Earth’s rotation

Interferometer parallel to Earth’s rotation

L 2QH RI WKH PRUH PRGHUQ WRROV LV WKH LQWHUIHURPHWHU 7KLV WRRO XVHV PLUURUV WKDW UHÀ HFW RQO\ VRPH OLJKW to create separate beams of light that have similar characteristics. This was used by Michelson and Morley to measure the speed of light. Ironically, they disproved what they were trying to prove using their modern tools. They were trying to detect the presence of luminiferous aether, which supposedly permeated space and was the carrier of light waves. They expected that light traveling with Earth’s rotation would move faster through the aether than light traveling at a right angle to Earth’s rotation, as shown in the images above. This was shown to not be the case. It was this experiment that helped inspire Albert Einstein to create the theory of special relativity, which showed that light travels at the same speed in a vacuum at all times—the speed of light.

More recent tools for observing electromagnetic radiation include various specialized telescopes, such as the Chandra X-ray Observatory, the Fermi Gamma-ray Space Telescope, and the James Webb Space Telescope. These telescopes specialize in X-rays, gamma rays, and infrared, respectively. Our view of the electromagnetic spectrum has broadened immensely! le tromagneti Spe trum

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STEMscopedia Dr. Anneila Sargent and Space Telescopes Dr. Anneila Sargent was born in Scotland. She earned a BSc in physics at the University of Edinburgh in 1963 and a PhD from the California Institute of Technology (Caltech) in 1978. She was a professor of astronomy at Caltech for many years, where she also served as the director of Caltech’s Owens Valley Radio Observatory. There, she led the effort to construct the Combined Array for Research in Millimeter-wave Astronomy (CARMA). She has also been involved with the planning of the international submillimeter wave array (Atacama Large Millimeter/Submillimeter Array, or ALMA) in Chile. She uses millimeter, submillimeter, and infrared observations of space to study how new stars are created in dense clouds of dust and gas and to look for potential sites for the formation of planets.

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le tromagneti Spe trum

STEMscopedia The electromagnetic spectrum arranges naturally existing electromagnetic waves according to their ZDYHOHQJWKV DQG IUHTXHQFLHV 7KH SURSHUWLHV RI WKH GLIIHUHQW FODVVL¿ FDWLRQV RI HOHFWURPDJQHWLF ZDYHV make them useful for a variety of applications.

Connect It How can a harmless television signal and dangerous radioactive waste be caused by the same type of energy?

Electromagnetic waves are one type of energy, but the amount of energy that is carried by different FODVVL¿ FDWLRQV RI HOHFWURPDJQHWLF ZDYHV GHSHQGV RQ DPSOLWXGH DQG IUHTXHQF\

is the y h y 5. W energ f o t amoun carried by t s that i es differen av t radio w the amoun from gy that is s er of en y dangerou d b carrie ma rays? gam

le tromagneti Spe trum

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STEMscopedia 1. What determines the wavelength of an electromagnetic wave?

A. Amplitude B. Frequency C. Energy D. Speed 2. :KDW GHWHUPLQHV WKH RUGHU RI ZDYH FODVVL¿ FDWLRQ RQ WKH HOHFWURPDJQHWLF VSHFWUXP" A. Speed and frequency B. Amplitude and speed C. Frequency and wavelength D. Wavelength and amplitude 3. Which types of electromagnetic waves can be most harmful to humans?

A. Microwaves, infrared rays, X-rays B. Gamma rays, ultraviolet rays, radio waves C. X-rays, ultraviolet waves, visible light D. Ultraviolet waves, gamma rays, X-rays 4. Why are different types of telescopes needed to study space?

Different celestial objects emit different types of electromagnetic waves. To effectively study these objects, telescopes that can detect these different types of waves are needed.

5. Why do ultraviolet waves from the Sun cause skin damage and cancer when visible light waves from the Sun do not?

Ultraviolet waves have a higher frequency than visible light waves do, so they carry more energy. The increased energy makes them more damaging to human tissues.

6. Why is there overlap in the categories of electromagnetic waves?

Electromagnetic waves are categorized based on their wavelength and frequency, but the spectrum is continuous. The waves on a continuous spectrum gradually change in wavelength and frequency, so WKHUH LV QRW D GH¿ QLWH GLVWLQFWLRQ EHWZHHQ WKH FODVVL¿ FDWLRQV

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le tromagneti Spe trum

Speed of Light

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241

STEMscopedia Think about what you hear when you see lightning. Do you hear thunder at the same time as you see lightning? No, you see the lightning before you hear the thunder that goes along with it. This tells you that light travels faster than sound. What is the speed at which light travels, and how do we measure it?

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Speed o Lig t

STEMscopedia Scientists have been fascinated with the behavior of light since the 1600s, when Sir Isaac Newton theorized that light was composed of particles. As time went on, scientists discovered that light actually consists of and behaves like waves, which explains how light is able to travel through space and does not need any matter to carry the waves along.

Amplitude, wavelength, and frequency can be observed when graphing the wave cycle of light.

Amplitude is the height of a wave from the midline to the crest or trough of the wave. Wavelength is the distance between the crests of waves, measured in meters, or how far apart the tops of the waves are from each other. Frequency is the speed of a wave, or the number of wave cycles in a given amount of time, and is often measured in cycles per second or hertz (Hz). Wavelength and frequency are inversely related, meaning that as the wavelength of light decreases, the frequency increases, and vice versa.

Visible light is one kind of electromagnetic radiation; the different kinds of electromagnetic radiation are described in the diagram of the electromagnetic spectrum below.

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STEMscopedia

are 1. How h and ngt wavele y related? nc freque

7KH ¿ UVW NQRZQ UHFRUG RI HYLGHQFH IRU WKH VSHHG RI OLJKW ZDV LQ ZKHQ D 'DQLVK DVWURQRPHU QDPHG Ole Romer observed the amount of time that it took for Jupiter’s moons to eclipse, or project their shadows onto the surface of the planet as they were crossing. He proclaimed that light must travel at a ¿ QLWH VSHHG EHFDXVH WKH GLVWDQFH IURP -XSLWHU FKDQJHG WKH DPRXQW RI WLPH WKDW LW WRRN IRU WKH LPDJH WR reach our eyes. Based on his data collection and calculations, he found the value of the speed of light ZLWKLQ D HUURU :KLOH WKLV PD\ EH D ODUJH PDUJLQ RI HUURU KLV FRQFOXVLRQ DERXW OLJKW WUDYHOLQJ DW D ¿ QLWH VSHHG ZDV DFFXUDWH DQG JURXQGEUHDNLQJ Scottish scientist James Clerk Maxwell further showed that all light waves, no matter the type or wavelength, travel at the same speed in a vacuum. While there are some atoms between the planets in our solar system and stars in the galaxies, they are minimal enough that light still travels at a ¿ QLWH VSHHG 7KLV VSHHG KDV EHFRPH NQRZQ DV WKH YDULDEOH c and is measured to be approximately P V RU [ P V 7KH WHUP speed of light, without additional information, refers to light traveling in a vacuum; however, when light travels through a medium such as air or water, it moves VORZHU ,Q VFLHQWLVWV ZHUH DEOH WR JHW OLJKW WR VORZ GRZQ WR P V DQG LQ WKH\ ZHUH able to make it stop completely—momentarily.

