conceptual energy hewitt-2

Annette Rappleyea usesa ballistic pendulum tocalculate the speed of afired ball.

Energy

Perhaps the concept most central to all of science is energy. The combinationof energy and matter makes up the universe: Matter is substance, and energy is themover of substance. The idea of matter is easy to grasp. Matter is stuff that we can see,smell, and feel. It has mass, and it occupies space. Energy, on the other hand, is abstract.We cannot see, smell, or feel most forms of energy. Surprisingly, the idea of energy wasunknown to Isaac Newton, and its existence was still being debated in the 1850s. Althoughenergy is familiar to us, it is difficult to define, because it is not only a "thing" but both athing and a process-similar to both a noun and a verb. Persons, places, and things haveenergy, but we usually observe energy only when it is being transferred or being transformed.It comes to us in the form of electromagnetic waves from the Sun, and we feel it as ther-mal energy; it is captured by plants and binds molecules of matter together; it is in the foodswe eat, and we receive it by digestion. Even matter itself is condensed, bottled-up energy,as set forth in Einstein's famous formula, E = me", which we'll return to in the last part ofthis book. For now, we'll begin our study of energy by considering a related concept: work.

Work

The word work, incommon usage,means physical ormental exertion. Don'tconfuse the physicsdefinition of workwith the everydaynotion of work.

110

In the previous chapter, we saw that changes in an object's motion depend bothon force and on how long the force acts. "How long" meant time. We called thequantity "force X time" impulse. But "how long" does not always mean time.It can mean distance also. When we consider the concept of force X distance,we are talking about an entirely different concept-work.

When we lift a load against Earth's gravity, work is done. The heavier theload or the higher we lift the load, the more work is done. Two things enterthe picture whenever work is done: (1) application of a force, and (2) themovement of something by that force. For the simplest case, where the forceis constant and the motion is in a straight line in the direction of the force, 1

1More generally, work is the product of only the component of force that acts in the direction of motion andthe distance moved. For example, if a force acts at an angle to the motion, the component of force parallel tomotion is multiplied by the distance moved. When a force acts at right angles to the direction of motion, withno force component in the direction of motion, no work is done. A common example is a satellite in a circularorbit; the force of gravity is at right angles to its circular path and no work is done on the satellite. Hence, itorbits with no change in speed.

FIGURE 7.1Work is done in lifting thebarbell.

FIGURE 7.2He may expend energy whenhe pushes on the wall, but,if the wall doesn't move,no work is done on the wall.

Chapter 7 Energy 111

we define the work done on an object by an applied force as the product ofthe force and the distance through which the object is moved. In shorter form:

Work = force X distance

W=Fd

If we lift two loads one story up, we do twice as much work as in liftingone load the same distance, because the force needed to lift twice the weight istwice as much. Similarly, if we lift a load two stories instead of one story, wedo twice as much work because the distance is twice as great.

We see that the definition of work involves both a force and a distance. Aweightlifter who holds a barbell weighing 1000 newtons overhead does nowork on the barbell. He may get really tired holding the barbell, but, if it isnot moved by the force he exerts, he does no work on the barbell. Work maybe done on the muscles by stretching and contracting, which is force times dis-tance on a biological scale, but this work is not done on the barbell. Liftingthe barbell, however, is a different story. When the weightlifter raises the bar-bell from the floor, he does work on it.

Work generally falls into two categories. One of these is the work done againstanother force. When an archer stretches her bowstring, she is doing work againstthe elastic forces of the bow. Similarly, when the ram of a pile driver is raised,work is required to raise the ram against the force of gravity. When you do push-ups, you do work against your own weight. You do work on something whenyou force it to move against the influence of an opposing force-often friction.

The other category of work is work done to change the speed of an object.This kind of work is done in bringing an automobile up to speed or in slow-ing it down. In both categories, work involves a transfer of energy.

The unit of measurement for work combines a unit of force (N) with a unitof distance (m); the unit of work is the newton-meter (Nm), also called the joule(J), which rhymes with cool. One joule of work is done when a force of 1 new-ton is exerted over a distance of 1 meter, as in lifting an apple over your head.For larger values, we speak of kilojoules (k], thousands of joules), or megajoules(MJ, millions of joules). The weightlifter in Figure 7.1 does work in kilojoules.To stop a loaded truck going at 100 km/h takes megajoules of work.

PowerThe definition of work says nothing about how long it takes to do the work.The same amount of work is done when carrying a load up a flight of stairs,whether we walk up or run up. So why are we more tired after running upstairsin a few seconds than after walking upstairs in a few minutes? To understandthis difference, we need to talk about a measure of how fast the work is done-power. Power is equal to the amount of work done per the time it takes to do it:

P_ work done

ower -.. Itime mterva

A high-power engine does work rapidly. An automobile engine that deliverstwice the power of another automobile engine does not necessarily produce

11 2 Part One Mechanics

FIGURE 7.3The three main engines ofa space shuttle can develop33,000 MW of power whenfuel is burned at the enor-mous rate of 3400 kg/so Thisis like emptying an average-size swimming pool in 20 S.

twice as much work or make a car go twice as fast as the less powerfulengine. Twice the power means the engine can do twice the work in the sametime or do the same amount of work in half the time. A more powerfulengine can get an automobile up to a given speed in less time than a lesspowerful engine can.

Here's another way to look at power: Aliter (L) of fuel can do a certainamount of work, but the power produced when we burn it can be any amount,depending on how fast it is burned. It can operate a lawnmower for a half houror a jet engine for a half second.

The unit of power is the joule per second (J/s), also known as the watt(in honor of James Watt, the eighteenth-century developer of the steamengine). One watt (W) of power is expended when 1 joule of work is donein 1 second. One kilowatt (kW) equals 1000 watts. One megawatt (MW)equals 1 million watts. In the United States, we customarily rate engines inunits of horsepower and electricity in kilowatts, but either may be used. In themetric system of units, automobiles are rated in kilowatts. (One horsepoweris the same as three-fourths of a kilowatt, so an engine rated at 134 horse-power is a lOO-kW engine.)

CHECI< YOURSELF

If a forklift is replaced with a new forklift that has twice the power, how muchgreater a load can it lift in the same amount of time? If it lifts the same load,how much faster can it operate?

Mechanical EnergyWhen work is done by an archer in drawing a bowstring, the bent bow acquiresthe ability to do work on the arrow. When work is done to raise the heavy ramof a pile driver, the ram acquires the ability to do work on the object it hits whenit falls. When work is done to wind a spring mechanism, the spring acquires theability to do work on various gears to run a clock, ring a bell, or sound an alarm.

In each case, something has been acquired that enables the object to dowork. It may be in the form of a compression of atoms in the material of anobject, a physical separation of attracting bodies, or a rearrangement of electriccharges in the molecules of a substance. This "something" that enables an objectto do work is energy.r Like work, energy is measured in joules. It appears inmany forms that will be discussed in the following chapters. For now, we willfocus on the two most common forms of mechanical energy-the energy due to

CHECK YOUR ANSWER

The forklift that delivers twice the power will lift twice the load in the same time orthe same load in half the time. Either way, the owner of the new forklift is happy.

2Strictly speaking, that which enables an object to do work is its available energy, for not all the energy in anobject can be transformed to work.

