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Work

Using Machines

Simple Machines

£06 Levers

Lab UsingSimple Machines

I Virtual Lab What is therelationship between work,

nd distance?

ifSk

It Seemed Longer going UpHave you ever thought of a mountain bikeas a machine? A mountain bike actually is acombination of simple machines. Like allmachines, a bicycle makes doing workeasier. A mountain bike, for example, getsyou uphill and downhill faster than you cantravel by walking or running.

Science Journal Diagram a bicycle and identify theparts you think are simple machines.

Start-Up Activities

'LABIDoing Work with a Simple MachineDid you know you can lift several timesyour own weight with the help of a pulley?Before the hydraulic lift was invented, a carmechanic used pulleys to raise a car off theground. In this lab you'll see how a pulley canincrease a force. •#*!• jgf "J^

1 1. Complete thesafety form.

2. Tiea rope severalmeters in lengthto the center of a

broom handle.

Have one student

old both ends of

ie handle.

3. Have another student hold the endsof a second broom handle and face the

first student as shown in the photo.

4. Have a thirdstudent loop the free end ofthe rope around the second handle, making six or seven loops.

5. The third student should stand to the side

of one of the handles and pull on the freeend ofthe rope. The two students holdingthe broom handles should preventthehandles from coming together.

6. Think Critically Describe how theappliedforce waschanged. What would happen ifthe number of rope loops were increased?

increase a force. <m

i *£4

fH

s, *•*

FOLDABLESWork and Machines Make the

following Foldableto help youunderstand how machines

make doing work easier.

|Study Organizer

Fold a sheet of

paper vertically inhalf from top tobottom.

Fold in half from

side to side with

the fold at the top.

Unfold the paperonce. Cut only thefold of the top flapto make two tabs.

Turn the papervertically and labelthe front tabs as

shown.

Work WithoutMachines

Work WithMachines

List Before you read thechapter, list five examplesof work you do without machines, and fiveexamplesof workyou do with machines. Next to eachexample, rate the effort needed to do the work ona scale of 1 (little effort) to 3 (much effort).

Science^ : : • :'

Preview thischapter's contentand activities at

gpescience.com

'153

ft ^m

\J WorkReading Guide

'Wfalt You'll Learn *W6f> It's ImportantDoing work is another way of transferring energy from one place toanother.

O Review Vocabularyenergy: the ability to cause change

New Vocabulary

• work

• power

Explain the meaning of work.Describe how work and energy

are related.

Calculate work.

Calculate power.

Figure 1 When you lift astackof books, yourarms applya

force upward and the books moveupward. Because the force anddistance are in the same direction,

your arms have done work onthebooks.

W

Force

Distance

What is work?Have you done any work today? To manypeople, the word work means something

they do to earn money. In that sense, work can be anything fromfilling fast-food orders or loading trucks to teaching or doing wordprocessing on a computer. The word work also means exerting aforce with your muscles. Aperson might say he orshe does workwhile pushing as hard as they can against awall that doesn't move.However, in science the word work is used in a different way.

Work Makes Something Move Press your hand againstthe surface of your desk as hard as you can. Have you doneany work? The answer is no, no matter how tired your effortmakes you feel. Remember that a force is a push or a pull. Forwork to be done, a force must make something move. Work isthe energy transferred when a force makes an object move. Ifyou push against the desk and it doesn't move, then youhaven't done any work on the desk.

Doing Work There are two conditions that have tobe satisfiedfor a force to do workon an object. One is that the applied forcemust make the object move, and the other is that the movementmust be in the same direction as the applied force.

For example, if you pick up a pile of books from the floor, asin Figure 1,you dowork on thebooks. The books move upward,in the direction of the force you are applying. If you hold thebooks inyour arms without moving thebooks, you are not doingwork on the books. You're stillapplying an upward force to keepthe books from falling, but no movement is taking place.