The speed of light is important to all studies of our universe. It is used to describe distance, time, atoms, gravity, electricity, and magnetism. The value of the speed of light is unique in its properties. If we were traveling in space at nearly the speed of light—not quite, but close—we would see light moving toward us or away from us with the same value of c [ P V © Accelerate Learning Inc. – All Rights Reserved

Speed o Lig t

STEMscopedia Doppler effect, there is a shift in the wavelength of light as it moves toward or away from us. Within the spectrum of visible light, this is apparent in a color change. Christian Doppler not only described the change in pitch of moving objects but also the colors of moving objects.

The image below shows how wavelengths of approaching sources are compressed and those of receding sources are stretched out. The light from approaching sources shifts to the blue end of the spectrum, and light from receding sources shifts to the red end of the spectrum. These shifts are aptly called blueshift and redshift, respectively. We notice this in the light shift from stars in the universe, which allows us to determine whether they are moving toward us or away from us. These shifts are also referred to as Doppler shifts after the scientist who enlightened us. The amount of Doppler shift depends on the speed at which light is approaching or receding.

do you y h W 2. slows t h g li think n passing whe down h a medium throug or water? like air

Speed o Lig t

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STEMscopedia Albert Einstein’s famous special theory of relativity impacted the study of energy by relating time, space, and mass to one’s frame of reference. He stated that time passes relative to one’s perspective, similar to how throwing a ball could be described differently from the perspective of the thrower and the catcher.

The frame of reference sets the coordinates that describe the motion that is being observed. The study of motion describes how speed and time are relative to an observer. For example, when a car is traveling ZHVWZDUG DW P V DQG SDVVHV D VHFRQG FDU WUDYHOLQJ WKDW LV HDVWZDUG DW P V SDVVHQJHUV LQ WKH ¿ UVW FDU ZLOO IHHO DV LI WKH\ DUH WUDYHOLQJ DW D VSHHG RI P V 6LPLODUO\ (DUWK LV URWDWLQJ QHDU P V EXW ZH GR QRW IHHO WKDW PRWLRQ LQ RXU RZQ IUDPH RI UHIHUHQFH The motion is relative to the perspective of the observer’s frame of reference. Einstein’s famous equation for special relativity, E = mc2, explains how small amounts of mass that are traveling at the speed of light can be transformed into large amounts of energy. His initial publication neglected the implications of gravity and focused on astronomical distances and traveling at immense speeds. His revision later included gravity and widened the applications for general relativity. Essentially, he stated that as objects PRYH QHDU WKH VSHHG RI OLJKW WKHLU PDVVHV EHFRPH QHDUO\ LQ¿ QLWH DORQJ ZLWK WKH HQHUJ\ WKDW LV UHTXLUHG to move them.

Einstein used an example of lightning striking two trees simultaneously with a train car halfway between them. He stated that a bystander on the track would observe the lightning strikes simultaneously, as they occurred. However, a person in the train car would see the bolt ahead of the train before the one behind the train because they were moving forward. Because the simultaneous events could be seen differently by each observer and the speed of light does not change, it must be that time moves differently at rest than it does when an observer is in motion. As the speed of the observer increases, time moves more slowly than it does when the observer is at rest, which is a phenomenon known as time dilation.

ld you u o w 3. How e passage e tim e imagin for someon feels ar the e n g n traveli of light? speed

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Speed o Lig t

STEMscopedia Newton’s Laws and the Speed of Light Newton’s laws are a limiting case of Einstein’s special theory of relativity at speeds that are much slower than the speed of light. It is not that Newton’s laws are incorrect and Einstein’s are correct. Both laws mathematically model what happens. Einstein’s laws just happen to cover a wider variety of cases. As both are models, we should assume that not every case necessarily needs to be covered.

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1HZWRQ¶V ¿ UVW ODZ VWDWHV WKDW DQ REMHFW ZLOO UHPDLQ DW UHVW RU LQ XQLIRUP PRWLRQ XQWLO LW LV DFWHG on by an external force. This law works well in special relativity—with one limiting factor. If an object keeps a constant speed that is near the speed of light but no force acts on it, it will keep moving at this constant speed that is near the speed of light. If a force acts on it, the limit is that it cannot go faster than the speed of light.

•

Newton’s second law states that force is equal to mass multiplied by acceleration. Acceleration depends on time. Time is relative to the observer’s motion. If the frame of reference is inertial, this equation for force acts as usual at lower speeds. However, if someone attempted to push an object from rest to relativistic speeds, the object would appear to become more massive and thus harder to accelerate. Again, the speed of light is still the limiting factor.

•

Newton’s third law states that every action has an equal and opposite reaction. This law works until you apply force to something that is already near the speed of light. Energy is added to the system, but it doesn’t move much faster. And the speed of light cannot be exceeded under any circumstance.

Einstein’s predictions have been backed up by multiple experiments. It has been thoroughly demonstrated that light moves at the same speed in any reference frame, and nothing goes faster than the speed of light. Implications of this led to higher-level physics concepts, such as the following.

• •

Time dilation: Time appears to move slower for someone who is going faster.

Length contraction: Faster objects measure smaller in length than slower objects.

It is not that Newton and Einstein contradict one another. It is more that Newton’s laws are more applicable when a large object is moving slowly (compared to the speed of light). Einstein’s laws, which DUH PRUH GLI¿ FXOW DQG LQFOXGH OHQJWK FDOFXODWLRQV DOORZ IRU ZRUNLQJ ZLWK REMHFWV WKDW DUH PRYLQJ YHU\ fast. When an object is moving too fast, Newton’s laws are no longer an accurate prediction of what the object will do. This is not because Newton was wrong but rather because of these limiting factors.

Speed o Lig t

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STEMscopedia Max Planck, a German physicist, observed that an object that began as black would appear red, then yellow, and then white as the temperature of the object increased. He determined that the color change was due to a change in energy as the temperature increased. From this, he established Planck’s constant (h), 6.626 X 10í J*s, where J (joule) is the unit of energy. ,Q +HLQULFK +HUW] ZDV ZRUNLQJ ZLWK UDGLR ZDYHV ZKHQ KH QRWLFHG XOWUDYLROHW OLJKW VKLQLQJ RQ WZR metal electrodes. The electrodes had a voltage applied across them, and the light changed the voltage of the electrode. This became known as the photoelectric effect. The photoelectric effect occurs when electrons are ejected as light shines on metal, creating an electric current, but not all frequencies of light will cause the effect.

At the turn of the 20th century, scientists were beginning to understand and agree on the nature of light behaving as a wave. Einstein used Planck’s theory to expand upon the photoelectric effect. He determined that light is a quantum of energy Wave Particle The Dual Nature Property that behaves like a stream of particles called Model Model photons. Einstein’s theory explains why of Light Reflection electrons are not ejected at all frequencies; so if the frequency and energy of a photon are too Refraction low, an electron will not be ejected, and the photoelectric effect will not occur. Therefore, Polarization different wavelengths of light must possess Waves different amounts of energy.

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Einstein’s revelation means that light can behave in one of two ways depending on how we view it—as a wave or as a particle. Tests ODWHU LQ WKH WK FHQWXU\ YHUL¿ HG WKDW OLJKW FRXOG act as both waves and particles, which is known as the dual nature of light.

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Speed o Lig t

STEMscopedia (QHUJ\ ( FDQ EH FDOFXODWHG IURP IUHTXHQF\ GLUHFWO\ XVLQJ ( K Y RU IURP ZDYHOHQJWK XVLQJ ( K F ૃ.

These variables can be calculated using the formulas in the examples below.

