chapter 14: work, power, and machines. sps8. students will determine relationships among force,...

Chapter 14: Work, Chapter 14: Work, Power, and MachinesPower, and Machines

SPS8. Students will determine SPS8. Students will determine relationships among force, mass and relationships among force, mass and motion.motion.• e. Calculate amounts of work and e. Calculate amounts of work and

mechanical advantage using simple mechanical advantage using simple machines.machines.

Section 14.1 – Work and PowerSection 14.1 – Work and Power In science, In science, workwork is the product of is the product of forceforce

and and distancedistance. Work is done when a . Work is done when a forceforce acts on an object in the acts on an object in the directiondirection the object the object movesmoves..

For a For a forceforce to do to do workwork on an object, some on an object, some of the force must act in the same of the force must act in the same directiondirection as the object moves. If there is as the object moves. If there is no no movement, no work is donemovement, no work is done..

Diagonal ForcesDiagonal Forces

A A forceforce does not have to act entirely in the does not have to act entirely in the directiondirection of movement to do of movement to do workwork..

Any part of a Any part of a forceforce that does not act in the that does not act in the direction of motion direction of motion does no workdoes no work on an on an object. object.

What is Work?What is Work?

1.1. A scientist delivers a speech to an A scientist delivers a speech to an audience of his peers. audience of his peers.

2.2. A body builder lifts 350 pounds above his A body builder lifts 350 pounds above his head. head.

3.3. A mother carries her baby from room to A mother carries her baby from room to room. room.

4.4. A father pushes a baby in a carriage.A father pushes a baby in a carriage.

5.5. A woman carries a 20 kg grocery bag to A woman carries a 20 kg grocery bag to her car? her car?

NONO

YESYES

NONO

YESYES

NONO

Formula for WorkFormula for Work

W = F x dW = F x d

work = force x distancework = force x distance

The unit of force is The unit of force is newtonsnewtons.. The unit of distance is The unit of distance is metersmeters.. The unit of work is The unit of work is newton-metersnewton-meters.. One One newton-meternewton-meter is equal to one is equal to one joule joule

(J).(J).

Sample ProblemSample Problem

1. If a man pushes a concrete block 10 1. If a man pushes a concrete block 10 meters with a force of 20 N, how much meters with a force of 20 N, how much work has he done?work has he done?

d = 10m W = F x dF = 20N W = 20N x 10m = 200J200JW = ?

PowerPower PowerPower is the is the raterate at which at which workwork is done. is done. Doing work at a Doing work at a fasterfaster rate requires more rate requires more

powerpower. . To increase To increase powerpower, you can increases the , you can increases the

amount of workamount of work done in a given time, or done in a given time, or you can do a given amount of work in you can do a given amount of work in less less timetime..

Formula for PowerFormula for Power

P = W/tP = W/t

Power = work/timePower = work/time

The unit of The unit of workwork is a is a Joule,Joule, and the unit of and the unit of time is a time is a secondsecond. .

A joule per second is a A joule per second is a watt (Wwatt (W) which is ) which is the SI unit for power.the SI unit for power.

Sample ProblemsSample Problems1.Two physics students, Ben and Bonnie, 1.Two physics students, Ben and Bonnie,

are in the weightlifting room. Bonnie lifts are in the weightlifting room. Bonnie lifts the 50 kg barbell over her head the 50 kg barbell over her head (approximately .60 m) 10 times in one (approximately .60 m) 10 times in one minute; Ben lifts the 50 kg barbell the minute; Ben lifts the 50 kg barbell the same distance over his head 10 times in same distance over his head 10 times in 10 seconds. 10 seconds.

Which student does the most work? Which student does the most work?

Which student delivers the most Which student delivers the most power?power?

Sample ProblemsSample Problems

2. How much work does a 25N force do to 2. How much work does a 25N force do to lift a potted plant from the floor to a shelf lift a potted plant from the floor to a shelf 1.5m high?1.5m high?

3. How much force is needed to complete 3. How much force is needed to complete 72.3J of work over a distance of 22.8m?72.3J of work over a distance of 22.8m?

