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152152
Work and Machines
sections
1 Work
2 Using Machines
3 Simple Machines
Lab Levers
Lab Using Simple Machines
Virtual Lab What is therelationship between workforce and distance
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
Diagram a bicycle and identify theparts you think are simple machinesScience Journal
(bkgd)Jakob HelbigGetty Images
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153153
Work and Machines Make thefollowing Foldable to help youunderstand how machinesmake doing work easier
Fold a sheet ofpaper vertically inhalf from top tobottom
Fold in half fromside to side withthe fold at the top
Unfold the paperonce Cut only thefold of the top flapto make two tabs
Turn the papervertically and labelthe front tabs asshown
List Before you read the chapter list five examplesof work you do without machines and five exam-ples of work you do with machines Next to eachexample rate the effort needed to do the work ona scale of 1 (little effort) to 3 (much effort)
STEP 4
STEP 3
STEP 2
STEP 1
Doing Work with a Simple MachineDid you know you can lift several timesyour own weight with the help of a pulleyBefore the hydraulic lift was invented a carmechanic used pulleys to raise a car off theground In this lab yoursquoll see how a pulley canincrease a force
1 Tie a rope severalmeters in lengthto the center of abroom handleHave one studenthold both ends ofthe handle
2 Have another stu-dent hold the ends
of a second broom handle and face thefirst student as shown in the photo
3 Have a third student loop the free end ofthe rope around the second handle mak-ing six or seven loops
4 The third student should stand to the sideof one of the handles and pull on the freeend of the rope The two students holdingthe broom handles should prevent thehandles from coming together
5 Think Critically Describe how theapplied force was changed What wouldhappen if the number of rope loops wereincreased
Start-Up Activities
Preview this chapterrsquos contentand activities at gpesciencecom
Work WithoutMachines
Work WithMachines
(bkgd)Jakob HelbigGetty Images (inset)Timothy Fuller
154 CHAPTER 6 Work and Machines
What is workHave 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 A person might say he or she does workwhile pushing as hard as they can against a wall that doesnrsquot moveHowever 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 doesnrsquot move then youhavenrsquot done any work on the desk
Doing Work There are two conditions that have to be satisfiedfor a force to do work on 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 do work on the books The books move upwardin the direction of the force you are applying If you hold thebooks in your arms without moving the books you are not doingwork on the books Yoursquore still applying an upward force to keepthe books from falling but no movement is taking place
WorkReading Guide
Explain the meaning of work Describe how work and energy
are related Calculate work Calculate power
Doing work is another way of trans-ferring energy from one place toanother
Review Vocabularyenergy the ability to cause change
New Vocabulary
bull work
bull power
Force
Distance
Figure 1 When you lift astack of books your arms apply aforce upward and the books moveupward Because the force anddistance are in the same directionyour arms have done work on thebooks
Tim CourlasHorizons Companies
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SECTION 1 Work 155
Force and Direction of Motion When you carry bookswhile walking like the student in Figure 2 you might 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 by yourarms on the books is upward but the books are moving hori-zontally 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
How are an applied force and an objectrsquos motionrelated when work is done
Work and Energy How 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 stairsRemember that when the height of an object above Earthrsquos surfaceincreases the gravitational potential energy of the objectincreases As you move up the stairs you increase the height of thebox above Earthrsquos 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 that object When you do work on an object youincrease its energy The student carrying the box in Figure 3 trans-fers chemical energy in his muscles to the box Energy is alwaystransferred from the object that is doing the work to the object onwhich the work is done
Figure 3 By carrying a box upthe stairs you are doing workYou transfer energy to the boxExplain how the energy of thebox changes as the student climbsthe stairs
Distance
Force
Figure 2 If you hold a stackof books and walk forward yourarms are exerting a force upwardHowever the distance the booksmove is horizontal Thereforeyour arms are not doing workon the books
a(t)Tim CourlasHorizons Companies (b)Michael NewmanPhotoEdit Inc
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156 CHAPTER 6 Work and Machines
Calculating Work The amount of work done depends onthe amount of force exerted and the distance over which theforce is applied When a force is exerted and an object moves inthe direction of the force the amount of work done can be cal-culated as follows
In this equation force is measured in newtons and distance ismeasured in meters Work like energy is measured in joulesOne joule is about the amount of work required to lift a baseballa vertical distance of 07 m
Solve a Simple Equation
1 A force of 75 N is exerted on a 45-kg couch and the couch is moved 5 m How muchwork is done in moving the couch
2 A lawn mower is pushed with a force of 80 N If 12000 J of work is done in mowing alawn what is the total distance the lawn mower was pushed
3 The brakes on a car do 240000 J of work in stopping the car If the car travels a distance of50 m while the brakes are being applied what is the force the brakes exert on the car
For more practice problems go to page 879 and visit Math Practice at gpesciencecom
WORK You push a refrigerator with a force of 100 N If you move the refrigerator a
distance of 5 m how much work do you do
known values and the unknown value
Identify the known values
you push a refrigerator with a force of 100 N F 100 N
you move the refrigerator a distance of 5 m d 5 m
Identify the unknown value
how much work you do W J
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 you
calculated by the force given in the problem The result should be the distance given in
the problem
CHECK
SOLVE
means
means
means
IDENTIFY
Work Equation
work (in joules) applied force (in newtons) distance (in meters)
W Fd
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SECTION 1 Work 157
When is work done Suppose you give a book a push 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 for-mula 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 funyou 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 You both do the same amount ofwork on the books because the boxes weigh the same and aremoved the same distance The only difference is the time it takesto do the work