FIGURE 7.4

The potential energy of the10-N ball is the same (30 J)in all three cases because thework done in elevating it 3 mis the same whether it is(a) lifted with 10 N offorce,(b) pushed with 6 N of forceup the 5-m incline, or(c) lifted with 10 N up each1-m stair. No work is donein moving it horizontally(neglecti ng friction).

k

FIGURE 7.5The potential energy of theelevated ram ofthe piledriver is converted to kineticenergy when it is released.


the position of something or the movement of something. Mechanical energy canbe in the form of potential energy, kinetic energy, or the sum of the two.

Potential EnergyAn object may store energy by virtue of its position. The energy that is storedand held in readiness is called potential energy (PE) because in the stored stateit has the potential for doing work. A stretched or compressed spring, for exam-ple, has the potential for doing work. When a bow is drawn, energy is storedin the bow. The bow can do work on the arrow. A stretched rubber band haspotential energy because of the relative position of its parts. If the rubber bandis part of a slingshot, it is capable of doing work.

The chemical energy in fuels is also potential energy. It is actually energyof position at the submicroscopic level. This energy is available when the posi-tions of electric charges within and between molecules are altered-that is, whena chemical change occurs. Any substance that can do work through chemicalaction possesses potential energy. Potential energy is found in fossil fuels, elec-tric batteries, and the foods we consume.

T3m

1 1II....-,I I\ ,/a b c

Work is required to elevate objects against Earth's gravity. The potentialenergy due to elevated positions is called gravitational potential energy. Waterin an elevated reservoir and the raised ram of a pile driver both have gravita-tional potential energy. Whenever work is done, energy changes.

The amount of gravitational potential energy possessed by an elevatedobject is equal to the work done against gravity in lifting it. The work doneequals the force required to move it upward times the vertical distance it ismoved (remember W = Fd). The upward force required while moving at con-stant velocity is equal to the weight, mg, of the object, so the work done mlifting it through a height h is the product mgh.

gravitational potential energy = weight X height

PE = mgh

Note that the height is the distance above some chosen reference level, suchas the ground or the floor of a building. The gravitational potential energy,mgh, is relative to that level and depends only on mg and h. We can see, inFigure 7.4, that the potential energy of the elevated ball does not depend onthe path taken to get it there.

114 Part One Mechanics

FIGURE 7.6Both do the same work inelevating the block.

--JVL) (') C

Weight = mg, so a1a-kg block of iceweighs 100 N.

FIGURE 7.7The potential energy ofTenny's drawn bow equalsthe work (average force Xdistance) that she did indrawing the arrow intoposition. When the arrow isreleased, most of the poten-tial energy of the drawn bowwill become the kinetic energyof the arrow.

Potential energy, gravitational or otherwise, has significance only when itchanges~when it does work or transforms to energy of some other form. Forexample, if the ball in Figure 7.4 falls from its elevated position and does20 joules of work when it lands, then it has lost 20 joules of potential energy.How much total potential energy the ball had when it was elevated is relativeto some reference level, and it isn't important. What's important is the amountof potential energy that is converted to some other form. Only changes in poten-tial energy are meaningful. One of the kinds of energy into which potentialenergy can change is energy of motion, or kinetic energy.

CHECK YOURSELF

1. How much work is done in lifting the 100-N block of ice a vertical distance of2 m, as shown in Figure 7.6?

2. How much work is done in pushing the same block of ice up the 4-m-longramp? (The force needed is only 50 N, which is the reason ramps are used).

3. What is the increase in the block's gravitational potential energy in each case?

Kinetic EnergyIf you push on an object, you can set it in motion. If an object is moving, thenit is capable of doing work. It has energy of motion. We say it has kineticenergy (KE). The kinetic energy of an object depends on the mass of the objectas well as its speed. It is equal to the mass multiplied by the square of the speed,multiplied by the constant !.

Kinetic energy = !mass X speed"KE =! mv2

When you throw a ball, you do work on it to give it speed as it leaves yourhand. The moving ball can then hit something and push it, doing work on whatit hits. The kinetic energy of a moving object is equal to the work required tobring it from rest to that speed, or the work the object can do while beingbrought to rest:

Net force X distance = kinetic energy

or, in equation notation,

Fd =! mu"Note that the speed is squared, so, if the speed of an object is doubled, its

kinetic energy is quadrupled (22 = 4). Consequently, it takes four times thework to double the speed. Whenever work is done, energy changes.

CHECK YOUR ANSWERS

1. W = Fd = 100 N X 2 m = 200 j.2. W = Fd = 50 N X 4 m = 200 j.3. Either way increases the block's potential energy by 200 J. The ramp simply

makes this work easier to perform.

FIGURE 7.8Energy transitions in a pen-dulum. PE is relative to thelowest point of the pendu-lum, when it is vertical.

Bowling Ball andConservation of Energy

II,,,

Peg......,.o ...----- __ ~J _... ;

.... - -'"FIGURE 7.9Interactive Figure ~

The pendulum bob willswing to its original heightwhether or not the peg ispresent.

FIGURE 7.10The downhill "fall" of theroller coaster results in itsroaring speed in the dip, andthis kinetic energy sends itup the steep track to thenext summit.

Chapter 7 Enerf)! 11 5

-Potential energy to Potential'"kinetic to Kinetic energy to Potential energyAnd soo~

Work-Energy TheoremWhen a car speeds up, its gain in kinetic energy comes from the work done onit. Or, when a moving car slows, work is done to reduce its kinetic energy. Wecan say''

Work = ilKE

Work equals change in kinetic energy. This is the work-energy theorem. The workin this equation is the net work-that is, the work based on the net force. If, forinstance, you push on an object and friction also acts on the object, the change ofkinetic energy is equal to the work done by the net force, which is your push minusfriction. In this case, only part of the total work that you do changes the object'skinetic energy. The rest is soaked up by friction, which goes into heat. If the forceof friction is equal and opposite to your push, the net force on the object is zeroand no net work is done. Then there is zero change in the object's kinetic energy.

The work-energy theorem applies to decreasing speed as well. When you slamon the brakes of a car, causing it to skid, the road does work on the car. This workis the friction force multiplied by the distance over which the friction force acts.

Interestingly, the maximum friction that the brakes can supply is nearly thesame whether the car moves slowly or quickly. In a panic stop with antilockbrakes, the only way for the brakes to do more work is to act over a longerdistance. A car moving at twice the speed of another takes four times (22 = 4)as much work to stop. Since the frictional force is nearly the same for bothcars, the faster one takes four times as much distance to stop. The same ruleapplies to older-model brakes that can lock the wheels. The force of friction ona skidding tire is also nearly independent of speed. So, as accident investigatorsare well aware, an automobile going 100 kilometers per hour, with four timesthe kinetic energy that it would have at 50 kilo meters per hour, skids four timesas far with its wheels locked as it would from a speed of 50 kilometers perhour. Kinetic energy depends on speed squared.

Automobile brakes convert kinetic energy to heat. Professional drivers arefamiliar with another way to slow a vehicle-shift to low gear and allow the engineto do the braking. Today's hybrid cars do the same and divert braking energy toelectrical storage batteries, where it is used to complement the energy produced bygasoline combustion. (Chapter 25 treats how they do this.) Hooray for hybrid cars!