W = ? W = F x dF = 25N W = 25N x 1.5m = 37.5J37.5Jd = 1.5m

F = ? W = F x dW = 72.3J F = W/dD = 22.8m F = 72.3J = 3.171N3.171N

22.8m

Sample ProblemsSample Problems4. You exert a vertical force of 72N to lift a 4. You exert a vertical force of 72N to lift a

box to a height of 2m in a time of 17s. How box to a height of 2m in a time of 17s. How much power is used to lift the box?much power is used to lift the box?

5. You lift a book from the floor to a bookshelf 5. You lift a book from the floor to a bookshelf 5.4m above the ground. How much power 5.4m above the ground. How much power is used if the upward force is 15.0N and you is used if the upward force is 15.0N and you do the work in 2.0s?do the work in 2.0s?

F = 72N W = F x dd = 2m W = 72N x 2m = 144Jt = 17s P = W/tP = ? P = 144J/17s = 8.47W8.47W

d = 5.4m W = F x dF = 15.0N W = 15.0N x 5.4m = 81Jt = 2.0s P = W/tP = ? P = 81J/2.0s = 40.5W40.5W

Section 14.1 AssessmentSection 14.1 Assessment1.1. What conditions must exist in order What conditions must exist in order

for a force to do work on an object?for a force to do work on an object?

2.2. What formula relates work and What formula relates work and power?power?

3.3. How much work is done when a How much work is done when a vertical force acts on an object vertical force acts on an object moving horizontally?moving horizontally?

4.4. A desk exerts an upward force on a A desk exerts an upward force on a computer resting on it. Does this computer resting on it. Does this force to work?force to work?

Section 14.1 AssessmentSection 14.1 Assessment

5.5. You lift a large bag of flour from the You lift a large bag of flour from the floor to a 1m high counter, doing floor to a 1m high counter, doing 100J of work in 2s. How much power 100J of work in 2s. How much power do you use to lift the bag of flour?do you use to lift the bag of flour?

W = 100J P = W/tt = 2s P = 100J = 50W50WP = ? 2s

Section 14.2 – Work and MachinesSection 14.2 – Work and Machines A A machinemachine is a device that is a device that changeschanges a a

force.force. Machines make work Machines make work easiereasier to do. They to do. They

change the change the sizesize of the force needed, the of the force needed, the directiondirection of a force, or the of a force, or the distancedistance over over which a force acts.which a force acts.

Increasing ForceIncreasing Force Each complete rotation of a car jack handle Each complete rotation of a car jack handle

applies a applies a small force over a large distancesmall force over a large distance.. A A small forcesmall force over a over a large distancelarge distance

becomes a becomes a large forcelarge force over a over a small small distancedistance..

If a machine increases the If a machine increases the distancedistance over over which you exert a force, then it decreases which you exert a force, then it decreases the the amount of forceamount of force

you need to exert.you need to exert.

Increasing DistanceIncreasing Distance

When you pull an oar a When you pull an oar a small distancesmall distance, the , the other end of the oar moves a other end of the oar moves a large large distancedistance through the water. through the water.

A machine that A machine that decreasesdecreases the distance the distance through which you exert a force through which you exert a force increasesincreases the amount of force required.the amount of force required.

Changing DirectionChanging Direction

Pulling on end of an oar causes the Pulling on end of an oar causes the other end of the oar to move in the other end of the oar to move in the opposite directionopposite direction..

Work InputWork Input Because of Because of frictionfriction, the work done by a machine , the work done by a machine

is always is always lessless than the work done on the than the work done on the machine.machine.

The The forceforce you exert on a machine is called the you exert on a machine is called the input forceinput force..

The The distancedistance the input force acts through is the input force acts through is known as the known as the input distanceinput distance..

The The workwork done by the done by the input forceinput force acting through acting through the the input distanceinput distance is called the is called the work inputwork input..

Work OutputWork Output

The The forceforce that is exerted by a machine is that is exerted by a machine is called the called the output forceoutput force..