In this game your friend has more power than you doPower is the amount of work done in one second It is a rate therate at which work is done
How is power related to work
Figure 4 A pitcher exerts aforce on the ball to throw it to thecatcher After the ball leaves herhand the pitcher no longer isexerting any force on the ball Shedoes work on the ball only while itis in her hand
Calculating Your Work and PowerProcedure1 Find a set of stairs that you
can safely walk and run upMeasure the vertical heightof the stairs in meters
2 Record how many secondsit takes you to walk andthen run up the stairs
3 Calculate the work youdid in both walking andrunning up the stairs Theforce is your weight in new-tons (your weight in poundstimes 45) The distance isthe vertical height of thestairs
4 Use the formula P Wtto calculate the power youneeded to both walk andto run up the stairs
Analysis1 Is the work you did walking
and running up the stepsthe same
2 Which required morepower walking or runningup the steps Why
Michelle BridwellPhotoEdit Inc
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158 CHAPTER 6 Work and Machines
Calculating Power Power is the rate at which work is doneTo calculate power divide the work done by the time that isrequired to do the work
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 unitpower often is expressed in kilowatts One kilowatt (kW) equals1000 W
Solve a Simple Equation
1 To lift a baby from a crib 50 J of work is done How much power is needed if the babyis lifted in 05 s
2 If a runnerrsquos 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 10000 J of work
For more practice problems go to page 879 and visit Math Practice at gpesciencecom
POWER You do 900 J of work in pushing a sofa If it took 5 s to move the sofa what was your
power
known values and the unknown value
Identify the known values
You do 900 J of work W 900 J
it took 5 s to move the sofa t = 5 s
Identify the unknown value
what was your power P W
the problem
Substitute the known values W 900 J and t = 5 s into the power equation
P Wt
905
0s
J 180 Js 180 W
your answer
Does your answer seem reasonable Check your answer by multiplying the power you
calculated by the time given in the problem The result should be the work given in the
problem
CHECK
SOLVE
means
means
means
IDENTIFY
The symbol forwork W is usuallyitalicized Howeverthe abbreviationfor watt W is notitalicized
Power Equation
power (in watts) work (in joules)time (in seconds)
P W
t
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SECTION 1 Work 159
Self Check1 Explain how the scientific definition of work is different
from the everyday meaning
2 Describe a situation in which a force is applied but nowork is done
3 Explain how work and energy are related
4 Think Critically In which of the following situations iswork being done
a A person shovels snow off a sidewalk
b A worker lifts bricks one at a time from the groundto the back of a truck
c A rooferrsquos assistant carries a bundle of shinglesacross a construction site
SummaryWork and Energy
bull Work is done on an object when a force isexerted on the object and it moves in thedirection of the force
bull If a force F is exerted on an object while theobject moves a distance d in the directionof the force the work done is
W Fd
bull When work is done on an object energy istransferred to the object
Power
bull Power is the rate at which work is done orenergy is transferred
bull When work is done power can be calculatedfrom the equation
P Wt
bull When energy is transferred power can becalculated from the equation
P Et
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
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 lightbulbconverts electrical energy into lightand heat at a rate of 100 Js
Power Equation for Energy Transfer
power (in watts) energy transferred (in joules)
time (in seconds)
P E
t
5 Calculate Force Find the force a person exerts inpulling a wagon 20 m if 1500 J of work is done
6 Calculate Work A carrsquos engine produces 100 kW ofpower How much work does the engine do in 5 s
7 Calculate Energy A color TV uses 120 W of powerHow much energy does the TV use in 1 hour
More Section Review gpesciencecomJules FrazierGetty Images
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What is a machineA machine is a device that makes doing work easier When
you think of a machine you may picture a device with an engineand many moving parts However machines can be simpleSome 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 A second way that machines can makework easier is by increasing the distance over which a force canbe applied A leaf 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 han-dle However the distance you push the handle down-ward is greater than the distance the car is pushedupward Because work is the product of force and dis-tance the work done by the jack is not greater than thework you do on the jack The jack increases the appliedforce but it doesnrsquot increase the work done
Forceexertedby jack
Distancejackmoves Distance
you push
Yourforce
Using MachinesReading Guide
Explain how machines makedoing work easier
Calculate the mechanicaladvantage of a machine
Calculate the efficiency of amachine
Cars stairs and teeth are all exam-ples of machines that make your lifeeasier
Review Vocabularyforce a push or a pull
New Vocabulary
bull machine
bull input force
bull output force
bull mechanical advantage
bull efficiency
Figure 6 A car jack is an exam-ple of a machine that increases anapplied force
Mic
hael
New
man
Get
ty im
ages
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SECTION 2 Using Machines 161
Force and Distance Why does the mover in Figure 7 pushthe heavy furniture up the ramp instead of lifting it into the truckIt 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 The same amount of work is done whetherthe mover pushes the furniture up the long ramp or lifts itstraight up If she uses a ramp to lift the furniture she moves thefurniture a longer distance than if she just raised it straight upIf the work stays the same and the distance is increased then lessforce will be needed to do the work
How does a ramp make lifting an objecteasier
Changing Direction Some machines change thedirection of the force you apply When you use the carjack you exert a force downward on the jack handle Theforce exerted by the jack on the car is upward The direc-tion of the force 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 of an 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
Figure 7 Whether the moverslides the chair up the ramp orlifts it directly into the truckshe will do the same amountof work Doing the work overa longer distance allows her touse less force