3This can be derived as follows: If we multiply both sides of F = ma (Newton's second law) by d, we getFd = mad. Recall from Chapter 3 that, for constant acceleration, d = ~ at", so we can say Fd ~ at2) =~ maar: ~ ~ m(at)2; and substituting !1v = at, we get Fd ~ !1~mu", That is, Work = !1KE.


FIGURE 7.11Due to friction, energy istransferred both into thefloor and into the tire whenthe bicycle skids to a stop.An infrared camera revealsthe heated tire track (the redstreak on the floor, left) andthe warmth ofthe tire (right).(Courtesy of MichaelVoIlmer. )

The work-energy theorem applies to more than changes in kinetic energy.Work can change the potential energy of a mechanical device, the heat energyin a thermal system, or the electrical energy in an electrical device. Work is nota form of energy, but a way of transferring energy from one place to anotheror one form to another.4

Kinetic energy and potential energy are two among many forms of energy,and they underlie other forms of energy, such as chemical energy, nuclear energy,sound, and light. Kinetic energy of random molecular motion is related to tem-perature; potential energies of electric charges account for voltage; and kineticand potential energies of vibrating air define sound intensity. Even light energyoriginates from the motion of electrons within atoms. Every form of energy canbe transformed into every other form.

CHECK YOURSELF

1. When you are driving at 90 krn/h, how much more distance do you need to stopthan if you were driving at 30 krri/h?

2. Can an object have energy?

3. Can an object have work?

CHECK YOUR ANSWERS

1. Nine times farther. The car has nine times as much kinetic energy when it travelsthree times as fast: ~ m(3v)2 = ~m9v2 = 9G mv2). The friction force will ordinar-ily be the same in either case; therefore, nine times as much work requires ninetimes as much distance.

2. Yes, but in a relative sense. For example, an elevated object may possess PErelative to the ground below, but none relative to a point at the same elevation.Similarly, the KE that an object has is relative to a frame of reference, usually theEarth's surface. (We will see that material objects have energy of being, E = mc2,the congealed energy that makes up their mass.) Read on!

3. No, unlike momentum or energy, work is not something that an object has.Work is something that an object does to some other object. An object can dowork only if it has energy.

Chapter 7 Energy 11 7

Conservation of Energy

PE = 10000KE=0

PE=7500KE=2500

PE = 5000KE= 5000

PE=2500KE=7500

PE=OKE=100QO

FIGURE 7.12Interactive Figure ~

A circus diver at the top of apole has a potential energyof 10,000 j. As he dives, hispotential energy converts tokinetic energy. Note that, atsuccessive positions one-fourth, one-half, three-fourths, and all the waydown, the total energy isconstant. (Adapted fromK. F. Kuhn andJ. S. Faughn,Physics in Your World.Philadelphia: Saunders,1980.)

More important than knowing what energy is is understanding how it behaves-how it transforms. We can better understand the processes and changes thatoccur in nature if we analyze them in terms of energy changes-transformationsfrom one form into another, or of transfers from one location to another. Energyis nature's way of keeping score.

Consider the changes in energy in the operation of the pile driver back inFigure 7.5. Work done to raise the ram, giving it potential energy, becomeskinetic energy when the ram is released. This energy transfers to the pilingbelow. The distance the piling penetrates into the ground multiplied by the aver-age force of impact is almost equal to the initial potential energy of the ram.We say almost because some energy goes into heating the ground and ram dur-ing penetration. Taking heat energy into account, we find energy transformswithout net loss or net gain. Quite remarkable!

The study of various forms of energy and their transformations from oneform into another has led to one of the greatest generalizations in physics-thelaw of conservation of energy:

Energy cannot be created or destroyed; it may be transformed fromone form into another, but the total amount of energy never changes.

When we consider any system in its entirety, whether it be as simple as aswinging pendulum or as complex as an exploding supernova, there is onequantity that isn't created or destroyed: energy. It may change form or it maysimply be transferred from one place to another, but, conventional wisdom tellsus, the total energy score stays the same. This energy score takes into accountthe fact that the atoms that make up matter are themselves concentrated bun-dles of energy. When the nuclei (cores) of atoms rearrange themselves, enor-mous amounts of energy can be released. The Sun shines because some of thisnuclear energy is transformed into radiant energy.

Enormous compression due to gravity and extremely high temperatures inthe deep interior of the Sun fuse the nuclei of hydrogen atoms together toform helium nuclei. This is thermonuclear fusion, a process that releases radi-ant energy, a small part of which reaches Earth. Part of the energy reachingEarth falls on plants (and on other photosynthetic organisms), and part ofthis, in turn, is later stored in the form of coal. Another part supports life inthe food chain that begins with plants (and other photosynthesizers) and partof this energy later is stored in oil. Part of the energy from the Sun goes intothe evaporation of water from the ocean, and part of this returns to Earth inrain that may be trapped behind a dam. By virtue of its elevated position, thewater behind a dam has energy that may be used to power a generating plantbelow, where it will be transformed to electric energy. The energy travelsthrough wires to homes, where it is used for lighting, heating, cooking, andoperating electrical gadgets. How wonderful that energy transforms from oneform to another!

4The work-energy theorem can he further stated as Work = !lE + Q, where Q is the energy transfer due to atemperature difference.


Try to imagine life before energy was something thathumans controlled. Imagine home life without electric lights,refrigerators, heating and cooling systems, the telephone,and radio and Tv -not to mention the family automobile.We may romanticize a better life without these, but onlyif we overlook the hours of daily toil devoted to doing laun-dry, cooking, and heating our homes. We'd also have tooverlook how difficult it was getting a doctor in times ofemergency before the advent of the telephone-when adoctor had little more in his bag than laxatives, aspirins, andsugar pills-and when infant death rates were staggering.

We have become so accustomed to the benefits oftechnology that we are only faintly aware of our depen-

dence on dams, power plants, mass transportation,electrification, modern medicine, and modern agriculturalscience for our very existence. When we dig into a goodmeal, we give little thought to the technology that wentinto growing, harvesting, and delivering the food on ourtable. When we turn on a light, we give little thought tothe centrally controlled power grid that links the widelyseparated power stations by long-distance transmissionlines. These lines serve as the productive life force ofindustry, transportation, and the electrification of oursociety. Anyone who thinks of science and technology as"inhuman" fails to grasp the ways in which they make ourlives more human.

CHALLENGE QUESTIONS

1. Does an automobile consume more fuel when its air conditioner is turnedon? When its lights are on? When its radio is on while it is sitting in theparking lot?

2. Rows of wind-powered generators are used in various windy locations to gener-ate electric power. Does the power generated affect the speed of the wind?That is, would locations behind the "windmills" have more wind if the windmillsweren't there?

Machines

FIGURE 7.13The lever.

Machines: Pulleys

A machine is a device for multiplying forces or simply changing the directionof forces. The principle underlying every machine is the conservation of energyconcept. Consider one of the simplest machines, the lever (Figure 7.13). At thesame time that we do work on one end of the lever, the other end does workon the load. We see that the direction of force is changed: if we push down,the load is lifted up. If the little work done by friction forces is small enough toneglect, the work input will be equal to the work output.