154 CHAPTER 6 Work and Machines

Force and Direction of Motion when you carry bookswhile walking, like the student in Figure 2, youmight think thatyour arms are doing work. After all, you are exerting a force onthe books with your arms, and the books are moving. Your armsmight even feel tired. However, in this case the force exerted byyour arms does no work on the books.The force exerted byyourarms on the books is upward, but the books are moving horizontally. The force you exert upward is at right angles to thedirection the books are moving. As a result, your arms exert noforce in the direction the books are moving.

Reading Check Howarean appliedforce and an object's motionrelated when work is done?

Work and EnergyHow are work and energy related? When work is done, a

transfer of energy always occurs. This is easier to understandwhen you think about carrying a heavy box up a flight of stairs.Remember that whenthe height of an object above Earth's surfaceincreases, the gravitational potential energy of the objectincreases. As you move up thestairs, you increase the height ofthebox above Earth's surface. This causes the gravitational potentialenergy of the box to increase.

You may recall that energy is the ability to cause change. Ifsomething has energy, it can transfer energy to another object bydoing work on thatobject. When you do work onan object, youincrease itsenergy. Thestudent carrying thebox in Figure 3 transfers chemical energy in his muscles to the box. Energy is alwaystransferred from the object that is doing the work tothe object onwhich the work is done.

Force

Distance

Figure 2 If you hold a stackof books and walkforward, yourarms are exerting a force upward.

However, the distance the books

move is horizontal. Therefore,

your arms are not doing work

on the books.

Figure 3 By carrying a box upthe stairs, you are doing work.You transfer energy to the box.Explain howthe energy of theboxchangesas thestudentclimbsthe stairs.

SECTION 1 Work 155

Calculating Work The amount of work done depends onthe amount of force exerted and the distance over which the

force is applied. When a force is exerted and an object moves inthe direction of the force, the amount of work done can be calculated as follows.

Work Equation

work (in joules) = applied force (in newtons) X distance (in meters)

W= FJ

In this equation, force is measured in newtons and distance ismeasured in meters. Work, like energy, is measured in joules.One joule isabout the amount of work required to lift a baseballa vertical distance of 0.7 m.

Applying Math Solve a Simple Equation

WORK You push a refrigerator with a force of 100 N. If you move the refrigerator adistance of 5 m, how much work do you do?

known values and the unknown value

Identify the known values:

you push arefrigerator with aforce of 100 N Imeans )> F= 100 Nyou move the refrigerator adistance of5m I means^ d—5m

Identify the unknown value:how much work you do I means ^ y/ = ?j

I the problem

Substitute the known values F= 100 N and d = 5 m into the work equation.

W= Fd= (100 N) (5 m) = 500 Nm - 500 Jyour answer

Does your answer seem reasonable? Check your answer by dividing the work youcalculated bythe force given in the problem. The result should be thedistance given inthe problem.

Practice Problems

1. Aforce of 75 N isexerted on a 45-kg couch, and the couch is moved 5 m. How muchwork is done in moving the couch?

2. Alawn mower ispushed with a force of 80 N. If 12,000 I ofwork isdone in mowing alawn, what is the total distance the lawn mower was pushed?

3. Thebrakes on a cardo 240,000 I of work in stopping the car. If the car travels a distance of50 m while thebrakes are being applied, what isthe force thebrakes exert on the car?

For more practice problems go to page 879, and visit Math Practice at gpescience.com.

156 CHAPTER 6 Work and Machines

When is Work done? Suppose you give abook apush and itslides along a table for a distance of 1 m before it comes to astop. The distance you use to calculate the work you did is howfar the object moved while the force was being applied. Eventhough the book moved 1 m, you did work on the book onlywhile your hand was in contact with it. The distance in the formula for work is the distance the book moved while your handwas pushing on the book. As Figure 4 shows,work is done on anobject only when a force is being applied to the object.

PowerSuppose you and another student are pushing boxes of

books up a ramp to load them into a truck. To make the job fun,you make a game of it, racing to see who can push a box up theramp faster. The boxes weigh the same, but your friend is able topush a box a little faster than you can. She moves a box up theramp in 30 s. It takes you 45 s.Youboth do the same amount ofwork on the books because the boxes weigh the same and aremoved the samedistance. The only difference is the time it takesto do the work.