HeightDistance
Resultingforce
Appliedforce
Figure 8 An ax blade changesthe direction of the force fromvertical to horizontal
(t)Mark Burnett (b)Tony FreemanPhotoEdit Inc
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162 CHAPTER 6 Work and Machines
The Work Done by MachinesTo pry the lid off a wooden crate with a crowbar yoursquod slip the
end of the crowbar under the edge of the crate lid and push downon the handle By moving the handle downward you do work onthe crowbar As the crowbar moves it does work on the lid liftingit up Figure 9 shows how the crowbar increases the amount offorce being applied and changes the direction of the 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 also coulduse a crowbar to move a large rock In this case you would beworking against gravitymdashthe 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 machinesuch as a bottle opener and the machine then exerts a force onthe object you are trying to move such as a bottle 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 a nail outof wood with a hammer as in Figure 10 you apply the inputforce on the handle The output force is the force the claw appliesto the nail
Two kinds of work need to be considered when you use amachine the work done by you 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 moveThe work done by you on a machine is called the input workand is symbolized by Win The work done by the machine iscalled the output work and is abbreviated Wout
Figure 9 A crowbar increasesthe force you apply and changes itsdirection
Forceexerted
by crowbarApplied force
Machines MultiplyingForceProcedure1 Open a can of food using a
manual can opener thathas circular blades WARNING Do not touchcan openerrsquos cutting bladesor the cut edges of the cansrsquolids
2 Open another can of foodbut this time grasp thehandle as close as you canto the handlersquos pivot point
Analysis1 Compare how difficult it
was to open the first canwith how difficult it was toopen the second can
2 Infer why a can openermakes it easier to open ametal can How would youdesign a can openerto make opening cans even easier
Joseph P SinnotFundamental Photographs
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SECTION 2 Using Machines 163
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 objectBecause 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 Wout is nevergreater than Win
However the machine does not transfer all of the energyit receives to the object In fact when a machine is usedsome of the input energy changes to thermal energy due tofriction The energy that changes to thermal energy cannotbe used to do work so Wout is always smaller than Win
Ideal Machines Remember that work is calculated by mul-tiplying force by distance The input work is the product of theinput force and the distance over which the input force is exertedThe output work is the product of the 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
Suppose the ideal machine increases the force applied to it Thismeans that the output force Fout is greater than the input force FinRecall that work is equal to force times distance If Fout is greaterthan Fin then Win 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 of 1 cm to remove a nail If an output force of 1500 N isexerted by the claw of the hammer and you move the handle of thehammer 5 cm you can find the input force as follows
Because the distance you move the hammer is longer thanthe distance the hammer moves the nail the input force is lessthan the output force
Win Wout
Fin din Fout dout
Fin (005 m) (1500 N) (001 m)
Fin (005 m) 15 Nmiddotm
Fin 300 N
Win Wout
Outputforce
Input force
Figure 10 When prying a nailout of a piece of wood with a clawhammer you exert the input forceon the handle of the hammer andthe claw exerts the output forceDescribe how the hammerchanges the input force
Topic Rube GoldbergVisit for Weblinks to information about RubeGoldberg devices
Activity Use the informationthat you find to sketch a Rube-Goldberg-like device designed toburst a balloon
gpesciencecom
Richard MegnaFundamental Photographs
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164 CHAPTER 6 Work and Machines
MechanicalAdvantage
Machines such as the carjack the ramp the crow barand the claw hammer makework easier by making theoutput force greater than theinput force The ratio of theoutput force to the input forceis the mechanical advantageof a machine The mechanicaladvantage (MA) of a machinecan be calculated with the fol-lowing equation
Figure 11 shows that the mechanical advantage equals one whenonly the direction of the input force changes
Ideal Mechanical Advantage The mechanical advantage of amachine without friction is called the ideal mechanical advantageor IMA The IMA can be calculated by dividing the input distanceby the output distance For a real machine the IMA would be themechanical advantage of the machine if there were no friction
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 the work 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
Why is the output work always less than theinput work for a real machine
Figure 11 Window blinds usea machine that changes the direc-tion of an input force A downwardpull on the cord is changed to anupward force on the blinds Theinput and output forces are equalso the MA is 1
Graphite LubricantGraphite is a solid thatsometimes is used as alubricant to increase theefficiency of machinesFind out what elementgraphite is made of andwhy graphite is a goodlubricant
Mechanical Advantage Equation
mechanical advantage output force (in newtons)
input force (in newtons)
MA FoutFin
Inputforce
Outputforce
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SECTION 2 Using Machines 165
Self Check1 Describe the circumstances for which the output work
would equal the input work in a machine
2 Infer how lubricating a machine affects the outputforce exerted by the machine
3 Explain why in a real machine the output work isalways less than the input work
4 Think Critically The mechanical advantage of amachine is less than one Compare the distances overwhich the input and output forces are applied
SummaryWork and Machines
bull Machines make doing work easier by chang-ing the applied force changing the distanceover which the force is applied or changingthe direction of the applied force
bull Because energy cannot be created ordestroyed the output work cannot be greaterthan the input work
bull In a real machine some of the input work isconverted into heat by friction
Mechanical Advantage and Efficiency
bull The mechanical advantage of a machine is theoutput force divided by the input force
MA FFo
i
u
n
t
bull The efficiency of a machine is the output workdivided by the input work times 100
efficiency WW
o
i
u
n
t 100
Calculating Efficiency To calculate the efficiency of amachine the output work is divided by the input workEfficiency is usually expressed as a percentage by this equation