Work input = work output

CHECK YOUR ANSWERS

1. The answer to all three questions is yes, for the energy they consume ultimatelycomes from the fuel. Even the energy taken from the battery must be given backto the battery by the alternator, which is turned by the engine, which runs fromthe energy of the fuel. There's no free lunch!

2. Windmills generate power by taking KE from the wind, so the wind is slowed byinteraction with the windmill blades. So, yes, it would be windier behind thewindmills if they weren't there.

FIGURE 7.14Applied force X applieddistance = output force Xoutput distance.

Output

FIGURE 7.15This pulley acts like a lever.It changes only the directionofthe input force.

FIGURE 7.16In this arrangement, a loadcan be lifted with half theinput force.

--.JVL) (') C

A machine canmultiply force, butnever energy-no way!


Since work equals force times distance, input force X input distance outputforce X output distance.

(Force X distance ) input = (force X distance )ourpur

The point of support on which a lever rotates is called a fulcrum. Whenthe fulcrum of a lever is relatively close to the load, then a small input forcewill produce a large output force. This is because the input force is exertedthrough a large distance and the load is moved through a correspondingly shortdistance. So a lever can be a force multiplier. But no machine can multiply workor multiply energy. That's a conservation-of-energy no-no!

The principle of the lever was understood by Archimedes, a famous Greekscientist in the third century BC. He said, "Give me where to stand, and I willmove the Earth."

Today, a child can use the principle of the lever to jack up the front end ofan automobile. By exerting a small force through a large distance, she can providea large force that acts through a small distance. Consider the ideal example illus-trated in Figure 7.14. Every time she pushes the jack handle down 25 centimeters,the car rises only a hundredth as far but with 100 times the force.

Another simple machine is a pulley. Can you see that it is a lever "in dis-guise"? When used as in Figure 7.15, it changes only the direction of the force;but, when used as in Figure 7.16, the output force is doubled. Force is increasedand distance moved is decreased. As with any machine, forces can change whilework input and work output are unchanged.

A block and tackle is a system of pulleys that multiplies force more than asingle pulley can do. With the ideal pulley system shown in Figure 7.17,the man pulls 7 meters of rope with a force of 50 newtons and lifts a load of500 newtons through a vertical distance of 0.7 meter. The energy the man expendsin pulling the rope is numerically equal to the increased potential energy of the500-newton block. Energy is transferred from the man to the load.

Any machine that multiplies force does so at the expense of distance. Like-wise, any machine that multiplies distance, such as your forearm and elbow,does so at the expense of force. No machine or device can put out more energythan is put into it. No machine can create energy; it can only transfer energyor transform it from one form to another.

FIGURE 7.17Applied force X applieddistance = output force Xoutput distance.


Efficiency

FIGURE 7.18Energy transitions. Thegraveyard of mechanicalenergy is thermal energy.

The three previous examples were of ideal machines; 100% of the work inputappeared as work output. An ideal machine would operate at 100% efficiency.In practice, this doesn't happen, and we can never expect it to happen. In anytransformation, some energy is dissipated to molecular kinetic energy-thermalenergy. This makes the machine and its surroundings warmer.

Even a lever rocks about its fulcrum and converts a small fraction of theinput energy into thermal energy. We may do 100 joules of work and get out98 joules of work. The lever is then 98% efficient, and we degrade only 2 joulesof work input into thermal energy. If the girl back in Figure 7.14 puts in 100 joulesof work and increases the potential energy of the car by 60 joules, the jack is60% efficient; 40 joules of her input work has been applied against friction,making its appearance as thermal energy.

In a pulley system, a considerable fraction of input energy typically goesinto thermal energy. If we do 100 joules of work, the forces of friction actingthrough the distances through which the pulleys turn and rub about their axlesmay dissipate 60 joules of energy as thermal energy. In that case, the work out-put is only 40 joules and the pulley system has an efficiency of 40%. The lowerthe efficiency of a machine, the greater the percentage of energy that is degradedto thermal energy.

Inefficiency exists whenever energy in the world around us is transformedfrom one form to another. Efficiency can be expressed by the ratio

useful energy outputEfficiency = .

total energy mput

An automobile engine is a machine that transforms chemical energy storedin fuel into mechanical energy. The bonds between the molecules in the petro-leum fuel break up when the fuel burns. Carbon atoms in the fuel combine withoxygen in the air to form carbon dioxide, hydrogen atoms in the fuel combinewith oxygen to form water, and energy is released. How nice if all this energy

Pote;Tenergy

";~~ .~

-: :-

Kinetic ener9'1(of weig~f) ;:{

+ more heat:i.~ ~ of moieculer~;". motion

Still moreheat (fostermolecular motion)

~m'.+ Heat of t. molecular~ ." : ,1: motion- - - --=----.," ' to" Less kinetic energ'l - -- - ....

,/., ~ +more potential energy

Conservation of Energy:Numerical Example

Chapter 7 Ener:g 121

could be converted into useful mechanical energy-that is to say, how nice itwould be if we could have an engine that is 100% efficient. This is impossible,however, because much of the energy is transformed into thermal energy, a lit-tle of which may be used to warm passengers in the winter but most of whichis wasted. Some goes out in the hot exhaust gases, and some is dissipated tothe air through the cooling system or directly from hot engine parts.'

CHALLENGE QUESTION

Consider an imaginary miracle car that has a 100% efficient engine and burns fuelthat has an energy content of 40 megajoules per liter. If the air drag and overallfrictional forces on the car traveling at highway speed is 500 N, how far could thecar travel per liter of fuel at this speed?

Look at the inefficiency that accompanies transformations of energy in thisway: In any transformation, there is a dilution of available useful energy. Theamount of usable energy decreases with each transformation until there is noth-ing left but thermal energy at ordinary temperature. When we study thermo-dynamics, we'll see that thermal energy is useless for doing work unless it canbe transformed to a lower temperature. Once it reaches the lowest practicaltemperature, that of our environment, it cannot be used. The environmentaround us is the graveyard of useful energy.

Comparison of Kinetic Energy and Momentum"..JVL) ('] C

Understanding thedistinction betweenmomentum andkinetic energy is high-level physics.

Kinetic energy and momentum are both properties of motion. But they aredifferent. Momentum, like velocity, is a vector quantity. Energy, on the otherhand, like mass, is a scalar quantity. When two objects move toward eachother, their momenta may partially or fully cancel. Their total momentum isless than the momentum of either one alone. But their kinetic energies cannot

CHECK YOUR ANSWER

From the definition work = force X distance, simple rearrangement gives distance =work/force. If all 40 million J of energy in 1 L were used to do the work of overcomingthe air drag and frictional forces, the distance would be:

work 40,000,000 J/Ldistance = -- = ------ = 80,000 m/L = 80 krn/L

force 500 N

(This is about 190 mpg.) The important point here is that, even with a hypotheticallyperfect engine, there is an upper limit of fuel economy dictated by the conservationof energy.

5When you study thermodynamics in Chapter 18, you'll learn that an internal combustion engine musttransform some of its fuel energy into thermal energy. A fuel cell, on the other hand, which could powerfuture automobiles, doesn't have this limitation. Watch for fuel-cell-powered automobiles in the future!