In this game, your friend has more power than you do.Power is the amount of work done in one second. It is a rate, therate at which work is done.

r Reading Check How is power related to work?

Figure 4 Apitcher exerts aforce on the ball to throw it to the

catcher. After the ball leaves her

hand, the pitcher no longer is

exerting any force on the ball. She

does work on the ball only while it

is in her hand.

Calculating YourWork and Power

Procedure

1. Complete the safety form.2. Find a set of stairs that you

can safely walk and run up.Measure the vertical heightof the stairs in meters.

3. Record how many secondsit takes you to walk andthen run up the stairs.

4. Calculate the workyoudid in both walking andrunning up the stairs. Theforce isyourweight in new-tons (yourweight in poundstimes 4.5). The distance isthe vertical height of thestairs.

5. Use the formula/5 = Wit

to calculate the power youneeded to both walk and

to run up the stairs.

Analysis1. Is the workyou did walking

and running up the stepsthe same?

2. Which required morepower, walking or runningup the steps? Why?

SECTION 1 Work 157

The symbol forwork, W, isusuallyitalicized. However,

the abbreviation

forwatt, W,isnot

italicized.

Calculating Power Power is the rate at which work is done.To calculate power, divide the work done by the time that isrequired to do the work.

Power Equation

power (in watts)

P =

work (in joules)

time (inseconds)

W

The SI unit for power is the watt (W). One watt equals one jouleof work done in one second. Because the watt is a small unit,power often is expressed in kilowatts. One kilowatt (kW) equals1,000 W.

Applying Math Solve a Simple Equation

POWER You do 900 J of work in pushing a sofa. If it took 5 s to move the sofa, what was yourpower?

PI known values and the unknown value

Identify the known values:You do 900 Jof work Imeans ^ w=900 J

it took 5sto move the sofa Imeans ^ f=5s

Identify the unknown value:what was your power? I means j^ p= ?w

I the problem

Substitute the known values W = 900 J and t = 5 s into the power equation.

p _ W- 9001 = 180 j/s = 180 Wt 5 s

your answer

Does your answer seem reasonable? Check your answer by multiplying the power youcalculated by the time given in the problem. The result should be the work given in theproblem.

Practice Problems

1. To lift a baby from a crib, 50 Jofwork is done. How much power is needed ifthe babyis lifted in 0.5 s?

2. If a runner's power is 130 W, how much work is done by the runner in 10 minutes?

3. The power produced by an electric motor is 500 W. How long will it take the motor todo 10,000 J of work?

For more practice problems go to page 879, and visit Math Practice at gpescience.com.

158 CHAPTER6 Work and Machines

Power and Energy Doing work is a way of transferringenergy from one object to another. Just as power is the rate atwhich work is done, power is also the rate at which energy istransferred. When energy is transferred, the power involved canbe calculated by dividing the energy transferred by the timeneeded for the transfer to occur.

Power Equation for Energy Transfer

power (in watts)

P

energy transferred (in joules)

time (in seconds)E^

For example, when the lightbulb in Figure 5 is connected to anelectric circuit, energy is transferred from the circuit to thelightbulb filament. The filament converts the electrical energysupplied to the lightbulb into heat and light. The power used bythe lightbulb is the amount of electrical energy transferred tothe lightbulb each second.

Figure 5 This 100-W lightbulbconvertselectrical energy into lightand heat at a rate of 100 J/s.

SummaryWork and Energy

• Work is done on an object when a force isexerted on the object and it moves in thedirection of the force.

• Ifa force, F, isexerted on an objectwhile theobject moves a distance, d, in the directionof the force, the work done is

W=Fd

• When work is done on an object, energy istransferred to the object.

Power

• Power is the rate at which work is done orenergy is transferred.