Example 1 'HWHUPLQH WKH HQHUJ\ RI D TXDQWXP RI UDGLDWLRQ WKDW LV WUDYHOLQJ ZLWK D IUHTXHQF\ RI [ 10 Hz. Energy (E = h v) E = (6.626 x 10í - V [ 10 Hz) ( [ í J Example 2 Calculate the frequency of a quantum of radiation with an energy of 2.12 x 10í J. Energy (E = hv) 2.12 x 10í J = (6.626 x 10í J*s) v Y [ 12 Hz Example 3 6XSSRVH WKDW WKHUH LV DQ HOHFWURPDJQHWLF ZDYH ZLWK D ZDYHOHQJWK HTXDOLQJ [ í cm. Calculate the frequency and energy associated with this wavelength.

3DUW , )UHTXHQF\ Y F NJ *Remember to change centimeters to meters (divide by 100).

Y [ P V [ í m) Y [ Hz Part II: Energy (E = h v) E = (6.626 x 10í - V [ Hz) ( [ í J

Speed o Lig t

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STEMscopedia g Luc Thévenaz, Physicist

/XF 7KpYHQD] ZDV ERUQ LQ LQ *HQHYD 6ZLW]HUODQG 7KLV 6ZLVV SURIHVVRU RI SK\VLFV VSHFLDOL]HV LQ WKH VWXG\ RI ¿ \ EHU RSWLFV DQG KHDGV WKH *URXS IRU )LEHU 2SWLFV 6FKRRO RI (QJLQHHULQJ DW D SXEOLF UHVHDUFK S S S J J S university known as École Polytechnique Fédérale de Lausanne. His team of researchers worked together WR GHYHORS D ZD\ WR VSHHG XS DQG VORZ GRZQ OLJKW XVLQJ ¿ EHU RSWLFV 6ORZLQJ WKH VSHHG DW ZKLFK OLJKW is transmitted leaves an optical memory or afterimage of the information, like an echo of a noise that was heard seconds before, and increasing the speed at which light travels can only be done in portions at this time. The implications of this stand to improve both telecommunication signals, which transmit LQIRUPDWLRQ WKURXJK ¿ EHU RSWLF OLQHV DQG PLFURZDYHV ZKLFK WUDQVPLW ZLUHOHVV VLJQDOV 7KHVH DUH currently bound by the speed at which equipment can process that information, as current technology is limited by the speed at which sensors can read the signals that are being transmitted.

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Speed o Lig t

STEMscopedia /LJKW FDQ EH PHDVXUHG FODVVL¿ HG JUDSKHG DQG FDOFXODWHG XVLQJ ZDYHOHQJWK IUHTXHQF\ DQG HQHUJ\ 7KH speed of light impacts how scientists study the universe. The way we understand distance, time, atoms, gravity, and more all centers on our understanding of the behavior of light. If we were able to travel at the speed of light through space, we would see light slow down due to the limitations of time and our frame of reference. Colors are determined through perceived wavelengths and frequencies of light, as demonstrated by the electromagnetic spectrum. However, that perception can be altered as objects move toward or away from our frame of reference. The speed of light impacts how the world around us is perceived, which alters our decisions in response to that perceived reality.

Connect It How is time affected by speed?

The observations that occur on Earth move at only a fraction of the speed of light. While there can be different frames of reference for events, special relativity assumes that light is traveling at a constant speed in all scenarios. Therefore, distance and time are the only factors that can change. Clocks that are traveling on a jet airplane move slower than those that are stationary on the ground, but because neither the plane nor Earth is moving anywhere near the speed of light, this difference in time is negligible.

e t wer je a 5. If \RX ZLWK DW ş \LQJ dlights on, a its he would you d ast how f the spee ive m perce coming fro t of ligh headlights? the

Speed o Lig t

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STEMscopedia 1. Which of the following travels the fastest?

A. Ultraviolet light B. Visible light C. Radio waves D. They all travel at the same speed.

2. What causes a shift in the appearance of a wave due to the motion of an observer?

A. Doppler effect B. Photoelectric effect C. Duality of light D. Frame of reference 3. What happens to the energy of a wave when the distance is increased?

A. Energy increases.

B. Energy decreases.

C. Energy remains unchanged.

D. Energy is relative to the frame of reference.

4. If two observers were moving at different speeds in a vacuum, how would they view light?

5. &DOFXODWH WKH HQHUJ\ RI D ZDYH WKDW LV WUDYHOLQJ ZLWK D IUHTXHQF\ RI [ 10 Hz.

6. Determine the energy that is produced from radiation with a wavelength of 2.6 x 10 m.

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Speed o Lig t

Patterns of Matter in the Universe

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255

STEMscopedia When you look up at the night sky, thousands of objects sparkle into view. If you gazed through a telescope, you would see many more of these objects. You are observing stars, which give off energy in the form of visible light.

However, the stars that you can see are only a very small portion of the universe. What objects in space, other than stars, make up the universe? What kinds of energy, other than light, do these objects give off? And how do scientists answer these and other questions about objects that are so far away?

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The Universe The universe contains everything that exists, from particles of matter that are smaller than an atom to the largest stars. The universe also includes all forms of energy, from the light that streams from stars to invisible radio waves and X-rays. Even time is part of the universe. Scientists think of time as beginning when the universe began.

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STEMscopedia been observed from Earth. The different colors are masses of matter as they were a short time after the universe was born. These masses of matter later became stars and galaxies.

All of the matter and energy in the universe is contained in a volume of space that scientists have discovered is constantly expanding. The expanding universe is similar to a balloon that is constantly LQÀDWLQJ 6FLHQWLVWV GR QRW NQRZ KRZ ODUJH WKH XQLYHUVH LV QRZ +RZHYHU WKH\ KDYH JDWKHUHG HYLGHQFH that the universe started very small and has grown in all directions ever since.

The most distant objects that have been detected are about 13.7 billion light-years away from Earth.

A light-year is a unit of distance. It is equal to the distance traveled by light in one year, which is approximately 9.5 trillion kilometers. So, light from the most distant objects that scientists have observed began its journey to Earth 13.7 billion years ago. If these objects are actually the most distant objects in space, they are also the farthest back in time. For these reasons, scientists estimate that the universe is about 13.7 billion years old.

To learn about the properties of objects in space, scientists study the energy that comes from these objects. The energy may be in the form of visible light or other components of the electromagnetic spectrum, such as radio waves and X-rays. The electromagnetic spectrum is an arrangement of forms of energy that travel through space in waves. Objects in space emit these forms of energy in different patterns. Scientists use special telescopes to detect these patterns and learn about the objects that emit them.

From its birth to the present, the universe has changed tremendously. Huge pockets of gas have been pulled together by gravity to form stars. In turn, these stars have been drawn together by gravity to form families of billions of stars. Stars that were born long ago developed, aged, and died. This process goes on today, and it will continue to go on in the future. <RX PD\ KDYH GLI¿FXOW\ LPDJLQLQJ KRZ JUDYLW\ FDQ ³SXOO WRJHWKHU´ JDVHV WR IRUP VWDUV 5HPHPEHU WKDW gases, like all forms of matter, are composed of particles in motion. These particles are tiny, but they have mass, so they are affected by gravity. As the density of a gas increases, gas particles collide more frequently and with greater force, causing the gas’s temperature to increase as well. Eventually, gases can become so hot that they ignite, becoming huge, burning spheres—stars.

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STEMscopedia Stars Stars are large objects in space that generate their own energy. Almost everything that you can see in the night sky with your unaided eyes is a star. (Exceptions include a few planets of our solar system, Earth’s Moon, and an occasional comet.) A star is a huge ball of gas that produces its own energy, mostly through nuclear reactions in its core. Light is the most obvious form of energy that is produced by a star. However, stars produce many other forms of energy, such as infrared radiation (or heat) and ultraviolet radiation. Gravity holds together the particles that make up the body of a star. In other words, a star is so massive that it is held together by its own gravity.