6This section may be skipped in a light treatment of mechanics.


HRMetal bullet penetrates

~

(;~il"";i-~ \.'Rubber bullet bounces

FIGURE 7.19Compared with the metalbullet with the samemomentum, the rubberbullet is more effective inknocking the block overbecause it bounces uponimpact. The rubber bulletundergoes the greaterchange in momentum andthereby imparts the greaterimpulse, or wallop, to theblock. Which bullet doesmore damage?

cancel. Since kinetic energies are always positive (or zero), the total kineticenergy of two moving objects is greater than the kinetic energy of either onealone.

For example, the momenta of two cars just before a head-on collision mayadd up to exactly zero, and the combined wreck after collision will have thesame zero value for the momentum. But the kinetic energies add, and this energyis still there after the collision, although it's in different forms-mainly in theform of thermal energy. Or the momenta of two firecrackers approaching eachother may cancel, but, when they explode, there is no way their energies cancancel. Energy comes in many forms; momentum has only one form. The vec-tor quantity momentum is different from the scalar quantity kinetic energy.

Another difference is the velocity dependence of the two. Whereas momen-tum is proportional to velocity (mv), kinetic energy is proportional to the squareof velocity (~mv2). An object that moves with twice the velocity of another objectof the same mass has twice the momentum, but it has four times the kineticenergy. It can provide twice the impulse to whatever it encounters, but it cando four times as much work.

Suppose you're carrying a football and are about to be slammed into andtackled by an approaching player whose oncoming momentum is equal but oppo-site to your own. The combined momentum of you and the approaching playerbefore impact is zero, but, on impact, you both stop short in your tracks. Thewallop or jarring exerted on each of you is the same. This is true whether you

FIGURE 7.20The author puts kinetic energy and momentum into the hammer, which strikes the block that rests on lab-manual authorPaul Robinson, who is bravely sandwiched between beds of nails. Paul is not harmed. Why? Except for the flying cementfragments, every bit of the momentum of the hammer at impact is imparted to Paul, and subsequently to the table and theEarth that supports him. But the momentum only provides the wallop; the energy does the damage. Most ofthe kinetic energynever gets to him, for it goes into smashing the block apart and into thermal energy. What energy remains is distributed overthe more than 200 nails that make contact with his body. The driving force per nail is not enough to puncture the skin.

Chapter 7 Eneryy 123

are tackled by a slow-moving heavy player or a fast-moving light player. If theproduct of his mass and his velocity matches yours, you're stopped short. Stop-ping power is one thing, but what about damage? Experienced football playersknow that it hurts more to be stopped by a fast-moving light player than by aslow-moving heavy player. Why? Because a light player moving with the samemomentum has more kinetic energy. If he has the same momentum as a heavyplayer but is only half as massive, he has twice the velocity. Twice the velocity andhalf the mass give the lighter player twice the kinetic energy of the heavier player. 7

He does twice the work on you, tends to deform you twice as much, and gener-ally does twice the damage to you. Watch out for the fast-moving little guys!

Energy for lifeYour body is a machine-an extraordinarily wonderful machine. It is made upof smaller machines-living cells. Like any machine, a living cell needs a sourceof energy. In animals-including you--eells feed on various hydrocarbon com-pounds that release energy when they react with oxygen. Like gasoline burnedin an automobile engine, there is more potential energy in the food moleculesthan there is in the reaction products after food metabolism. The energy dif-ference is what sustains life.

We see inefficiency at work in the food chain. Larger creatures feed on smallercreatures, who, in turn, eat smaller creatures, and so on down the line to landplants and ocean plankton that are nourished by the Sun. Advancing each step upthe food chain involves inefficiency. In the African bush, 10 kilograms of grassmay produce 1 kilogram of gazelle. However, it will require 10 kilograms of gazelleto sustain 1 kilogram of lion. We see that each energy transformation alongthe food chain contributes to overall inefficiency. Interestingly enough, some ofthe largest creatures on the planet, the elephant and the blue whale, consumelower down on the food chain. Humans also are considering such tiny organismsas krill and yeast as efficient sources of nourishment.

-JVL) (') C

Energy is nature's wayof keeping score.

Sources of EnergyExcept for nuclear and geothermal power, the source of practically all ourenergy is the Sun. Sunlight evaporates water, which later falls as rain; rainwa-ter flows into rivers and turns water wheels or modern generator turbines andthen returns to the sea. On a longer time scale, the energy of sunlight produceswood and, on a still longer time scale, petroleum, coal, and natural gas. Thesematerials are the result of photosynthesis, a biological process that incorporatesthe Sun's radiant energy into plant tissue. The world's present supply of fossilenergy is being exhausted in the wink of an eye (a few hundred years) relativeto the time required to produce it (millions of years). Whereas petroleum andcoal fueled the industries of the twentieth century, their roles will diminish inthis present century. So we look to alternative sources of energy.

7Note that J:Cmj2)(2v/ = mu", which is twice the value Jmv2 of the heavier player of mass m and speed v.


FIGURE 7.21Dry-rock geothermal power.(a) A hole is sunk severalkilometers into dry granite.(b) Water is pumped intothe hole at high pressureand fractures surroundingrock to form a cavity with in-creased surface area. (c) Asecond hole is sunk to inter-cept the cavity. (d) Water iscirculated down one holeand through the cavity,where it is superheated,before rising through thesecond hole. After driving aturbine, it is recirculated intothe hot cavity again, makinga closed cycle.

Sooner or later, allthe sunlight that fallson Earth will be radi-ated back into space.Energy in any ecosys-tem is always intransit-you can rent it,but you can't own it.

a.

--tFirstII/hofe....--JL.,

TliIi11

b. d.Powerpfant

j[J[L

c.

Pump-rI' Second~ hole,,_

~ Hydraulic* fracturing

Energy in sunlight is nicely captured by way of photovoltaic cells to gen-erate electricity. They're found in solar-powered calculators and, more recently,in flexible solar shingles on the roof tops of buildings. Solar-energy technologyoffers a promising future because photovoltaic cells can generate large quanti-ties of electricity for nations with sufficient sunlight and sufficient land area. Tomeet all the energy needs of the United States through photovoltaic sources, anarea as large as Massachusetts might be needed. But it is not expected photo-voltaic sources alone will supply the electricity we will need in the future.

Even the wind, caused by unequal warming of Earth's surface, is a form ofsolar power. The energy of wind can be used to turn generator turbines withinspecially equipped windmills. Because wind power can't be turned on and offat will, it is now only a supplement to fossil and nuclear fuels for large-scalepower production. Harnessing the wind is most practical when the energy itproduces is stored for future use, such as in the form of hydrogen.

The most concentrated form of usable energy is in uranium-a nuclear fuelthat could provide large quantities of energy for many decades. Advanced fissiontechnology that involves breeder reactors and the use of thorium could extend thattime line to many hundreds of years (Chapter 34). Nuclear power plants do notrequire much land area and are dependent on location only to the extent that theyneed cooling water. Present-day plants use nuclear fission, but it is likely thatnuclear fusion will predominate in the future. Controlled nuclear fusion remainsan intriguing energy alternative of vast magnitude. At the present time, public con-cern about anything nuclear prevents the growth of nuclear power in the UnitedStates. It is interesting to note that Earth's interior is kept hot because of a formof nuclear power, radioactive decay, which has been with us since time zero.