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 of a realmachine is always less than 100 percent
Increasing Efficiency Machines can be made more efficientby reducing friction This usually is done by adding a lubricantsuch as oil or grease to surfaces that rub together as shown inFigure 12 A lubricant fills in the gaps between the surfacesenabling the surfaces to slide past each other more easily
Figure 12 Oil reduces the frictionbetween two surfaces Oil fills thespace between the surfaces so highspots donrsquot rub against each other
Oil
Surface
Surface
Surface
Surface
Efficiency Equation
efficiency () 100output work (in joules)
input work (in joules)
efficiency 100WoutWin
5 Calculate the mechanical advantage of a hammer if theinput force is 125 N and the output force is 2000 N
6 Calculate Efficiency Find the efficiency of a machinethat does 800 J of work if the input work is 2400 J
7 Calculate Force Find the force needed to lift a 2000-Nweight using a machine with a mechanical advantage of 15
More Section Review gpesciencecom
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166 CHAPTER 6 Work and Machines
Types of Simple MachinesIf you cut your food with a knife use a screwdriver or even
chew your food you are using a simple machine A simplemachine is a machine that does work with only one movementof the machine There are six types of simple machines leverpulley wheel and axle inclined plane screw and wedge Thepulley and the wheel and axle are modified levers and the screwand the wedge are modified inclined planes
LeversYoursquove used a lever if yoursquove used a wheelbarrow a lawn rake
or swung a baseball bat A lever is a bar that is free to pivot orturn around a fixed point The fixed point the lever pivots on iscalled the fulcrum The input arm of the lever is the distancefrom the fulcrum to the point where the input force is appliedThe output arm is the distance from the fulcrum to the pointwhere the output force is exerted by the lever
The output force produced by a lever depends on the lengthsof the input arm and the output arm If the output arm is longerthan the input arm the law of conservation of energy requiresthat the output force be less than the input force If the outputarm is shorter than the input arm then the output force isgreater than the input force
There are three classes of levers as shown in Figure 13 Thedifferences among the three classes of levers depend on the loca-tions of the fulcrum the input force and the output force
Simple MachinesReading Guide
Describe the six types of simplemachines
Explain how the different typesof simple machines make doingwork easier
Calculate the ideal mechanicaladvantage of the different typesof simple machines
All complex machines such as carsare made of simple machines Evenyour body contains simple machines
Review Vocabularycompound composed of separateelements or parts
New Vocabulary
bull simple machine
bull lever
bull pulley
bull wheel and axle
bull inclined plane
bull screw
bull wedge
bull compound machine
Outputforce
Inputforce
Fulcrum
Figure 13 There are threeclasses of levers
First-Class LeverThe fulcrum is between the inputforce and the output force
Third-Class LeverThe input force is between the ful-crum and the output force
Second-Class LeverThe output force is between thefulcrum and the input force
Outputforce
InputforceFulcrum
Outputforce
InputforceFulcrum
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SECTION 3 Simple Machines 167
First-Class Lever The screwdriver used to openthe paint can in Figure 14A is an example of a first-class lever For a first-class lever the fulcrum islocated between the input and output forces Theoutput force is always in the opposite direction to theinput force in a first-class lever
Second-Class Lever For a second-class lever theoutput force is located between the input force andthe fulcrum Look at the wheelbarrow in Figure 14B The girlapplies an upward input force on the handles and the wheel isthe fulcrum The output force is exerted between the input forceand the fulcrum For a second-class lever the output force isalways greater than the input force
Third-Class Lever Many pieces of sports equipment such asa baseball bat are third-class levers For a third-class lever theinput force is applied between the output force and the ful-crum The right-handed batter in Figure 14C applies the inputforce with the right hand and the left hand is the fulcrum Theoutput force is exerted by the bat above the right hand Theoutput force is always less than the input force in a third-classlever Instead the distance over which the output force isapplied is increased
Every lever can be placed in one of these classes Eachclass can be found in your body as shown in Figure 15 on thenext page
A baseball bat is a third-classlever The fulcrum here is the bat-terrsquos left hand
Figure 14 Levers are classified by the locations ofthe input force the output force and the fulcrum
The screwdriver is being used as a first-classlever The fulcrum is the paint can rim
A wheelbarrow is a second-class lever Thefulcrum is the wheel
Archimedes and the LeverThe Greek mathematicianArchimedes (287ndash212 BC)described how a levercould be used to increaseforce He also supposedlysaid ldquoGive me a place tostand and I will move theEarthrdquo Research one ofArchimedesrsquo inventionsand write a paragraphdescribing it
(t)Mark Burnett (l)Tom Pantages (r)Tony FreemanPhotoEdit Inc
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Figure 15
VISUALIZING LEVERS IN THE HUMAN BODY
168 CHAPTER 6 Work and Machines
All three types of leversmdashfirst-class second-class andthird-classmdashare found in
the human body The forces exertedby muscles in your body can beincreased by first-class and second-class levers while third-class leversincrease the range of movementof a body part Examples of how thebody uses levers to help it move areshown here
FIRST-CLASS LEVER The fulcrumlies between the input force and theoutput force Your head acts like a first-class lever Your neck muscles providethe input force to support the weightof your head
THIRD-CLASS LEVER The inputforce is between the fulcrum andthe output force A third-class leverincreases the range of motion ofthe output force When you do acurl with a dumbbell your forearmis a third-class lever
SECOND-CLASS LEVER The outputforce is between the fulcrum and theinput force Your foot becomes a second-class lever when you stand on your toes
Fulcrum
Input force
Output force
(t)Richard T Nowitz (c)David MadisonStone (b)John HenleyThe Stock Market
SECTION 3 Simple Machines 169
Ideal Mechanical Advantage of a Lever The ideal mechan-ical advantage or IMA for a lever can be calculated by dividing thelength of the input arm by the length of the output arm
PulleysA pulley is a grooved wheel with a rope chain or cable run-