(DUWK 7KH QH[W FORVHVW VWDU 3UR[LPD &HQWDXUL LV OLJKW \HDUV DZD\ 5HFDOO WKDW D OLJKW \HDU HTXDOV 9.5 trillion kilometers; therefore, Proxima Centauri is about 40 trillion kilometers from Earth. Light from this star takes 4.22 years to reach Earth. So, when we see Proxima Centauri through a telescope, we see the star as it existed 4.22 years ago.

Scientists don’t know for certain how stars form. The most commonly accepted hypothesis is that stars form from vast clouds of dust and gas called nebulae (singular: nebula). The force of gravity is strong between the countless particles of dust and gas. Gravity causes the cloud to condense and eventually collapse on itself. As the center of the cloud becomes denser, it starts to spin and heat up. Gravity pulls more gas and dust particles into the hot, spinning mass—a process that continues for millions of years. Finally, the matter becomes so hot that it ignites. Nuclear reactions begin, and the nebula forms a star.

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STEMscopedia The stars in the universe are not all the same. Some are very large whereas others are relatively small.

Some are extremely hot; others are cooler. Some emit great amounts of energy; others emit less energy. Stars may be young, middle aged, old, or dying. They may be composed primarily of hydrogen, or they may contain mostly helium and heavier elements. Some are very bright; others are dimmer.

Their colors range from blue and white to yellow and red. ,Q WKH HDUO\ V 'DQLVK DVWURQRPHU (MQDU +HUW]VSUXQJ DQG $PHULFDQ DVWURQRPHU +HQU\ 1RUULV 5XVVHOO developed a way to classify stars according to their luminosity, temperature, and color. (Luminosity is the brightness of a star relative to the brightness of other stars. Luminosity is also called absolute EULJKWQHVV 7KLV UHODWLRQVKLS LV VKRZQ LQ D JUDSK FDOOHG WKH +HUW]VSUXQJ 5XVVHOO + 5 GLDJUDP ZKLFK LV shown below.

2Q WKH + 5 GLDJUDP VWDUV DUH SORWWHG DORQJ WKH ERWWRP D[LV E\ LQFUHDVLQJ VXUIDFH WHPSHUDWXUH ZKLFK LV measured in units called kelvins (K). (To convert a measurement in kelvins to degrees Celsius, subtract 273 from the Kelvin measurement.) Hotter stars are plotted on the left side of the diagram, and cooler stars are plotted on the right side.

Betelgeuse

SUPERGIANTS Rigel

10,000

Antares

Luminosity (the Sun = 1)

Pole star 100

Arcturus

GIANTS MAIN SEQUENCE

1

The Sun

0.01

WHITE DWARFS

0.0001 30,000

20,000

10,000

7,000

6,000

4,000

3,000

Temperature (Kelvin)/Stellar classification

Stars are plotted along the y axis by increasing luminosity. Brighter stars are plotted at the top of the diagram. Less-bright stars are plotted at the bottom of the diagram. The diagram shows a star’s luminosity relative to Earth’s Sun. So, stars alongside the 102 (100) tick mark are 100 times brighter than the Sun, and stars alongside the 10–2 (0.01) tick mark are 100 times dimmer than the Sun. Stars are plotted along the x axis by color. Blue and white stars are plotted on the left side of the diagram. Yellow stars are plotted at the FHQWHU RI WKH GLDJUDP 5HG DQG RUDQJH VWDUV DUH SORWWHG RQ WKH ULJKW side of the diagram.

0RVW VWDUV RQ WKH + 5 GLDJUDP IDOO LQWR RQH RI IRXU JURXSV 6WDUV in the main sequence make up the vast majority of stars in the universe. In general, the hotter a star is on the main sequence, the brighter and bluer it is. As stars age, they fall outside the main sequence and become giants or supergiants depending on their mass. As less-massive stars die, they become relatively tiny white dwarfs. More-massive stars die by exploding into powerful supernovas. (Even smaller stars live for billions of years. The Sun, which is an average-sized star in the main sequence, is about midway through its 10 billion–year life cycle.)

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e the r a t a 4. Wh roups of four g on an stars ram? iag H-R d

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STEMscopedia Habitable Zone Named after the developer of the planetary laws, the Kepler Space Telescope hunts for planets that may be able to contain life. These planets are located within the habitable zones around stars. The habitable zone is a zone that is in the range of distance from a star where liquid water might pool on WKH VXUIDFH RI DQ RUELWLQJ SODQHW +DYLQJ OLTXLG ZDWHU RQ WKH VXUIDFH LV GHSHQGHQW RQ VXI¿ FLHQW SUHVVXUH and temperature.

Water and Potential for Life: There are several chemical properties of water that make it a crucial component for life. Water is capable of dissolving almost anything. Water can exist in solid, liquid, and gaseous forms in a relatively narrow range of temperatures; this is a rare property.

Life as we know it on Earth uses a membrane to separate an organism from its environment. Staying alive requires taking in important materials for energy creation while at the same time keeping out toxic VXEVWDQFHV DQG ZDVWH SURGXFWV :DWHU LV OLTXLG DW (DUWK OLNH WHPSHUDWXUHV DQG EHFDXVH LW À RZV WKLV SURYLGHV DQ HI¿ FLHQW ZD\ WR WUDQVIHU VXEVWDQFHV IURP FHOO WR FHOO 'HULYLQJ HQHUJ\ IURP D VROLG LV SRVVLEOH EXW PXFK PRUH GLI¿ FXOW WKXV OLTXLG LV SUHIHUDEOH 7KH IDFW WKDW ZDWHU FDQ FDUU\ PDWHULDOV LQWR DQG RXW RI D FHOO UHODWHV WR WKH XQLTXH FKHPLFDO FRQ¿ JXUDWLRQ RI ZDWHU :DWHU¶V &KHPLFDO &RQ¿ JXUDWLRQ Water molecules are made of two hydrogen atoms bonded to an oxygen atom. The way they bond makes water a universal solvent; in other words, almost every substance can dissolve in water. Water molecules have polarity, with hydrogen atoms grouping together on one side of the molecule. This creates a positive region while oxygen holds the negative end of the charge. The positive hydrogen end attracts negative ions while the negative region attracts positive ions. With these properties, water makes the perfect medium for transmitting substances into and out of a cell. In particular, elements that are essential for life, such as phosphates or calcium ions, can be transmitted.

Phases of Water: Water can act as a solid, liquid, or gas in temperatures such as those on Earth.

Other molecules that meet the criteria to support life tend to be found in liquid form at temperatures or pressures that are not considered hospitable to known life-forms. Finding water in all three phases in VXFK D VPDOO UDQJH RI SUHVVXUH DQG WHPSHUDWXUH FUHDWHV RSSRUWXQLWLHV IRU OLIH WR À RXULVK Evolution of Life: :DWHU LV QRW RQO\ D À XLG WKDW KHOSV ZLWK OLIH¶V HVVHQWLDO SURFHVVHV LW DOVR PD\ have been the catalyst for carrying life to Earth. One of the theories about the origin of life, called panspermia, contends that icy comets crashed into Earth, carrying tiny organic molecules that formed as WKH SUHGHFHVVRUV RI OLIH 7UDYHOLQJ WKURXJK VSDFH KRZHYHU LV D GLI¿ FXOW MRXUQH\ ZLWK KLJK UDGLDWLRQ WKDW would destroy such delicate molecules. In solid form, water provided a shield from the radiation.