A by-product of radioactive decay in Earth's interior is geothermal energy-heat that can be tapped beneath the Earth's surface. Geothermal energy is com-monly found in areas of volcanic activity, such as Iceland, New Zealand, Japan,and Hawaii, where heated water near Earth's surface is tapped to provide steamfor running turbogenerators. In locations where heat from volcanic activity isnear the ground surface in the absence of groundwater, another method holdspromise for producing electricity: dry-rock geothermal power, where cavities aremade in deep, dry, hot rock into which water is introduced. When the waterturns to steam, it is piped to a turbine at the surface. Then it is returned to thecavity for reheating.

-JVL) (J C

Inventors take heed:When introducing anew idea, first be sureit is in context withwhat is presentlyknown. For example,it should be consistentwith the conservationof energy.

[Insi ts


Geothermal power, like solar, wind, and water power, is friendly to the envi-ronment. Other methods for obtaining energy have serious environmental con-sequences. Although nuclear power isn't a polluter of the atmosphere, it remainscontroversial because of the nuclear wastes that are generated. The combustionof fossil fuels, on the other hand, leads to increased atmospheric concentrationsof carbon dioxide, sulfur dioxide, and other pollutants, and to excess warming ofthe atmosphere.

Current attention is acknowledging hydrogen-powered vehicles, part of apotential future hydrogen economy. It must be emphasized that hydrogen is notan energy source. Like electricity, hydrogen is a carrier or storehouse of energythat requires an energy source. Only part of the work required to separatehydrogen from water or hydrocarbons is the energy available for use. Again,for emphasis, hydrogen is not a source of energy.

As the world population increases, so does our need for energy--especiallysince per capita demand is also growing. With the rules of physics to guidethem, technologists are presently researching newer and cleaner ways to developenergy sources. But they race to keep ahead of a growing world population andgreater demand in the developing world. Unfortunately, so long as controllingpopulation is politically and religiously incorrect, human misery becomes thecheck to unrestrained population growth. H.G. Wells once wrote (in The Out-line of History), "Human history becomes more and more a race between edu-cation and catastrophe."

Summary of TermsWork The product ofthe force and the distance moved

by the force:W= Fd

(More generally, work is the component offorce in thedirection of motion times the distance moved.)

Power The time rate ofwork:work

Power =--time

(More generally, power is the rate at which energy isexpended.)

EnI!rgyThe property of a system that enables it to dowork.

Mechanical energy Energy due to the position of some-thing or the movement of something.

Potential energy The energy that something possessesbecause of its position.

Kinetic energy Energy of motion, quantified by therelationship

Kinetic energy = ~mv".Work-energy theorem The work done on an object

equals the change in kinetic energy of the object.Work = ~KE

(Work can also transfer other forms of energy to asystem. )

Conservation of energy Energy cannot be created ordestroyed; it may be transformed from one forminto another, but the total amount of energy neverchanges.

Machine A device, such as a lever or pulley, that increases(or decreases) a force or simply changes the directionofa force.

Conservation of energy for machines The work output ofany machine cannot exceed the work input. In an idealmachine, where no energy is transformed into thermalenergy, workinput= workoutput;(Fd)input= (Fd)output.

lever Simple machine consisting ofa rigid rod pivoted ata fixed point called the fulcrum.

Efficiency The percentage of the work put into a machinethat is converted into useful work output. (Moregenerally, useful energy output divided by total energyinput. )

Suggested ReadingBodanis, David. E = mc2.A Biography of the World's

Most Famous Equation. New York: Berkley PublishingGroup, 2002. A delightful and engaging history of ourunderstanding of energy.


Review Questions1. When is energy most evident?

Work2. A force sets an object in motion. When the force is

multiplied by the time of its application, we call thequantity impulse, which changes the momentum of thatobject. What do we call the quantity force X distance?

3. Cite an example in which a force is exerted on anobject without doing work on the object.

4. Which requires more work-lifting a 50-kg sack avertical distance of 2 m or lifting a 2S-kg sack avertical distance of 4 m?

PowerS. If both sacks in the preceding question are lifted their

respective distances in the same time, how does thepower required for each compare? How about for thecase in which the lighter sack is moved its distance inhalf the time?

Mechanical Energy6. Exactly what is it that enables an object to do work?

Potential Energy7. A car is raised a certain distance in a service-station

lift and therefore has potential energy relative to thefloor. Ifit were raised twice as high, how muchpotential energy would it have?

8. Two cars are raised to the same elevation on service-station lifts. If one car is twice as massive as theother, how do their potential energies compare?

9. When is the potential energy of something significant?

Kinetic Energy10. A moving car has kinetic energy. If it speeds up until

it is going four times as fast, how much kinetic energydoes it have in comparison?

Work-Energy Theorem11. Compared with some original speed, how much

work must the brakes ofa car supply to stop a carthat is moving four times as fast? How will the stop-ping distance compare?

12. If you push a crate horizontally with 100 N across a1O-m factory floor, and friction between the crateand the floor is a steady 70 N, how much kineticenergy is gained by the crate?

13. How does speed affect the friction between a roadand a skidding tire?

Conservation of Energy14. What will be the kinetic energy of a pile driver ram

when it undergoes a 10 kJ decrease in potentialenergy?

15. An apple hanging from a limb has potential energybecause of its height. If it falls, what becomes of thisenergy just before it hits the ground? When it hitsthe ground?

16. What is the source of energy in sunshine?

Machines17. Can a machine multiply input force? Input distance?

Input energy? (If your three answers are the same, seekhelp, for the last question is especially important.)

18. If a machine multiplies force by a factor offour, whatother quantity is diminished, and by how much?

19. A force of 50 N is applied to the end of a lever, whichis moved a certain distance. If the other end of thelever moves one-third as far, how much force canit exert?

Efficiency20. What is the efficiency of a machine that miraculously

converts all the input energy to useful output energy?

21. How does the useful work output ofa machine andthe total energy input relate to its efficiency?

22. What happens to the percentage of useful energy asit is transformed from one form to another?

Comparison of Kinetic Energy and Momentum23. What does it mean to say that momentum is a vector

quantity and that energy is a scalar quantity?

24. Can momenta cancel? Can energies cancel?

25. If a moving object doubles its speed, how much moremomentum does it have? How much more energy?

26. If a moving object doubles its speed, how muchmore impulse does it provide to whatever it bumpsinto (how much more wallop)? How much morework does it do as it is stopped (how much moredamage)?

Energy for Life27. In what sense are our bodies machines?

Sources of Energy28. What is the ultimate source of energies for the burn-

ing of fossil fuels, dams, and windmills?

29. What is the ultimate source of geothermal energy?

30. Can we correctly say that a new source of energy ishydrogen? Why or why not?

One-Step CalculationsWork = force X distance: W = Fd

1. Calculate the work done when a force ofl N moves abook 2 m.

2. Calculate the work done when a 20-N force pushes acart 3.5 m.

3. Calculate the work done in lifting a 500-N barbell2.2 m above the floor, (What is the potential energyof the barbell when it is lifted to this height?)