ning along the groove A fixed pulley as shown in Figure 16 isa modified first-class lever The axle of the pulley acts as the ful-crum The two sides of the pulley are the input arm and outputarm A pulley can change the direction of the input force orincrease the output force depending on whether the pulley isfixed or movable A system of pulleys can change the directionof the input force and make the output force larger
What are the input arm output arm andfulcrum of a pulley
Fixed Pulleys The cable attached to an elevator passes over afixed pulley at the top of the elevator shaft A fixed pulley suchas the one in Figure 17 is attached to something that doesnrsquotmove such as a ceiling or wall Because a fixed pulley changesonly the direction of force the IMA is 1
Figure 16 A fixed pulley isanother form of the leverInfer the lengths of the input armand output arm in a pulley
Figure 17 A fixed pulleychanges only the direction of aforce You need to apply an inputforce of 4 N to lift the 4-N weight
Outputforce
Inputforce
4 N
4 N
IMA of a Lever
ideal mechanical advantage length of input arm (m)length of output arm (m)
IMA LinLout
AJ CopleyVisuals Unlimited
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7424011
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170 CHAPTER 6 Work and Machines
Movable Pulleys A pulley in which one end of the ropeis fixed and the wheel is free to move is called a movable pul-ley Unlike a fixed pulley a movable pulley does multiplyforce Suppose a 4-N weight is hung from the movable pulleyin Figure 18A The ceiling acts like someone helping you tolift the weight The rope attached to the ceiling will support halfof the weightmdash2 N You need to exert only the other halfof the weightmdash2 Nmdashto support and lift the weight The outputforce exerted on the weight is 4 N and the applied input forceis 2 N Therefore the IMA of the movable pulley is 2
For a fixed pulley the distance you pull the rope downwardequals the distance the weight moves upward For a movablepulley the distance you pull the rope upward is twice the dis-tance the weight moves upward
How does a movable pulley reduce the inputforce needed to lift a weight
The Block and Tackle A system of pulleys consisting offixed and movable pulleys is called a block and tackleFigure 18B shows a block and tackle made up of two fixed pul-leys and two movable pulleys If a 4-N weight is suspended fromthe movable pulley each rope segment supports one-fourth ofthe weight reducing the input force to 1 N The IMA of a pulleysystem is equal to the number of rope segments that support theweight The block and tackle shown in Figure 18B has an IMAof 4 The IMA of a block and tackle can be increased by increas-ing the number of pulleys in the pulley system
Figure 18 A movable pulleyand a pulley system called a blockand tackle reduce the force neededto lift a weight
With a movable pulley theattached side of the rope supportshalf of the 4-N weight You have toapply a 2-N force to lift the weight
4 N
2 N
2 N
4 N
1 N
1 N
1 N
1 N
1 N
In a block-and-tackle system the 4-Nweight is divided equallyamong each supportingrope segment In thiscase four rope segmentsare supporting theweight So you have toapply only a 1-N forceto lift the weight
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103495735
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Figure 19 The handle on a pencil sharpener is part of a wheel and axleYou apply a force to the handle This force is made larger by the wheel andaxle making it easy to turn the sharpening mechanism
SECTION 3 Simple Machines 171
Wheel and AxleCould you use the pencil sharpener in Figure 19 if the han-
dle werenrsquot attached The handle on the pencil sharpener is partof a wheel and axle A wheel and axle is a simple machine con-sisting of a shaft or axle attached to the center of a larger wheelso that the wheel and axle rotate together Doorknobs screw-drivers and faucet handles are examples of wheel and axlesUsually the input force is applied to the wheel and the outputforce is exerted by the axle
Mechanical Advantage of a Wheel and Axle Recall thatthe mechanical advantage of a lever is the length of the input armdivided by the length of the output arm A wheel and axle isanother modified lever The center of the axle is the fulcrum Theinput force is applied at the rim of the wheel So the length of theinput arm is the radius of the wheel The output force is exerted atthe rim of the axle So the length of the output arm is the radius ofthe axle The IMA of a wheel and axle is
According to this equation the IMA of a wheel and axle can beincreased by increasing the radius of the wheel
Wheel
Axle
Axle
IMA of a Wheel and Axle
ideal mechanical advantage radius of wheel (m)
radius of axle (m)
IMA rwra
Mark Burnett
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7350872
eng - iTunNORM 00000408 00000000 00003108 00000000 000033F0 00000000 00006042 00000000 00011572 00000000
172 CHAPTER 6 Work and Machines
Gears A gear is a wheel and axle with thewheel having teeth around its rim Whenthe teeth of two gears interlock the turningof one gear causes the other gear to turn
When two gears of different sizes areinterlocked they rotate at different ratesEach rotation of the larger gear causes thesmaller gear to make more than one rota-tion If the input force is applied to thelarger gear the output force exerted by thesmaller gear is less than the input force
Gears also may change the directionof the force as shown in Figure 20 When
the larger gear in is rotated clockwise the smaller gear rotatescounterclockwise
Inclined PlanesWhy do the roads and paths on mountains zigzag Would it
be easier to climb directly up a steep incline or walk a longerpath gently sloped around the mountain An inclined plane is asloping surface such as a ramp that reduces the amount of forcerequired to do work
Mechanical Advantage of an Inclined Plane You do thesame work by lifting a box straight up or pushing it up aninclined plane By pushing the box up an inclined plane how-ever the input force is exerted over a longer distance comparedto lifting the box straight up As a result the input force is lessthan the force needed to lift the box straight upward The IMA ofan inclined plane can be calculated from the following equation
The IMA of an inclined plane for a given height is increased bymaking the plane longer
When you think of an inclined plane you might think ofmoving an object up a rampmdashyou move and the inclined planeremains stationary The screw and the wedge however are vari-ations of the inclined plane in which the inclined plane movesand the object remains stationary
Figure 20 If an input force isapplied to the larger gear andit rotates clockwise the smallergear rotates counterclockwiseThe output force exerted by thesmaller gear is less than the inputforce applied to the larger gear