• When work is done, power can be calculatedfrom the equation

t

• When energy is transferred, power can becalculated from the equation

£

rP = ±

More Section Review gpescience.com

Self Check

1. Explain how the scientific definition of workis differentfrom the everyday meaning.

2. Describe a situation in which a force isapplied but nowork is done.

3. Explain howwork and energyare related.

4. Think Critically In which ofthe following situations iswork being done?

a. A person shovels snow off a sidewalk.

b. Aworker lifts bricks, one at a time, from the groundto the back of a truck.

c. Aroofer's assistant carries a bundle of shinglesacross a construction site.

Applying Math

Calculate Force Find the force a person exerts inpullinga wagon 20 m if 1,500 J of work is done.

Calculate Work Acar's engine produces 100 kW ofpower. How much work does the engine do in 5 s?

Calculate Energy Acolor TV uses 120Wof power.How much energy does the TV use in 1 hour?

SECTION 1 Work 159

u

C Using Machines

Ti/^at You'll Learn• Explain how machines make

doing work easier.• Calculate the mechanical

advantage of a machine.• Calculate the efficiency of a

machine.

Figure 6 Acar jack is an example of a machinethat increases an

applied force.

Reading Guide

Ti/ty It's ImportantCars, stairs, and teeth are all examplesof machines that makeyour lifeeasier.

9 ReviewVocabularyforce: a push or a pull

New Vocabulary

• machine

• input force• output force• mechanical advantage• efficiency

What is a machine?A machine is a device that makes doing work easier. When

you think ofamachine, you may picture adevice with an engineand many moving parts. However, machines can be simple.Some machines, such as knives, scissors, and doorknobs, areused every day to make doing work easier.

Making Work EasierMachines can make work easier by increasing the force that

can be applied to an object. A screwdriver increases the forceyou apply to a screw. Asecond way that machines can makework easier is by increasing the distance over which a force canbe applied. Aleaf rake is an example of this type of machine.

Machines also can make work easier by changing thedirection of an applied force. A simple pulley changesa downward force to an upward force.

Increasing Force A car jack, such as the one inFigure 6, is an example of a machine that increases anapplied force. The upward force exerted by the jack isgreater than the downward force you exert on the handle. However, the distance you push the handle downward is greater than the distance the car is pushedupward. Because work is the product of force and distance, the work donebythe jack isnot greater than thework you do onthe jack. The jack increases theappliedforce, but it doesn't increase the work done.

Force and Distance why does the mover in Figure 7pushthe heavy furniture up the ramp instead oflifting itinto the truck?It is easier because less force is needed to push the furniture up theramp than is needed to lift it.

The work done in lifting an object depends on the change inheight of the object. Thesame amount of work is done whetherthe mover pushes the furniture up the long ramp or lifts itstraight up. If she uses a ramp to liftthe furniture, she moves thefurniture alonger distance than ifshe just raised it straight up.Ifthe work stays the same and the distance is increased, then lessforce will be needed to do the work.

Reading Check How does a ramp make lifting an objecteasier?

Figure 7 Whether the moverslidesthe chair up the ramp orlifts it directly into the truck,

she will do the same amount

of work. Doing the work overa longer distance allows her to

use less force.

Figure 8 An ax blade changesthe direction of the force from

vertical to horizontal.

Changing Direction Some machines change thedirection of the force you apply. When you use the carjack, you exert a force downward onthe jack handle. Theforce exerted by the jack on the car is upward. The directionof theforce you apply is changed from downward toupward. Some machines change the direction of theforce that is applied to them in another way. The wedge-shaped blade ofan ax is one example. When you use anax to split wood, you exert a downward force as youswing the ax toward the wood. As Figure 8 shows, theblade changes the downward force into a horizontal forcethat splits the wood apart. K •* **

SECTION 2 Using Machines 161

Figure 9 Acrowbar increasesthe force you applyand changes itsdirection.

Machines MultiplyingForce

Procedure IL* ^2 IE1. Complete the safety form.2. Open a can of food using a

manual can opener thathas circular blades.