Other Possibilities: While water is essential to life on our planet, is it possible that there are life-forms out there that don’t follow the same criteria? Scientists have looked at other liquids that may play roles that are similar to water’s. They have searched for something that mimics our universal solvent and transport medium. Ammonia and methane are top choices. Ammonia is a polar molecule (as is water) DQG LV IDLUO\ DEXQGDQW LQ WKH XQLYHUVH +RZHYHU VFLHQWLVWV KDYH IDLOHG WR ¿ QG ODUJH DPRXQWV RI DPPRQLD in the solar system. Methane is not polar, but it can dissolve many substances. However, methane becomes liquid only at very cold temperatures (–296°F, or –182°C). Large lakes of liquid methane exist on Titan, which is a moon of Saturn. This is a possible spot for future exploration.

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STEMscopedia Every star in our night sky is part of a galaxy called the Milky Way. This is our home galaxy. However, the Milky Way is only one of billions of galaxies in the universe, and each one contains hundreds of billions of stars, planets, gases, and dust that are held together by the force of gravity. Most galaxies are invisible to the unaided eye. However, if you have keen vision, you might spot one on a clear night.

It would look like a faint, fuzzy patch of light. Viewed through powerful telescopes, galaxies appear in various shapes.

Spiral: Spiral galaxies are shaped like disks with arms spiraling out from a central hub. Most of the galaxies that are known to scientists—including the Milky Way—are spiral galaxies. The stars and other objects in a spiral galaxy rotate in the same direction around the galaxy’s center, like an incredibly fast-spinning pinwheel.

Lenticular: Lenticular galaxies form a subgroup of spiral galaxies. Lenticular PHDQV ³OHQV VKDSHG ´ /LNH r spiral galaxies, lenticular galaxies have a central hub, but they lack arms. They are sometimes referred WR DV ³DUPOHVV´ VSLUDO JDOD[LHV

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STEMscopedia Elliptical galaxies look a bit like footballs. (An ellipse is an oval.) The stars and matter in an elliptical galaxy rotate around the galaxy’s center in a variety of directions. The largest galaxies in the universe are elliptical. They may be millions of light-years across and hold trillions of stars.

Irregular: ,UUHJXODU JDOD[LHV KDYH VKDSHV WKDW DUH GLI¿FXOW WR FODVVLI\ 6RPH DUH ORQJ DQG WKLQ OLNH needles. Others are shaped like rings or clouds. Astronomers think that the gravities of nearby galaxies may be pulling irregular galaxies into their disorganized shapes.

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STEMscopedia The universe includes everything that exists—all matter, energy, space, and time. But how did the XQLYHUVH FRPH LQWR H[LVWHQFH" ,W PD\ EH GLI¿FXOW WR LPDJLQH WKH RULJLQV RI WKH XQLYHUVH :KHUH GLG WKH universe and its components come from? Scientists have found solid evidence that the universe had a beginning.

The big bang theory is the most widely accepted theory to explain the origin of the universe. According to this theory, the universe began as a single, tiny point—smaller than an atom—called a singularity. This VLQJXODULW\ ZDV LQ¿QLWHO\ KRW DQG LQ¿QLWHO\ GHQVH LW FRQWDLQHG DOO WKH PDWWHU DQG HQHUJ\ WKDW LV FXUUHQWO\ in the universe. The Big Bang was the moment when all of this matter and energy suddenly expanded out from this singularity. The universe has been expanding ever since. The laws of physics, including JUDYLW\ FDPH LQWR HIIHFW GXULQJ WKH %LJ %DQJ ,Q WKH ¿UVW VHFRQGV DIWHU WKH %LJ %DQJ JUDYLW\ FDXVHG matter to come together to form the particles from which all of the components in the universe are made: protons, neutrons, and electrons.

During these seconds, the universe was too hot for these particles to form atoms. Also, the clouds of subatomic particles—these protons, neutrons, and electrons—were so dense that no light could shine through them. About three seconds after the Big Bang, the universe had cooled enough for protons and neutrons to come together to form simple nuclei.

After about 300,000 years, electrons joined with these nuclei to form the atoms of the simplest HOHPHQWV +\GURJHQ ZKLFK FRQWDLQV RQO\ RQH SURWRQ SHU DWRP ZDV WKH ¿UVW HOHPHQW WR IRUP +HOLXP which contains two protons per atom, formed next. To this day, hydrogen and helium remain the most common elements in the universe. As atoms continued to form, the dense cloud of subatomic particles EHJDQ WR FOHDU )RU WKH ¿UVW WLPH OLJKW FRXOG VKLQH WKURXJK WKH XQLYHUVH Prior to the discovery of the Big Bang, many scientists thought that the universe had always existed— and would always exist—in an unchanging state. This was called the steady state theory. The steady state theory was disproved in the 1920s by a scientist named Edwin Hubble. By analyzing light from distant stars, Hubble discovered that the universe is actually expanding. This discovery led to the big bang theory. Scientists reasoned that if the universe is expanding, it must once have been compressed into a much smaller, denser space. Later discoveries have continued to support the big bang theory.

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STEMscopedia The fact that the universe is expanding was one of the most important early pieces of evidence for the big bang theory. To understand how scientists know that the universe is expanding, you need to know a bit about light waves. When stars give off light, the light travels in waves through space. Some waves are longer; longer waves are seen as red light. Some waves are shorter; shorter waves are seen as blue light.

As a star moves away from Earth, light waves from the star that reach Earth seem to have stretched.

As a result, the star appears redder. This is called redshift. In contrast, as a star moves toward Earth, light waves from the star that reach Earth seem to compress. As a result, the star appears bluer. This is called blueshift.

1 2 3 4

BLUESHIFT

P4

P3

P2

P1

REDSHIFT

The stars and galaxies that Edwin Hubble observed experienced redshift. In other words, they were moving away from Earth. If galaxies are moving away from Earth (and each other), the universe cannot exist in a steady state. Hubble ultimately concluded that the universe must be expanding. He also discovered that galaxies that are farther from Earth experience greater redshift. In other words, the farther a galaxy is from Earth, the faster it is moving away from Earth. Hubble concluded that not only is the universe expanding, but it must be expanding more quickly all the time!

Scientists can now measure the intensity of a galaxy’s redshift and use this value to calculate the galaxy’s distance from Earth and the speed at which it is moving. Scientists still have not developed a way to measure the current size of the universe.

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STEMscopedia Visible light is a form of electromagnetic radiation; energy that travels through space in wave-like patterns at high speeds. In fact, this energy is the fastest thing in the universe. Electromagnetic radiation travels at a constant rate of about 300,000 km/s. (We call this the speed of light.) Because the universe is so vast and light moves so quickly, light gives scientists a useful tool for measuring distances in space. As you will discover, scientists can also use light to measure the universe’s age.

A light-year is the distance that light travels in one year, which is about 9.5 trillion kilometers. If a star is four light-years from Earth, light from that star takes four years to reach Earth. If a star is 4 million light-years from Earth, light from that star takes 4 million years to reach Earth. This means that scientists are looking into the past when they observe electromagnetic radiation in space. Scientists can estimate the age of the universe by observing the universe’s oldest stars and the intensity of their redshift. Scientists can use these observations to calculate the rate of the expansion of the universe and work backward to determine when the expansion began. Using this method, scientists have estimated that the universe is about 13.7 billion years old. In other words, the Big Bang occurred 13.7 billion years ago.