The The distancedistance the output force is exerted the output force is exerted though is the though is the output distanceoutput distance..

The The work outputwork output of a machine is the of a machine is the output output forceforce multiplied by the multiplied by the output distanceoutput distance..

You cannot get more work out of a You cannot get more work out of a machine than machine than you put into ityou put into it..


1.1. How can using a machine make a How can using a machine make a task easier to perform?task easier to perform?

2.2. How does the work done on a How does the work done on a machine compare to the work done machine compare to the work done by a machine?by a machine?

3.3. A machine produces a larger force A machine produces a larger force than you exert. How does the input than you exert. How does the input distance of the machine compare to distance of the machine compare to the output distance?the output distance?


4.4. You do 200J of work pulling the oars You do 200J of work pulling the oars of a rowboat. What can you say of a rowboat. What can you say about the amount of work the oars about the amount of work the oars doe to move the boat?doe to move the boat?

5.5. How can you increase the work How can you increase the work output of a machine?output of a machine?

6.6. When you swing a baseball bat, When you swing a baseball bat, how does the output distance the how does the output distance the end of the bat moves compare with end of the bat moves compare with the distance you move your hands the distance you move your hands through?through?

Section 14.3 – Mechanical Section 14.3 – Mechanical Advantage and EfficiencyAdvantage and Efficiency

The The mechanical advantagemechanical advantage of a machine of a machine is the number of times that the machine is the number of times that the machine increases the increases the input forceinput force..

The The actual mechanical advantage (AMA)actual mechanical advantage (AMA) is the ratio of the is the ratio of the output forceoutput force to the to the input input forceforce..

AMA = AMA = output forceoutput force input forceinput force

Ideal Mechanical AdvantageIdeal Mechanical Advantage

The The ideal mechanical advantage (IMA)ideal mechanical advantage (IMA) of of a machine is the mechanical advantage in a machine is the mechanical advantage in the absence of the absence of frictionfriction..

Because Because friction friction is always present, the is always present, the actual mechanical advantageactual mechanical advantage is always is always less than the less than the ideal mechanical advantageideal mechanical advantage..

Ideal Mechanical AdvantageIdeal Mechanical Advantage

The The ideal mechanical advantage ideal mechanical advantage (IMA)(IMA) is the ratio of the is the ratio of the input input distancedistance to the to the output distance.output distance.

IMA = IMA = input distanceinput distance

output distanceoutput distance

Sample ProblemsSample Problems

1. A woman drives a car up a ramp that is 1. A woman drives a car up a ramp that is 1.8m long. The ramp lifts the car a height 1.8m long. The ramp lifts the car a height of 0.3m. What is the IMA?of 0.3m. What is the IMA?

input distance = 1.8m IMA = input distanceoutput distance = 0.3m output distanceIMA = ? IMA = 1.8m = 66

3m

Sample ProblemsSample Problems2. A construction worker moves a crowbar 2. A construction worker moves a crowbar

through a distance of 0.50m to lift a load through a distance of 0.50m to lift a load 0.05m off the ground. What is the IMA of 0.05m off the ground. What is the IMA of the crowbar? the crowbar?

3. The IMA of a simple machine is 2.5. If the 3. The IMA of a simple machine is 2.5. If the output distance of the machine is 1.0m, output distance of the machine is 1.0m, what is the input distance?what is the input distance?

input distance = 0.50m IMA = input distanceoutput distance = 0.05m output distanceIMA = ? IMA = 0.50m = 1010

0.05m

IMA = 2.5 IMA = input distance / output distanceoutput distance = 1.0m input distance = IMA x output distanceinput distance = ? input distance = 2.5 x 1.0m = 2.5m2.5m

EfficiencyEfficiency

Some Some output forceoutput force is lost due to is lost due to frictionfriction.. The The percentagepercentage of work input that of work input that

becomes work output is the becomes work output is the efficiencyefficiency of of the machine. the machine.

No machine has No machine has 100 percent100 percent efficiency efficiency due to due to frictionfriction. .