WARNING: Do not touchcan opener's cutting bladesorthecutedges of the cans'lids.

3. Open another can of food,but this time grasp thehandle as close as you canto the handle's pivot point.

Analysis1. Compare how difficult it

was to open the first canwith how difficult it was to

open the second can.2. Infer why a can opener

makes it easier to open a

metal can. How would youdesign a can openerto make openingcans even

easier? m -^rV 8t %v unlTtfi Vwoffle

The Work Done by MachinesTo pry the lid off awooden crate with acrowbar, you'd slip the

endof thecrowbar under theedge of thecrate lidandpush downon the handle. By moving the handle downward, you do work onthe crowbar. As the crowbarmoves, it doeswork on the lid, liftingit up. Figure 9 shows how the crowbar increases the amount offorce being applied and changes the direction ofthe force.

When you use a machine such as a crowbar, you are movingsomething that resists being moved. For example, if you use acrowbar to pry the lid off a crate, you are working against thefriction between the nails in the lid and the crate.You alsocoulduse a crowbar to move a large rock. In this case, you would beworking against gravity—the weight of the rock.

Input and Output Forces Two forces are involved when amachine is used to do work. You exert a force on the machine,such as a bottle opener, and the machine then exerts a force onthe object you are trying to move, such as abottle cap. The forcethat is applied to the machine is called the input force. Fin standsfor the input force. The force applied by the machine is called theoutput force, symbolized by Fout. When you try to pull anail outof wood with a hammer, as in Figure 10, you apply the inputforce on thehandle. The outputforce isthe force theclaw appliesto the nail.

Two kinds of work need to be considered when you use amachine: the work done byyou on the machine and the workdone by the machine. When you use a crowbar, you do workwhen you apply force to the crowbar handle and make it move.The work done by you on a machine is called the input workand is symbolized by W[n. The work done by the machine iscalled the output work and is abbreviated Wout.

162 CHAPTER 6 Work and Machines

Conserving Energy Remember that energy is alwaysconserved. When you do work on a machine, you transferenergy to the machine. When the machine does work on anobject, energy is transferred from the machine to the object.Because energy cannot be created or destroyed, the amountof energy the machine transfers to the object cannot begreater than the amount of energy you transfer to themachine. A machine cannot create energy, so W is nevergreater than W- .° in

However, the machine does not transfer all of the energyit receives to the object. In fact, when a machine is used,some of the input energy changes to thermal energy due tofriction. The energy that changes to thermal energy cannotbe used to do work, so WQut is always smaller than W-m.

Ideal Machines Remember that work is calculated by multiplying force by distance. The input work is the product oftheinput force and the distance over which the input force is exerted.The output work is the product ofthe output force and the distanceover which that force is exerted.

Suppose a perfect machine could be built in which therewere no friction. None of the input work or output work wouldbe converted to thermal energy. For such an ideal machine, theinput work would equal the output work. For an ideal machine,

WL Wout

Suppose the ideal machine increases the force applied to it. Thismeans that the output force, FoaP is greater than the input force, E .Recall that work is equal to force times distance. If F is greaterthan Pin, then W-m and Wout can be equal only if the input force isapplied over a greater distance than the output force.

For example, suppose the hammer claw in Figure 10 moves adistance of1cm to remove anail. Ifan output force of1,500 Nisexerted by the claw ofthe hammer, and you move the handle ofthehammer 5 cm, you can find the input force as follows.

^inFin 4n

^in (0.05 m)

Fin (0.05 m)

= W"out

" out "out

F- =in

(1,500 N) (0.01m)

15N-m

300 N

Because the distance you move the hammer is longer thanthe distance the hammer moves the nail, the input force is lessthan the output force.

Figure 10 When prying a nailout of a piece of wood with a claw

hammer, you exert the input forceon the handle of the hammer, and

the clawexerts the output force.Describe how the hammer

changes the input force.

Science^Topic: Rube GoldbergVisit gpescience.com for Web

links to information about Rube

Goldberg devices.