The speed of light in a vacuum is a universal physical constant that equals exactly 299,792,458 m/s DERXW NP V 7KH VSHHG RI OLJKW ZKLFK LV GH¿ QHG DV WKH PD[LPXP VSHHG DW ZKLFK DOO PDWWHU DQG LQIRUPDWLRQ LQ WKH XQLYHUVH FDQ WUDYHO ZDV GH¿ QHG LQ $OEHUW (LQVWHLQ¶V WKHRU\ RI UHODWLYLW\ ,W LV WKH speed at which all massless particles (including electromagnetic radiation such as light) and gravitational waves travel in a vacuum. These particles and waves travel at the speed of light regardless of the motion of the source or the inertial frame of reference of the observer. Nothing travels faster than the speed of light in a vacuum, which is the same for all observers, no matter how fast they or the light source are moving. In other words, regardless of the speed of an observer or a source, in a vacuum, the speed of light is always c (3 x 108 m/s).

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STEMscopedia 1. The principle of relativity: All the laws of physics are valid in any inertial reference frame.

2. /LJKW DOZD\V WUDYHOV WKURXJK D YDFXXP DW D ¿ [HG VSHHG c, relative to any inertial reference frame independent of the motion of the light source.

The theory of relativity describes the relationship between mass, energy, and the speed of light as E = mc2. The speed at which light propagates through transparent materials, such as glass or air, is less than c. The ratio between c and the speed, v, at which light travels in a material is called the refractive index, n, of the material: n = c/v.

In many cases, light and other electromagnetic waves are assumed to propagate instantaneously, but for long distances and very sensitive measurements, the exact speed of light is important to calculate very distant objects in the universe, such as planets and stars. The light that we observe from stars took many years to travel to us, and from these properties, scientists discover the history of the universe.

7KH ¿ QLWH VSHHG RI OLJKW DOVR OLPLWV WKH WKHRUHWLFDO PD[LPXP VSHHG RI FRPSXWHUV EHFDXVH LQIRUPDWLRQ must be sent within the computer from chip to chip. After centuries of increasingly precise measurements, in 1975, the speed of light was found to be 299,792,458 m/s with a measurement XQFHUWDLQW\ RI SDUWV SHU ELOOLRQ ,Q WKH PHWHU WKH XQLW RI OHQJWK ZDV UHGH¿ QHG LQ WKH International System of Units (SI) as the distance that is traveled by light in a vacuum in 1/299,792,458 of a second. As a result, the numerical value of c c LQ PHWHUV SHU VHFRQG LV QRZ ¿ [HG H[DFWO\ E\ WKH GH¿ QLWLRQ RI WKH PHWHU

Frame of Reference The energy, E, and the momentum, p, depend on the frame of reference in which they are measured (e.g., Lorentz contraction). Kinetic energy is the energy of motion and consequently is a function of velocity. This means that an object’s energy and its momentum depend on the object and the observer’s frame of reference. Energy and momentum are frame dependent. According to Einstein, the measures for length, time, and mass depend on an observer’s motion relative to a chosen frame of reference. In special relativity, a stationary observer who is watching a fast-moving object will see that (A) the length of a fast-moving object is shorter than if the object were at rest (Lorentz contraction) and (B) time passes more slowly on the fast-moving object than when it is at rest. From an observer with a different frame of reference, such as one inside the fast-moving object, everything inside looks like a normal length, and time passes normally. For those outside this frame of reference, lengths are foreshortened, and clocks are slow.

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STEMscopedia g Edwin Hubble, Astronomer

:KHQ (GZLQ +XEEOH ± ¿ UVW EHFDPH DFWLYH LQ DVWURQRP\ many of the things that we view today as separate galaxies were viewed as nebulae that were part of the Milky Way galaxy. Hubble proved that stars in these nebulae were so distant that they were millions of light-years away, beyond the Milky Way itself. Hubble DOVR FUHDWHG WKH PRGHUQ FODVVL¿ FDWLRQ RI JDOD[LHV WKDW ZH XVH WRGD\ (spiral, elliptical, and irregular) and showed that all galaxies except local ones are moving away from us. It was his research that showed that the universe is expanding. The Hubble Space Telescope was named in his honor.

The Big Picture The light from distant stars helps us understand the universe. Because distance is time, we are able to peer into the past, seeing the universe as it was by looking ever farther away. When we gaze deep into the cosmos, we can note several things. The universe is full of stars and galaxies. Those galaxies are far apart from each other. It is the attractive force of gravity that tries to bring random clouds of dust and gas together to form stars and galaxies. It is the expansion of the universe that tries to tear those clouds of dust and gas apart, spreading them thinner and thinner. And it is the interplay between these two forces that allows the universe to exist as we see it today and allows us to predict its future.

Connect It How is matter in the universe distributed?

Matter in the universe is distributed in clusters and clumps. It is not evenly distributed; rather, it forms galaxies, clusters, stars, and planets. There are two forces that drive this distribution: the expansion of the universe and the force of gravity. Gravity pulls matter together while the expansion of the universe spreads it out. The combination of these two forces is what makes the structure of the universe possible.

gravity e r a 5. How xpansion and e to produce ing combin tructure of the s iverse? the un

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STEMscopedia 1. Which of the following is a component of the universe?

A. Matter B. Light C. Gravity D. All of the above 2. Which of the following is evidence of the big bang theory?

A. 5HGVKLIW RI JDOD[LHV B. Presence of galaxies C. Dust quantities D. Frame of reference 3. What effect does gravity have on matter as it is distributed across the universe?

A. It spreads matter out.

B. It pulls matter together.

C. Matter remains unchanged.

D. It is impossible to predict the effect.

4. Describe how matter is distributed in the universe.

5. What evidence exists for the Big Bang?

6. How does distance equal time in astronomy?

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GLOSSARY OF TERMS acceleration

atomic theory

acceleration: the rate of change in

atom: the smallest unit of an element that

velocity; speeding up, slowing down, or

has all of the properties of that element;

changing direction

contains a nucleus within a surrounding electron cloud

acceleration due to gravity: the constant acceleration on an object because of

atomic model: a model that lists the

gravitational force; on Earth it is 9.81 m/s2.

three subatomic particles that make up atoms; gives the mass and charge of each

action-reaction pair: a pair of forces that

subatomic particle

obeys the statement “for every action force, there is an equal and opposite reaction force”

atomic nucleus: the tiny, very dense, positively charged region in the center of an

air resistance: the frictional force that air

atom; made up of protons and neutrons

exerts against a moving object atomic orbital: a model that describes alpha particle: a positively charged particle

the likelihood, or probability, of finding an

identical to the helium atom nucleus, with

electron at a specific location and position

two protons and two neutrons, that is

around the nucleus

emitted from radioactive decay of a nucleus atomic theory: a scientific theory of the amplitude: the height of a wave from the

nature of matter, which states that matter is

origin to the crest or trough

composed of discrete units called atoms

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GLOSSARY OF TERMS big bang theory

conductor

big bang theory: a theory that says

closed system: a system that does not

the universe began as a small point that

exchange matter but does exchange energy

expanded rapidly about 13.7 billion years ago with its surrounding environment centripetal force: the force pulling on an

compound: a substance composed of multiple

object traveling in a circular path toward the elements combined in fixed proportions center of the path compression: a force that tries to collapse chemical change: a change that occurs

an object; an increase in density caused by

when a new substance is created with

external pressure

different properties; observable as a color change, the production of gas or a

concave mirror: a mirror with a surface that

precipitate, or the release of heat or light

curves inward

chemical energy: energy stored in

conduction: the transfer of energy from one

chemical bonds; can be released in a

medium to another through direct contact

chemical reaction conductive: having the ability to transfer chemical property: characteristic that can