Topic NanobotsVisit for Weblinks to information about howtiny robots called nanobots mightbe used as microsurgicalinstruments
Activity Use the informationyou find to make a diagram of ananobot that might be used toperform surgery
gpesciencecom
IMA of an Inclined Plane
ideal mechanical advantage length of slope (m)height of slope (m)
IMA lh
Tom Pantages
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11373521
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SECTION 3 Simple Machines 173
The ScrewA screw is an inclined plane wrapped in a spiral around a
cylindrical post If you look closely at the screw in Figure 21 yoursquollsee that the threads form a tiny ramp that runs upward from its tipYou apply the input force by turning the screw The output force isexerted along the threads of the screw The IMA of a screw isrelated to the spacing of the threads The IMA is larger when thethreads are closer together However when the IMA is larger moreturns of the screw are needed to drive it into a material
How do you remove the lid from a jar of peanut butter suchas the one in Figure 21 If you look closely you will see threadssimilar to the ones on the screw in Figure 21 Where else can youfind examples of a screw
The WedgeLike the screw the wedge is also a simple
machine in which the inclined plane movesthrough an object or material A wedge is aninclined plane with one or two sloping sides Itchanges the direction of the input force
Look closely at the knife in Figure 22One edge is sharp and it slopesoutward at both sidesforming an inclined planeAs it moves through theapple the downward inputforce is changed to a hori-zontal force forcing theapple apart
Figure 21 A screw has an inclinedplane that wraps around the post ofthe screw
The thread gets thinner farther fromthe post This helps the screw force itsway into materials
Many lids such as those on peanutbutter jars also contain threads
Figure 22 A knife blade is awedge As you cut through theapple the blade pushes the halvesof the apple apart
(tl)file photo (tr)Mark Burnett (b)Amanita Pictures
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83904915
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174 CHAPTER 6 Work and Machines
Self Check1 Classify a screwdriver being used to turn a screw as one
of the six types of simple machines Explain how theIMA of a screwdriver could be increased
2 Determine for which class of lever the output force isalways greater than the input force For which class isthe output force always less than the input force
3 Make a diagram of a bicycle and label the parts of abicycle that are simple machines
4 Think Critically Use the law of conservation of energyto explain why in a second-class lever the distance overwhich the input force is applied is always greater thanthe distance over which the output force is applied
SummaryThe Lever Family
bull A lever is a bar that is free to pivot about afixed point called the fulcrum
bull There are three classes of levers based on therelative locations of the input force the out-put force and the fulcrum
bull A pulley is a grooved wheel with a ropechain or cable placed in the groove and is amodified form of a lever
bull The IMA of a lever is the length of the inputarm divided by the length of the output arm
bull A wheel and axle consists of a shaft or axleattached to the center of a larger wheel
The Inclined Plane Family
bull An inclined plane is a ramp or sloping surfacethat reduces the force needed to do work
bull The IMA of an inclined plane is the length ofthe plane divided by the height of the plane
bull A screw consists of an inclined plane wrappedaround a shaft
bull A wedge is an inclined plane that moves andcan have one or two sloping surfaces
Compound MachinesSome of the machines you use every day are
made up of several simple machines Two ormore simple machines that operate togetherform a compound machine
Look at the can opener in Figure 23 To openthe can you first squeeze the handles togetherThe handles act as levers and increase the forceapplied on a wedge which then pierces the can
You then turn the handle a wheel and axle to open the canA car is also a compound machine Burning fuel in the cylin-
ders of the engine causes the pistons to move up and down Thisup-and-down motion makes the crankshaft rotate The forceexerted by the rotating crankshaft is transmitted to the wheelsthrough other parts of the car such as the transmission and thedifferential Both of these parts contain gears which can changethe rate at which the wheels rotate the force exerted by thewheels and even reverse the direction of rotation
Wheel and axle Lever
Wedge
Figure 23 A compoundmachine such as a can opener ismade up of simple machines
5 Calculate IMA What is the IMA of a carrsquos steering wheelif the wheel has a diameter of 40 cm and the shaft itrsquosattached to has a diameter of 4 cm
6 Calculate Output Arm Length A lever has an IMA of 4 Ifthe length of the input arm is 10 m what is the lengthof the output arm
7 Calculate IMA A 60-m ramp runs from a sidewalk to aporch that is 20 m above the sidewalk What is theideal mechanical advantage of this ramp
More Section Review gpesciencecomSuperStock
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60656776
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Have you ever tried to balance a friend on aseesaw If your friend was lighter you had tomove toward the fulcrum In this lab you willuse the same method to measure the mass ofa coin
Real-World ProblemHow can a lever be used to measure mass
Goals Measure the lengths of the input arm and
output arm of a lever Calculate the ideal mechanical advantage
of a lever Determine the mass of a coin
Materialsstiff cardboard 3 cm by 30 cmcoins (one quarter one dime one nickel)balancemetric ruler
Safety Precautions
Procedure1 Measure the mass of each coin
2 Mark a line 2 cm from one end of the card-board strip Label this line Output
3 Slide the other end of the cardboard stripover the edge of a table until the stripbegins to tip Mark a line across the strip atthe table edge and label this line Input
4 Measure the mass of the strip to the near-est 01 g Write this mass on the input line
5 Center a dime on the output line Slide thecardboard strip until it begins to tip Markthe balance line Label it Fulcrum 1
6 Measure the lengths of the output andinput arms to the nearest 01 cm
7 Calculate the IMA of the lever Multiply theIMA by the mass of the lever to find theapproximate mass of the coin
8 Repeat steps 5 through 7 with the nickeland the quarter Mark the fulcrum lineFulcrum 2 for the nickel and Fulcrum 3 forthe quarter
Conclude and Apply1 Explain why there might be a difference
between the mass of each coin measuredby the balance and the mass measuredusing the lever
2 Explain what provides the input and outputforces for the lever