Power = work/time: P = W/t4. Calculate the watts of power expended when a force

of 1 N moves a book 2 m in a time interval of 1 s?

S. Calculate the power expended when a 20-N forcepushes a cart 3.5 m in a time of 0.5 s.

6. Calculate the power expended when a 500-N barbellis lifted 2.2 m in 2 s.

Gravitational potential energy = weight X height:PE = mgh

7. How many joules of potential energy does a l-kg bookgain when it is elevated 4 m? When it is elevated 8 m?

8. Calculate the increase in potential energy when a20-kg block of ice is lifted a vertical distance of2 m.

9. Calculate the change in potential energy of8 millionkg of water dropping 50 m over Niagara Falls.

Kinetic energy = 1/2 mass X speed2: KE = 1/2 mv210. Calculate the number of joules of kinetic energy a

l-kg book has when tossed across the room at aspeed of 2 m/so

11. Calculate the kinetic energy of a 3-kg toy cart thatmoves at 4 m/so

12. Calculate the kinetic energy ofthe same cart movingat twice the speed.

Work-energy theorem: Work = 6.KE13. How much work is required to increase the kinetic

energy of a car by 5000 J?

14. What change in kinetic energy does an airplane expe-rience on takeoff if it is moved a distance of 500 mby a sustained net force of 5000 N?

Exercises1. Why is it easier to stop a lightly loaded truck than a

heavier one that has equal speed?

2. Which requires more work to stop-a light truck or aheavy truck moving with the same momentum?


3. How much work do you do on a 25-kg backpackwhen you walk a horizontal distance of 100 m?

4. If your friend pushes a lawnmower four times as faras you do while exerting only half the force, whichone of you does more work? How much more?

S. Why does one get tired when pushing against astationary wall when no work is done on the wall?

6. Which requires more work: stretching a strong springa certain distance or stretching a weak spring thesame distance? Defend your answer.

7. Two people who weigh the same climb a Aight ofstairs. The first person climbs the stairs in 30 s, whilethe second person climbs them in 40 s. Whichperson does more work? Which uses more power?

8. Is more work required to bring a fully loaded truckup to a given speed, than the same truck lightlyloaded? Defend your answer.

9. In determining the potential energy ofTenny's drawnbow (Figure 7.7), would it be an underestimate or anoverestimate to multiply the force with which sheholds the arrow in its drawn position by the distanceshe pulled it? Why do we say the work done is theaverage force X distance?

10. A cart gains energy as it rolls down a hill. What is theforce that does the work? (Don't just say "gravity.")

11. When a rifle with a longer barrel is fired, the force ofexpanding gases acts on the bullet for a longerdistance. What effect does this have on the velocityof the emerging bullet? (Do you see why long-rangecannons have such long barrels?)

12. Your friend says that the kinetic energy of an objectdepends on the reference frame of the observer.Explain why you agree or disagree.

13. You and a Aight attendant toss a ball back and forth inan airplane in Aight. Does the KE of the ball depend onthe speed ofthe airplane? Carefully explain.

14. You watch your friend take off in a jet plane, and youcomment on the kinetic energy she has acquired. Butshe says she has no such increase in kinetic energy.Who is correct?

1S. When a jumbo jet lands, there is a decrease in both itskinetic and potential energy. Where does this energy go?

16. A baseball and a golfball have the same momentum.Which has the greater kinetic energy?

17. You have a choice of catch ing a baseball or a bowl ingball, both with the same KE. Which is safer?

18. Explain how the sport of pole vaulting dramaticallychanged when flexible fiberglass poles replaced stiffwooden poles.

19. At what point in its motion is the KE of a pendulumbob at a maximum? At what point is its PE at a


maximum? When its KE is at half its maximum value,how much PE does it have?

20. A physics instructor demonstratesenergy conservation by releasing aheavy pendulum bob, as shown inthe sketch, allowing it to swing toand fro. What would happen if, inhis exuberance, he gave the bob a slight shove as itleft his nose? Explain.

21. Does the International Space Station have gravita-tional PE? KE? Explain.

22. What does the work-energy theorem say about thespeed ofa satellite in circular orbit?

23. A moving hammer hits a nail and drives it into a wall.If the hammer hits the nail with twice the speed, howmuch deeper will the nail be driven? Ifit hits withthree times the speed?

24. Why does the force of gravity do no work on (a) abowling ball rolling along a bowling alley, and (b) asatellite in circular orbit about the Earth?

25. Why does the force of gravity do work on a car thatrolls down a hill, but no work when it rolls along alevel part of the road?

26. Does the string that supports a pendulum bob dowork on the bob as its swings to and fro? Does theforce of gravity do any work on the bob?

27. A crate is pulled across a horizontal floor by a rope.At the same time, the crate pulls back on the rope,in accord with Newton's third law. Does the workdone on the crate by the rope then equal zero?Explain.

28. On a playground slide, a child has potential energythat decreases by 1000 J while her kinetic energyincreases by 900 J. What other form of energy isinvolved, and how much?

29. Someone wanting to sell you a SuperBall claims thatit will bounce to a height greater than the heightfrom which it is dropped. Can this be?

30. Why can't a SuperBall released from rest reach itsoriginal height when it bounces from a rigid floor?

31. Consider a ball thrown straight up in the air. Atwhat position is its kinetic energy at a maximum?Where is its gravitational potential energy at amaximum?

32. Discuss the design of the roller coaster shown in thesketch in terms of the conservation of energy.

!'

33. Suppose that you and two classmates are discussingthe design of a roller coaster. One classmate saysthat each summit must be lower than the previousone. Your other classmate says this is nonsense, foras long as the first one is the highest, it doesn't mat-ter what height the others are. What do you say?

34. Consider the identical balls released from rest onTracks A and B, as shown. When they reach the rightends of the tracks, which will have the greater speed?Why is this question easier to answer than the similarone (Exercise 40) in Chapter 3?

35. Suppose an object is set sliding, with a speed lessthan escape velocity, on an infinite friction less planein contact with the surface of the Earth, as shown.Describe its motion. (Will it slide forever at a con-stant velocity? Will it slide to a stop? In what way willits energy changes be similar to that ofa pendulum?)

36. If a golf ball and a Ping-Pong ball both move with thesame kinetic energy, can you say which has thegreater speed? Explain in terms of the definition ofKE. Similarly, in a gaseous mixture of massive mole-cules and light molecules with the same average KE,can you say which have the greater speed?

37. Does a car burn more gasoline when its lights areturned on? Does the overall consumption of gasolinedepend on whether or not the engine is running whilethe lights are on? Defend your answer.

38. Running a car's air conditioner usually increases fuelconsumption. But, at certain speeds, a car with itswindows open and with the air conditioner turnedoff can consume more fuel. Explain.

39. When the girl in Figure 7.14 jacks up a car, how canapplying so little force produce sufficient work toraise the car?

40. Why bother using a machine ifit cannot multiplywork input to achieve greater work output?

41. You tell your friend that no machine can possibly putout more energy than is put into it, and your friendstates that a nuclear reactor puts out more energythan is put into it. What do you say?

42. What famous equation describes the relationship be-tween mass and energy?

43. This may seem like an easy question for a physicstype to answer: With what force does a rock thatweighs 10 N strike the ground if dropped from a restposition 10 m high? In fact, the question cannot beanswered unless you know more. Why?