Formula for EfficiencyFormula for Efficiency

Efficiency = Efficiency = work outputwork output x 100 x 100

work inputwork input

Reducing Reducing frictionfriction increases the increases the efficiencyefficiency of a machine. of a machine.

Section 14.3 AssessmentSection 14.3 Assessment1. Why is the actual mechanical advantage 1. Why is the actual mechanical advantage

of a machine always less than its ideal of a machine always less than its ideal mechanical advantage?mechanical advantage?

2. Why can no machine be 100% efficient?2. Why can no machine be 100% efficient?

3. What information would you use to 3. What information would you use to calculate the efficiency of a machine?calculate the efficiency of a machine?

4. What is the actual mechanical advantage 4. What is the actual mechanical advantage of a machine that exerts 5N for each 1N of of a machine that exerts 5N for each 1N of force you exert on the machine?force you exert on the machine?

AMA = ? AMA = output force / input force output force = 5N AMA = 5N / 1N = 55input force = 1N

Section 14.3 AssessmentSection 14.3 Assessment5. You have just designed a machine that 5. You have just designed a machine that

uses 1000J of work from a motor for every uses 1000J of work from a motor for every 800J of useful work the machine supplies. 800J of useful work the machine supplies. What is the efficiency of your machine?What is the efficiency of your machine?

6. If a machine has an efficiency of 40%, and 6. If a machine has an efficiency of 40%, and you do 1000J of work on the machine, you do 1000J of work on the machine, what will be the work output of the what will be the work output of the machine?machine?

work input = 1000J Efficiency = work output x 100work output = 800J work inputEfficiency = ? Efficiency = (800J / 1000J) x 100 = 80%80%

Efficiency = 40% Efficiency = work output x 100 work input = 1000J work inputwork output = ? work output = (Efficiency x work input) / 100

work output = (40% x 1000J) / 100 = 400J400J

Section 14.4 – Simple MachinesSection 14.4 – Simple Machines Many Many mechanical devicesmechanical devices are combinations of are combinations of

two or more of the six different two or more of the six different simple machinessimple machines.. The six simple machines are:The six simple machines are:

The LeverThe Lever A A leverlever is a rigid bar that rotates around a is a rigid bar that rotates around a

fixed pointfixed point called the called the fulcrumfulcrum.. The The input arminput arm of a lever is the distance of a lever is the distance

between the between the input forceinput force and the and the fulcrumfulcrum.. The The output armoutput arm is the distance between is the distance between

the the output forceoutput force and the and the fulcrumfulcrum. .

3 Classes of Levers3 Classes of Levers

The The classclass of a lever is determined by the of a lever is determined by the locationlocation of the of the effort forceeffort force and the and the loadload relative to the relative to the fulcrumfulcrum. .

First Class LeversFirst Class Levers

In a In a first-classfirst-class lever the lever the fulcrumfulcrum is located is located at some point at some point betweenbetween the effort and the effort and resistance forces.resistance forces.

Common examples of first-class levers Common examples of first-class levers include include crowbars, scissors, pliers, tin snips crowbars, scissors, pliers, tin snips and seesawsand seesaws. .

A first-class lever always changes the A first-class lever always changes the directiondirection of force (I.e. a downward effort of force (I.e. a downward effort force on the lever results in an upward force on the lever results in an upward movement of the resistance force). movement of the resistance force).

First Class LeverFirst Class Lever

Fulcrum is between EF (effort) and RF Fulcrum is between EF (effort) and RF (load)(load)

Second Class LeverSecond Class Lever With a With a second-classsecond-class lever, the lever, the loadload is is

located located betweenbetween the the fulcrumfulcrum and the and the effort effort forceforce..

Common examples of second-class levers Common examples of second-class levers include include nut crackers, wheel barrows, nut crackers, wheel barrows, doors, and bottle openersdoors, and bottle openers..

A A second-classsecond-class lever does not change the lever does not change the directiondirection of force. When the fulcrum is of force. When the fulcrum is located closer to the load than to the effort located closer to the load than to the effort force, an force, an increase in forceincrease in force (mechanical (mechanical advantage) results. advantage) results.