3 Explain why the IMA of the lever changesas the mass of the coin changes
Levers
Compare your results with those of otherstudents in your class For more help referto the Science Skill Handbook
LAB 175
inpu
t
ou
tpu
t
Mark Burnett
Model and InventModel and Invent
176 CHAPTER 6 Work and Machines
Real-World ProblemSuppose that you are the contractor on a one-story building with alarge air conditioner How can you get the air conditioner to the roofHow can you minimize the force needed to lift an object Whatmachines could you use Consider a fixed pulley a block and tacklesystem of pulleys and an inclined plane How can you find the effi-ciency of machines
Make a Model1 Work in teams of at least two Collect all the needed equipment
2 Sketch a model for each lifting machine Include a control in whichthe weight is lifted while being suspended directly from the springscale Model the inclined plane with a board 40-cm long andraised 10 cm at one end
3 Make a data table like the one below
4 Is the pulley support high enough that the block and tackle can lifta weight 10 cm
5 Obtain your teacherrsquos approval of your sketches and data tablebefore proceeding
Goals Model lifting devices
based on a block andtackle and on aninclined plane
Calculate the outputwork that will beaccomplished
Measure the forceneeded by eachmachine to lift aweight
Calculate the inputwork and efficiency foreach model machine
Select the bestmachine for your jobbased on the forcerequired
Possible Materialsspring scale 0ndash10 N range98-N weight (1-kg mass)double pulleysingle pulley string for the pulleysstand or support for
the pulleyswooden board 40 cm longsupport for board 10 cm
high
Safety Precautions
UsNng S Mmple Machines
Problem Data
d
Ideal Mechanical Advantage IMA
Input force FinFF N
Input distance din m
Output force FoutF N
Output distance doutd m
Workin FinFF din Joules
Workout FoutF doutd Joules
Efficiency (Workout Workin)
Do not write in this book
Test Your Model1 Tie the weight to the spring scale and measure the force required
to lift it Record the input force in your data table under Controlalong with the 10-cm input distance
2 Assemble the inclined plane so that the weight can be pulled upthe ramp at a constant rate The 40-cm board should be supportedso that one end is 10 cm higher than the other end
3 Tie the string to the spring scale and measure the force required tomove the weight up the ramp at a constant speed Record thisinput force under Inclined Plane in your data table Record 40 cmas the input distance for the inclined plane
4 Assemble the block and tackle using one fixed double pulley andone movable single pulley
5 Tie the weight to the single pulley and tie the spring scale to thestring at the top of the upper double pulley
6 Measure the force required to lift the weight with the block andtackle Record this input force
7 Measure the length of string that must be pulled to raise theweight 10 cm Record this input distance
Analyze Your Data1 Calculate the output work for all three methods of lifting the
98-N weight a distance of 10 cm
2 Calculate the input work and the efficiency for the control theinclined plane and the block and tackle
3 Compare the efficiencies of each of the three methods of lifting
Conclude and Apply1 Explain how you might improve the efficiency of the machine in
each case
2 Infer what types of situations would require theuse of a ramp over a pulley to help lift something
3 Infer which machines would be most likely tobe affected by friction
LAB 177
Make a poster showing how the bestmachine would be used to lift the airconditioner to the roof of the building
Hickson-Bender
SCIENCEANDSocietySCIENCEISSUES
THAT AFFECTYOU
The
Science of very very small
The
Science of very very small
Imagine an army of tiny robots each no biggerthan a bacterium swimming through yourbloodstream Welcome to the world of nanotechnology
the science of creating molecular-sizedmachines These machines are called nanobots
The smallest of these machines are only bil-lionths of a meter in size They are so tiny thatthey can do work on the molecular scale
Small Smaller SmallestNanotechnologists are predicting that within
a few decades they will be creating nanobotsthat can do just about anything as long as itrsquossmall Already nanotechnologists have builtgears 10000 times thinner than a human hairTheyrsquove also built tiny molecular ldquomotorsrdquo only50 atoms long At Cornell University nanotech-nologists created the worldrsquos smallest guitar It isappoximately the size of a white blood cell and iteven has six strings
In the future nanobots might transmit yourinternal vital signs to a nanocomputer implantedunder your skin There the data could be ana-lyzed for signs of disease Other nanomachinesthen could be sent to scrub your arteries clean ofdangerous blockages or mop up cancer cells oreven vaporize blood clots with tiny lasers Theseare just some of the possibilities in the imagina-tions of those studying the new science ofnanotechnology
This is the smallest guitar inthe world It is about as big as ahuman white blood cell Each ofits six silicon strings is 100 atomswide You can see the guitar onlywith an electron microscope
Acoustic relayattached to anonboard computersends andreceivesultrasound tocommunicatewith medicalteam
Pumpsremovetoxins fromthe body anddispensedrugs
Outershell madeof strongchemicallyinertdiamondsSensors and
manipulatorsdetect illnesses and perform cell-by-cell surgery
Up to 10 trillion nanobots each as small as 1200th thewidth of a human hair might be injected at once
TYPICAL PROBE S IZE
WIDTH OF A HUMAN HAIR
A N A T O M Y O F A
N A N O P R O B E
Design Think up a very small simple or complex machine thatcould go inside the body and do something What would themachine do Where would it go Share your diagram or design withyour classmates
For more information visit gpesciencecom
(t)courtesy D Carr amp H Craighead Cornell University (b)Joe Lertola
Work
1 Work is the energy transferred when a forcemakes an object move
2 Work is done only when a force producesmotion in the direction of the force
3 Power is the amount of work or theamount of energy transferred in a certainamount of time
Using Machines
1 A machinemakes workeasier bychanging thesize of theforce appliedby increasingthe distance anobject ismoved or bychanging thedirection of the applied force
2 The number of times a machine multipliesthe force applied to it is the mechanicaladvantage of the machine The actualmechanical advantage is always less thanthe ideal mechanical advantage
3 The efficiency of a machine equals the out-put work divided by the input work
4 Friction always causes the output work tobe less than the input work so no realmachine can be 100 percent efficient
Simple Machines
1 A simple machine is a machine that can dowork with a single movement
2 A simple machine can increase an appliedforce change its direction or both