energy from one medium to another

only be observed or measured through a

through direct contact

chemical reaction conductor: a material that allows electrons circuit: a closed loop of conductors

to flow freely from particle to particle

through which an electric current can flow

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GLOSSARY OF TERMS constructive interference

displacement

constructive interference: when the crest

Coulomb’s law: a law describing the

of one wave meets the crest of another

electrostatic force of interaction between

wave at the same point, increasing the

charged particles based on the strength of

wave’s amplitude

the charges and the distance between the particles

convection: the transfer of thermal energy through currents in fluids

crest: the highest part of a wave

convection current: a circular movement

current: the flow of an electric charge

of fluids that is caused by the rising of

through an object or medium

hotter, less dense fluid and the falling of cooler, denser fluid

destructive interference: when the crest of one wave meets the trough of another

convex lens: a lens with a surface that

wave at the same point, decreasing the

curves outward

wave’s amplitude

convex mirror: a mirror with a surface that

diffraction: the behavior of a wave as it

curves outward

bends around a sharp edge; occurs when a wave passes through a single narrow slit or

coulomb: the SI unit of electric charge;

multiple narrow slits

equal to the quantity of electricity conveyed in 1 second by a current of 1 ampere

displacement: the vector quantity that gives the straight-line distance from a starting position to an ending position

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GLOSSARY OF TERMS distance

electromagnetic force

distance: a measure of how far apart two

electrical energy: energy produced as a

objects are

result of moving electric charges

Doppler effect: an apparent shift in the

electrical force: the interaction between

frequency of a wave due to the motion of

a charged particle and an electromagnetic

the observer or the source of the wave

field or between two charged particles

elastic collisions: an encounter between

electricity: a physical phenomenon

objects in which the total kinetic energy of the

associated with the presence and

objects before and after the collision is equal

movement of electric charge

electric field: a region around a charged

electromagentic radiation: energy in the

particle or object within which a force

form of oscillating electric and magnetic

would be exerted on other charged

fields that is released in electromagnetic

particles or objects

processes; characterized based on the frequency and wavelength of the

electric potential: an expression of the

oscillations as radio waves, microwaves,

voltage of a circuit or the pressure for

infrared radiation, visible light, ultraviolet

pushing current through a circuit

radiation, X-rays, and gamma rays

electric potential energy: the potential

electromagnetic force: the interaction

energy per unit of charge that an object

between a charged particle and an

would have at a point in space as the result

electromagnetic field or between two

of the object’s charge and the charges of

charged particles

other objects at other points in space 274

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GLOSSARY OF TERMS electromagnetic spectrum

focal length

electromagnetic spectrum: a continuum

element: one of the primary substances

of all electromagnetic waves arranged

that make up matter and cannot be

according to frequency and wavelength

chemically broken down or converted into other substances

electromagnetic waves: oscillations of electromagnetic fields that carry energy

energy: the ability of a system to do work or

through a medium or vacuum

produce heat

electron: a negatively charged subatomic

energy transformation: the change of

particle of the electron cloud; involved in

energy from one type to another (kinetic to

the formation of chemical bonds

potential or potential to kinetic)

electron cloud: all of the area inside an

equilibrium: a condition in which all

atom surrounding the nucleus where

competing influences are balanced

electrons are found fission: a nuclear reaction in which a heavy electron orbital: the specific regions

nucleus breaks into two lighter nuclei,

around the nucleus of an atom in which

releasing energy

electrons travel focal length: the distance between the electrostatic attraction: an attraction

surface of a mirror or the center of a lens

related to the relative charge of an object

and the point at which light rays that were initially parallel intersect after being

electrostatic force: a force that is created by redirected by the mirror or lens the interaction of stationary electric charges © Accelerate Learning Inc. - All Rights Reserved

275

GLOSSARY OF TERMS focal point

gravitational potential energy

focal point: the point at which light rays

fusion: a nuclear reaction in which two

that were initially parallel intersect after

lighter nuclei combine to form a single

being redirected by the mirror or lens

heavier nucleus and some of the original mass is converted to energy

force: an interaction between an object and another object or a field that acts to change

galaxy: a large grouping of stars, planets, gas,

the motion of the object

and dust in space held together by gravity

frame of reference: a set of space-time

gamma rays: electromagnetic waves

coordinates that describes motion of a body with the highest energy; produced by relative to something else

supernovas, the destruction of atoms, or the decay of radioactive material

free-body diagram: a diagram showing an object and the directions and magnitudes

gas: a state of matter where the shape and

of all the forces that are acting on the object

volume are variable and dependent on the shape of the closed container, and where

frequency: the number of wave cycles that

the particles are completely independent of

pass a given point per unit of time

each other

friction: a force that resists the relative

gravitational force: a force of attraction

motion of two objects or substances sliding

between two masses

against one another gravitational potential energy: the energy that is stored in an object due to its position

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GLOSSARY OF TERMS gravity

isolated system

gravity: a mutually attractive, physical

impulse: force exerted over a time

force of nature that causes two bodies to

interval that causes a change in an

attract each other

object’s momentum

heat: energy transferred between two

inelastic collisions: an encounter between

objects of different temperatures, moving

objects in which some of the kinetic energy

continually in a predictable pattern from

is converted into other forms of energy

a warmer site to a cooler site until all sites have reached the same temperature

inertia: an object’s tendency to resist changes in its motion

heat transfer: the exchange of thermal energy from one physical system to another

infrared waves: electromagnetic waves with wavelengths that are longer than

homeostasis: the tendency for a system,

visible light but shorter than radio waves

such as a cell, to maintain relatively constant internal conditions

insulator: a substance that does not allow electrical or thermal energy to pass through it

hydrogen bond: an attraction between a hydrogen atom that is covalently bonded

interference: the combination of two or

to a highly electronegative atom (e.g.,

more of the same type of wave

oxygen or nitrogen) and another highly electronegative atom to which the hydrogen isolated system: a system that does is not covalently bonded

not exchange matter or energy with its surrounding environment

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GLOSSARY OF TERMS joule

longitudinal wave

joule: the SI unit of energy equal to

law of conservation of momentum: a law

1 newton of force applied over 1 meter

stating that for collisions in a closed system,

of distance

the total momentum remains the same

Kepler’s law of ellipses (1st): the law that

law of inertia: a law stating that an object

states that all planets move in an elliptical

at rest will remain at rest and an object in

orbit around the Sun

motion will stay in motion at a constant velocity unless it is acted upon by an

Kepler’s law of equal areas (2nd): the law

unbalanced force

that describes the speed of planets that orbit the Sun

light energy: energy that is carried by an electromagnetic wave as it travels through space

Kepler’s law of harmonies (3rd): the law that describes the size of a planet’s orbit

liquid: a state of matter where the shape is variable and dependent on the bottom

Kepler’s laws: three laws that describe the

of the container, where the volume is

motion of planets around the Sun

constant, and where the particles move independently within the liquid

kinetic energy: the energy of motion longitudinal wave: a wave that is law of conservation of energy: a law

propagated in the same direction as the

stating that energy cannot be created or

displacement of the transmitting field or

destroyed—it can only change forms

medium

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GLOSSARY OF TERMS magnetic force

net force

magnetic force: a force of attraction or

microwaves: electromagnetic waves that

repulsion that arises between electrically

are between radio waves and infrared waves

charged particles because of their motion

on the electromagnetic spectrum

mass: a measure of how much matter is

molecule: a group of two or more atoms

present in a substance

bonded together by chemical forces, representing the smallest possible

mass defect: the difference between the

unit of a chemical compound that can

mass of an atomic nucleus and the sum

participate in a reaction

of the masses of the subatomic particles within the atomic nucleus

momentum: a property of a moving object; determined by the product of its

mass-energy equivalence: the principle

mass and velocity

that mass is concentrated energy; the amount of energy in a given amount of

motion: the change in an object’s position

mass can be calculated with the formula.