44. Your friend is confused about ideas discussed inChapter 4 that seem to contradict ideas discussedin this chapter. For example, in Chapter 4, welearned that the net force is zero for a car travelingalong a level road at constant velocity, and, in thischapter, we learned that work is done in such acase. Your friend asks, "How can work be donewhen the net force equals zero?" Explain.

45. In the absence of air resistance, a ball thrown verticallyupward with a certain initial KE will return to itsoriginal level with the same KE. When air resistance isa factor affecting the ball, will it return to its originallevel with the same, less, or more KE? Does youranswer contradict the law of energy conservation?

46. You're on a rooftop and you throw one ball downwardto the ground below and another upward. The secondball, after rising, falls and also strikes the groundbelow. If air resistance can be neglected, and if yourdownward and upward initial speeds are the same,how will the speeds of the balls compare upon strikingthe ground? (Use the idea of energy conservation toarrive at your answer.)

47. Going uphill, the gasoline engine in a gasoline-electrichybrid car provides 75 horsepower while the totalpower propelling the car is 90 horsepower. Burninggasoline provides the 75 horsepower. What providesthe other 15 horsepower?

48. When a driver applies brakes to keep a car goingdownhill at constant speed and constant kineticenergy, the potential energy of the car decreases.Where does this energy go? Where does most of itgo with a hybrid vehicle?

49. Does the KE of a car change more when it goes from10 to 20 km/h or when it goes from 20 to 30 krn/h?

SO. Can something have energy without having momen-tum? Explain. Can something have momentum with-out having energy? Defend your answer.

51. When the mass ofa moving object is doubled with nochange in speed, by what factor is its momentumchanged? Bywhat factor is its kinetic energy changed?

52. When the velocity of an object is doubled, by whatfactor is its momentum changed? By what factor isits kinetic energy changed?

53. Which, if either, has greater momentum: a 1-kg ballmoving at 2 m/s or a 2-kg ball moving at 1 m/s?Which has greater kinetic energy?


54. A car has the same kinetic energy when travelingnorth as when it turns around and travels south. Isthe momentum of the carthe same in both cases?

ss. If an object's KE is zero, what is its momentum?56. If your momentum is zero, is your kinetic energy

necessarily zero also?

57. Iftwo objects have equal kinetic energies, do theynecessarily have the same momentum? Defend youranswer.

58. Two lumps of clay with equal and opposite momentahave a head-on collision and come to rest. Is momen-tum conserved? Is kinetic energy conserved? Why areyour answers the same or different?

59. You may choose between two head-on collisions withkids on skateboards. One is with a light kid movingrather fast, and the other is with a twice-as-heavy kidmoving half as fast. Considering only the issues ofmass and speed, which collision do you prefer?

60. Scissors for cutting paper have long blades and shorthandles, whereas metal-cutting shears have longhandles and short blades. Bolt cutters have very longhandles and very short blades. Why is this so?

61. Discuss the fate of the physics instructor sandwichedbetween the beds of nails (Figure 7.20) if the blockwere less massive and unbreakable and the bedscontained fewer nails.

62. Consider the swinging-balls apparatus. If two ballsare lifted and released, momentum is conserved astwo balls pop out the other side with the same speedas the released balls at impact. But momentumwould also be conserved if one ball popped out attwice the speed. Can you explain why this neverhappens? (And can you explain why this exercise is inChapter 7 rather than in Chapter 6?)

63. An inefficient machine is said to "waste energy."Does this mean that energy is actually lost? Explain.

64. If an automobile were to have a 100% efficient engi ne,transferring all of the fuel's energy to work, would theengine be warm to your touch? Would its exhaust heat


the surrounding air? Would it make any noise? Wouldit vibrate? Would any of its fuel go unused?

65. To combat wasteful habits, we often speak of"conserving energy," by which we mean turning offlights and hot water when they are not being used,and keeping thermostats at a moderate level. In thischapter, we also speak of "energy conservation."Distinguish between these two usages.

66. When an electric company can't meet its customers'demand for electricity on a hot summer day, shouldthe problem be called an "energy crisis" or a "powercrisis"? Explain.

67. Your friend says that one way to improve air qualityin a city is to have traffic lights synchronized so thatmotorists can travel long distances at constantspeed. What physics principle supports this claim?

68. The energy we require to live comes from the chemi-cally stored potential energy in food, which istransformed into other energy forms during themetabolism process. What happens to a personwhose combined work and heat output is less thanthe energy consumed? What happens when the per-son's work and heat output is greater than theenergy consumed? Can an undernourished personperform extra work without extra food? Defend youranswers.

69. Once used, can energy be regenerated? Is your answerconsistent with the common term "renewable energy"?

70. What do international peace, cooperation, andsecurity have to do with addressing the world'senergy needs?

Problems1. The second floor of a house is 6 m above street level.

How much work is required to lift a 300-kg refrigeratorto the second-floor level?

2. Belly-flop Bernie dives from atop a tall flagpole into aswimming pool below. His potential energy at thetop is 10,000 J. What is his kinetic energy when hispotential energy reduces to 1000 J?

3. Which produces the greater change in kinetic energy:exerting a 1O-N force for a distance of 5 m, or exertinga 20-N force over a distance of 2 m? (Assume that allof the work goes into KE.)

4. This question is typical on some driver's-licenseexams: A car moving at 50 krn/h skids 15 m withlocked brakes. How far will the car skid with lockedbrakes at 150 km/h?

5. A lever is used to lift a heavy load. When a 50-Nforce pushes one end of the lever down 1.2 m, theload rises 0.2 m. Calculate the weight of the load.

6. In raising a 5000-N piano with a pulley system, theworkers note that, for every 2 m of rope pulleddown, the piano rises 0.2 m. Ideally, how much forceis required to lift the piano?

7. In the hydraulic machineshown, it is observed that,when the small piston ispushed down 10 cm, thelarge piston is raised 1 cm. Ifthe small piston is pusheddown with a force of 100 N,what is the most force thatthe large piston could exert?

8. A 60-kg skydiver moving at terminal speed falls 50 m in1 s. What power is the skydiver expending on the air?

9. Consider the inelastic collision between the twofreight cars in the previous chapter (Figure 6.14). Themomentum before and after the collision is thesame. The KE, however, is less after the collision thanbefore the collision. How much less, and whatbecomes of th is energy?

10. Using the definitions of momentum and kineticenergy, p = mv and KE = G)mv2, show, by algebraicmanipulation, that you can write KE = p2/2m . Thisequation tells us that, if two objects have the samemomentum, the one of less mass has the greaterkinetic energy (see Exercise 2).

11. How many kilometers per literwill a car obtain ifitsengine is 25% efficient and it encounters an averageretarding force of 500 N at highway speed? Assumethat the energy content of gasoline is 40 MJ/liter.

12. The power we derive from metabolism can do workand can generate heat. (a) What is the mechanicalefficiency of a relatively inactive person who expends100 W of power to produce about 1 W of power inthe form of work, while generating about 99 Wofheat? (b) What is the mechanical efficiency of acyclist who, in a burst of effort, produces 100 W ofmechanical power from 1000 W of metabolic power?

t?I

conceptual energy hewitt-2

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