3 A lever is a bar that is free to pivot about afixed point called a fulcrum A pulley is agrooved wheel with a rope running alongthe groove A wheel and axle consists of twodifferent-sized wheels that rotate togetherAn inclined plane is a sloping surface usedto raise objects The screw and the wedgeare special types of inclined planes
4 A combination of two or more simplemachines is called a compound machine
CHAPTER STUDY GUIDE 179
Use the Foldable that you made at the begin-ning of this chapter to help you review how machines makedoing work easier
Interactive Tutor gpesciencecom(t)Ed LalloLiaison Agency (bl)file photo (r)C Squared StudiosPhotoDisc
Complete each statement using a word(s) fromthe vocabulary list above
1 A combination of two or more simplemachines is a(n) _________
2 A wedge is another form of a(n) _________
3 The ratio of the output force to the inputforce is the _________ of a machine
4 A(n) _________ is a grooved wheel with arope chain or cable in the groove
5 The force exerted by a machine is the_________
6 Energy is transferred when _________ isdone
7 _________ is the rate at which work is doneor energy is transferred
Choose the word or phrase that best answers thequestion
8 Which of these is not done by a machine A) multiply forceB) multiply energyC) change direction of a forceD) work
9 Which of the following increases as the efficiency of a machine increases A) work input C) frictionB) work output D) IMA
10 In an ideal machine which of the follow-ing is trueA) Work input is equal to work outputB) Work input is greater than work outputC) Work input is less than work outputD) The IMA is always equal to one
Use the picture below to answer question 11
11 What simple machines make up a pair ofscissorsA) lever and pulleyB) pulley and wheel and axleC) wedge and pulleyD) wedge and lever
12 What term indicates the number of times amachine multiplies the input force A) efficiencyB) powerC) mechanical advantageD) resistance
13 How could you increase the IMA of aninclined planeA) increase its lengthB) increase its heightC) decrease its lengthD) make its surface smoother
14 What is the IMA of a screwdriver with ashaft radius of 3 mm and a handle radiusof 10 mmA) 03 C) 30B) 33 D) 13
15 What is the IMA of an inclined plane thatis 21 m long and 07 m highA) 03 C) 15B) 28 D) 30
180 CHAPTER REVIEW
compound machine p 174efficiency p 164inclined plane p 172input force p 162lever p 166machine p 160mechanical advantage
p 164
output force p 162power p 157pulley p 169screw p 173simple machine p 166wedge p 173wheel and axle p 171work p 154
Vocabulary PuzzleMaker gpesciencecom
22 Calculate Work Find the work needed tolift a 200-N book 20 m
23 Calculate Axle Radius A doorknob has anIMA equal to 85 If the diameter ofthe doorknob is 80 cm what is theradius of the shaft the doorknob isconnected to
24 Calculate Input Work A machine has anefficiency of 61 percent Find the inputwork if the output work is 140 J
25 Calculate Efficiency Using a ramp 6 mlong workers apply an input force of1250 N to move a 2000-N crate onto aplatform 2 m high What is the effi-ciency of the ramp
26 Calculate Power A person weighing 500 Nclimbs 3 m How much power isneeded to make the climb in 5 s
CHAPTER REVIEW 181
16 Copy and complete the concept map ofsimple machines using the followingterms compound machines mechanicaladvantage output force work
Use the table below to answer questions 17 and 18
17 Determine which of the levers listed in thetable above has the largest IMA
18 Calculate An input force of 50 N is appliedto lever B If the lever is 100 percent effi-cient what is the output force
19 Describe how the input force output forceand fulcrum should be arranged so that achild can lift an adult using his own bodyweight on a seesaw
20 Determine what arrangement of movableand fixed pulleys would give a mechanicaladvantage of 3
21 Explain which would give the best mechani-cal advantage for driving a screw downinto a board a screwdriver with a longthin handle or a screwdriver with a shortthick handle
Interpreting Graphics
2 m
6 m
input force
SimpleMachines
do
compares
combineto make
Lever Input and Output Arms
t Armm)
5
2
6
9
0
More Chapter Review gpesciencecom
Use the figure below to answer questions 1 and 2
1 The figure above shows a doorknob with aradius of 48 cm and a mechanical advan-tage of 40 What is the radius of the innerrod that connects the knob to the door
A 06 cm
B 12 cm
C 18 cm
D 24 cm
2 What would happen to the mechanicaladvantage if the radius of the doorknobwere doubled
A It would be multiplied by 4
B It would be multiplied by 2
C It would be divided by 4
D It would be divided by 2
3 A ramp is 28 m long and 12 m high Howmuch power is needed to push a box up theramp in 46 s with a force of 96 N
A 21 W
B 25 W
C 58 W
D 270 W
4 How much work is done in lifting a 910-kgbox onto a shelf 180 m high
A 506 J
B 164 J
C 495 J
D 161 J
5 An input force of 80 N is used to lift anobject weighing 240 N with a system ofpulleys How far down must the ropearound the pulleys be pulled to lift theobject a distance of 14 m
A 047 m
B 14 m
C 28 m
D 42 m
Use the figure below to answer questions 6 and 7
6 If a leverrsquos input arm is 8 cm and its outputarm is 24 cm what is the ideal mechanicaladvantage of the lever
A 4
B 3
C 033
D 025
Inputforce
Outputforce
182 STANDARDIZED TEST PRACTICE
Record your answers on the answer sheet provided by your teacher or on a sheet of paper
STANDARDIZED TEST PRACTICE 183
7 How much more work is done to push abox 25 m with a force of 30 N than topush a box 20 m with a force of 26 N
8 As you throw a ball you exert a force of42 N on the ball You exert this force onthe ball while the ball moves a distance of045 m The ball leaves your hand and trav-els a horizontal distance of 85 m to yourfriend How much work have you doneon the ball
Use the illustration below to answer questions 9
and 10
9 What is the ideal mechanical advantageof the pulley system shown in the figureabove
10 If the block supported by the pulley sys-tem has a weight of 20 N what isthe input force on the rope
11 Use the law of conservation of energy toexplain why it is impossible for the outputwork of a machine to be greater than themachinersquos input work
Use the illustration below to answer question 12
12 The boy in the figure below is carrying abox to the top of the stairs
PART A Describe how the work that the boydoes on the box is related to theenergy transfer that occurs Howdoes the energy of the box changeform as the boy carries the box upthe stairs
PART B Explain how the work power andenergy would change if the boywalked faster How would the workpower and energy change if thesteps were the same height butsteeper
Donrsquot Panic Stay calm during the test If you feel yourselfgetting nervous close your eyes and take five slow deep breaths
Standardized Test Practice gpesciencecomMichael NewmanPhotoEdit Inc