with respect to time and in comparison to the positions of other objects used as

matter: anything that has volume and mass reference points mechanical energy: the sum of the potential

net force: the overall force acting on a

energy and kinetic energy of an object; changes system or object after opposing or balanced when work is done on the object

forces cancel each other out

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GLOSSARY OF TERMS neutron

orbit

neutron: a subatomic particle of the

Newton’s third law of motion: the law

nucleus of an atom that is without charge

stating that for every action force, there is an

and contributes to the mass of an atom

equal, opposite reaction force

newton: the SI unit of force

normal force: the force that is generated by a surface in opposition to an object that is

Newton’s first law of motion: the law

pressed upon it

stating that an object at rest stays at rest and an object in motion stays in motion

nucleon: a particle that is part of the

with the same speed and in the same

nucleus; a proton or neutron

direction unless it is acted upon by an unbalanced force

nucleus: the tiny, very dense, positively charged region in the center of an atom that

Newton’s law of universal gravitation:

is made of protons and neutrons

the law stating that every piece of matter is attracted to every other piece of matter; the

object: the source of light that forms the image

force is directly proportional to their masses but inversely proportional to the square of

Ohm’s law: the relationship between

the distance between them

potential difference, current, and resistance

Newton’s second law of motion: the law

open system: a system that exchanges matter

stating the relationship between the force

and energy with its surrounding environment

applied to an object and the object’s mass and acceleration

orbit: a curved path followed by a satellite as it revolves around an object in space

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GLOSSARY OF TERMS parallel circuit

plasma

parallel circuit: a circuit with components

physical change: any alteration to

that are connected so that there are

a substance that does not change its

multiple current paths, each component

chemical identity; examples include

has the same voltage across its ends, and

changing phase, dissolving into a solution,

the total current in the circuit is the sum of

or breaking up into smaller pieces.

the currents in the components physical property: property that describes period: the time that something takes

matter, including color, feel, smell, boiling

to happen; the time required for the

point, melting point, and density

completion of one wave cycle or one revolution

Planck’s constant: the constant that gives the unvarying ratio of the energy

photoelectric effect: the observation that

of a quantum of radiation to its

when certain wavelengths of light strike

frequency; as an approximate value of

a piece of metal, electrons are emitted,

6.626 x 10−34 joule-seconds; represented

potentially creating an electric current

by the symbol h

photon: an elementary particle that is the

plane mirror: a mirror with a flat surface

smallest possible amount of light and all other forms of electromagnetic radiation

plasma: a physical state of matter that

that can interact with anything

exists at extremely high temperatures in which all molecules are dissociated and most atoms are ionized

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GLOSSARY OF TERMS polarization

refraction

polarization: the restriction of the

rarefaction: the less dense, more spread-

vibrations of light (electromagnetic

out regions of longitudinal waves

radiation) to a single plane or direction ray diagram: a diagram that is used to potential energy: the energy that an object

show how an image is formed using a

has because of its position relative to a force mirror or lens field or because of the relative positions of its components

real image: the point at which multiple waves converge to produce an image

power: the rate of work or energy transfer per unit of time

redshift and blueshift: the change in wavelength that allows us to determine if an

proton: a positively charged subatomic

object is moving toward us or away from us

particle of the nucleus of an atom that contributes to the mass of the atom

reflection: a change in the direction of a wave at an interface between two media

radiant energy: electromagnetic

that sends the wave back into the medium

waves given off by a source into the

from which it came

surrounding environment refraction: a change in the direction of a radiation: the emission or transmission of

wave as the wave moves from one medium

energy as particles or waves

into another

radio waves: electromagnetic waves with long wavelengths and low frequencies 282

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GLOSSARY OF TERMS repulsion

space-time

repulsion: the force that tends to

series circuit: a circuit with components

separate bodies of like electric charge or

that are connected end to end so that

magnetic polarity

there is only one path for the current to flow along and each component has the

repulsive force: the force that acts between same current; has a total voltage across bodies of like electric charge or magnetic

the circuit that is equal to the sum of the

polarity, tending to separate them

voltages across the components

resistance: the ability of a material to

simple machine: device that reduces the

oppose the flow of an electric current

amount of force needed to move an object

through it solid: a state of matter where the shape resting position: an object’s default

is constant and rigid, where the volume is

position outside of external forces

constant, and where the particles vibrate in a fixed position

scalar quantity: a quantity that is fully described by magnitude and does not

sound energy: a form of energy that is

have a direction

made by vibrations traveling as waves and requires a medium (air, water, or solids) in

semiconductor: a material with electric

order to travel

conductivity between that of a conductor and an insulator

space-time: the four-dimensional view of physical reality that makes up the universe

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GLOSSARY OF TERMS speed

thermal energy

speed: the measurement of the rate of

strong nuclear force: the force that binds

change of position with respect to time

the protons and neutrons together in the nucleus

speed of light: the maximum speed at which all matter and information in the

subatomic particles: particles that are

universe can travel, or the measurement of

smaller than the atom

the rate of light’s movement through a given substance over a specific unit of time

superposition: when two (or more) waves travel through a medium at the same time

standing waves: the vibration of a system in which some particular points remain

system: a group of interacting, interrelated,

fixed while others between them vibrate

or interdependent elements forming a

with the maximum amplitude

complex whole

star: a self-luminous celestial body

temperature: the hotness or coldness of

consisting of a mass of gas held together by

matter related to the average kinetic energy

its own gravity and emitting energy that is

of the molecules of that substance

generated by nuclear reactions in its interior tension: a force that tries to stretch an static electricity: the accumulation of

object or is provided by strings, ropes, or

electric charge on the surface of an object

chains

static friction: the friction between two

thermal energy: the internal energy of a

surfaces when there is no relative motion

system, including the kinetic and potential

between them

energy of its particles

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GLOSSARY OF TERMS thin lens equation

wave

thin lens equation: an equation relating

vector quantity: a quantity with both a

object distance, image distance, and focal

magnitude and a direction

length velocity: the rate of change of the position of time: measurements, such as minutes and

an object that is moving in a specific direction

hours, used to quantify intervals, durations, and sequences

virtual image: an optical image that is produced from the apparent divergence of

transverse waves: a wave that is

light rays

propagated in a direction that is perpendicular to the displacement of the

visible light: electromagnetic waves with

transmitting field or medium

wavelengths that are longer than ultraviolet light but shorter than infrared waves

trough: the lowest part of a wave voltage: the difference in electric potential ultraviolet waves: electromagnetic waves

between two points

with wavelengths that are longer than X-rays but shorter than visible light

watt: SI unit for power

unbalanced force: a situation in which the

wave: a disturbance in particles or a field

net force on a system is not zero

that transfers energy progressively from point to point without the field or particles

universe: all space and the matter space

having any net movement themselves

contains

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GLOSSARY OF TERMS wavelength

X-rays

wavelength: the distance between two adjacent crests or troughs of a wave weak nuclear force: a weaker, noncontact force that governs the radioactive decay of subatomic particles work: the measure of energy transfer that occurs when an object is moved over a distance by an external force X-rays: electromagnetic waves that are the second highest in energy and are used in medical and astronomical applications

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