Activity Use the informationthat you find to sketch a Rube-

Goldberg-like device designedtoburst a balloon.

SECTION 2 Using Machines 163

Figure 11 Window blinds usea machine that changes the direc

tion ofan input force. Adownwardpull on the cord is changed to anupward force on the blinds. Theinputand output forces are equal,so the AM is 1.

INTEGRATE

Chemistry

Graphite LubricantGraphite is a solid thatsometimes is used as a

lubricant to increase the

efficiency of machines.Find out what element

graphite is made of andwhy graphite is a goodlubricant.

Mechanical

AdvantageMachines such as the car

jack, the ramp, the crow bar,and the claw hammer make

work easier by making theoutput force greater than theinput force. The ratio of theoutput force to the input forceis the mechanical advantageof a machine. The mechanical

advantage (MA) of a machinecan be calculated with the fol

lowing equation.

Mechanical Advantage Equation

mechanical advantageoutput force (in newtons)

input force (in newtons)

MA— QllL

F

Figure 11 shows that the mechanical advantage equals one whenonly the direction of the input force changes.

Ideal IVlechanical Advantage The mechanical advantage ofamachine without friction is called the ideal mechanical advantage,or IMA. The IMA canbe calculated by dividing the input distanceby the output distance. For a real machine, the IMA would be themechanical advantage ofthe machine if there were nofriction.

EfficiencyFor real machines, some of the energy put into a machine is

always converted to thermal energy by frictional forces. For thisreason, the output work of a machine is always less than thework put into the machine.

Efficiency is a measure of how much of thework put into amachine is changed into useful output work by the machine. Amachine with high efficiency produces less thermal energy fromfriction, so more of the input work is changed to useful outputwork.

I lleaaingcneckWhy isthe output work always less than theinput work fora realmachine?

164 CHAPTER 6 Work and Machines

Calculating Efficiency To calculate the efficiency of amachine, the output work is divided by the input work.Efficiency is usually expressed as a percentage by this equation:

Efficiency Equation

efficiency (%)

efficiency

output work (in joules)

(in joules)X 100%

En X 100%

In an ideal machine, there is no friction and the output workequals the input work. So the efficiency of an ideal machine is100 percent. In a real machine, friction causes the output workto always be less than the input work. So the efficiency ofa realmachine is always less than 100 percent.

Increasing Efficiency Machines can be made more efficientby reducing friction. This usually is done by adding a lubricant,such as oil or grease, to surfaces that rub together, as shown inFigure 12. A lubricant fills in the gaps between the surfaces,enabling the surfaces to slide past each other more easily.

Figure 12 Oil reduces the frictionbetween two surfaces. Oilfills the

space between the surfaces so highspots don't rubagainst each other.

SummaryWork and Machines

• Machines make doing work easier by changing the applied force, changing the distanceover which the force is applied, orchangingthe direction of the applied force.

• Because energy cannot be created ordestroyed, the output work cannot begreaterthan the input work.

• In a real machine, some ofthe input work isconverted into heat by friction.

Mechanical Advantage and Efficiency• The mechanical advantage ofa machine is the

output force divided bythe input force:FoutMA

• The efficiency ofa machine is the output workdivided by the input work times 100%:

efficiency = —^ x 100%W;„

More Section Review gpescience.com

Self Check

1. Describe the circumstances for which the outputworkwould equal the input work in a machine.

2. Infer how lubricating a machine affects the outputforce exerted by the machine.

3. Explain why, ina real machine, the output work isalways less than the input work.

4. Think Critically The mechanical advantage ofamachine is less than one. Compare the distances overwhich the input and output forces areapplied.

Applying Math5. Calculate the mechanical advantage ofa hammer ifthe

inputforce is 125Nand the outputforce is 2,000 N.

6. Calculate Efficiency Find the efficiency ofa machinethat does 800J ofwork ifthe inputwork is 2,400 J.

7. Calculate Force Find the force needed to lift a 2,000-Nweight using a machine with a mechanical advantageof 15.

SECTION 2 Using Machines 165