Second Class LeverSecond Class Lever

RF (load) is between fulcrum and EFRF (load) is between fulcrum and EF

Third Class LeverThird Class Lever With a With a third-classthird-class lever, the lever, the effort forceeffort force is is

applied applied betweenbetween the the fulcrumfulcrum and the and the resistance forceresistance force..

Examples of third-class levers include Examples of third-class levers include tweezers and sweepingtweezers and sweeping..

A A third-classthird-class lever does not change the lever does not change the direction direction of force; third-class levers always of force; third-class levers always produce a produce a gain in speed and distancegain in speed and distance and and a corresponding decrease in a corresponding decrease in forceforce. .

Third Class LeverThird Class Lever

EF is between fulcrum and RF (load)EF is between fulcrum and RF (load)

Wheel and AxleWheel and Axle

The The wheel and axlewheel and axle is a simple machine is a simple machine consisting of a consisting of a large disk (wheel)large disk (wheel) rigidly rigidly secured to a secured to a smaller disk (axle).smaller disk (axle).

To calculate the To calculate the IMAIMA, divide the , divide the radiusradius where the input force is located by the where the input force is located by the radius where the radius where the output forceoutput force is located. is located.

Inclined PlaneInclined Plane

An An inclined planeinclined plane is a slanted surface is a slanted surface along which a force moves an object to a along which a force moves an object to a different elevationdifferent elevation..

Inclined PlaneInclined Plane The The mechanical advantagemechanical advantage of an inclined of an inclined

plane is equal to the length of the plane is equal to the length of the slopeslope divided by the divided by the heightheight of the inclined plane. of the inclined plane.

While the inclined plane produces a While the inclined plane produces a mechanical advantage, it does so by mechanical advantage, it does so by increasing the distance through which the increasing the distance through which the force must move. force must move.

WedgeWedge

The The wedgewedge is a V-shaped object whose is a V-shaped object whose sides are two sides are two inclined planesinclined planes..

A A thinthin wedge of a given length has a wedge of a given length has a greatergreater IMA than a IMA than a thickthick wedge of the wedge of the same length since same length since lessless force is needed. force is needed.

ScrewScrew

The The screwscrew is an inclined plane wrapped is an inclined plane wrapped around a around a cylindercylinder. .

Screws with Screws with threadsthreads that are closer that are closer together have a together have a greatergreater IMA since it takes IMA since it takes less less forceforce..

PulleyPulley

A A pulleypulley is a simple machine that consists is a simple machine that consists of a of a roperope that fits into a groove in a that fits into a groove in a wheelwheel..

A pulley can be used to simply change the A pulley can be used to simply change the directiondirection of a force or to gain a of a force or to gain a mechanical mechanical advantageadvantage, depending on how the pulley is , depending on how the pulley is arranged. arranged.

TheThe IMA IMA of a pulley is equal to the number of a pulley is equal to the number of ropes sections supporting the load being of ropes sections supporting the load being lifted. lifted.

PulleyPulley A pulley is said to be a A pulley is said to be a fixed pulleyfixed pulley if it if it

does not rise or fall with the load being does not rise or fall with the load being moved. A fixed pulley changes the moved. A fixed pulley changes the directiondirection of a force; however, it does not of a force; however, it does not create a mechanical advantage. create a mechanical advantage.

A A moveable pulleymoveable pulley rises and falls with the rises and falls with the load that is being moved. A single load that is being moved. A single moveable pulley creates a mechanical moveable pulley creates a mechanical advantage; however, it does not change advantage; however, it does not change the the directiondirection of a force. of a force.

Movable pulleys are used to reduce the Movable pulleys are used to reduce the input forceinput force needed to lift a heavy object. needed to lift a heavy object.

PulleyPulley

Fixed Pulley

Movable Pulley

Combined Pulley

Compound MachinesCompound Machines

A A compound machinecompound machine is a is a combination of two or more combination of two or more simple simple machinesmachines that operate together. that operate together.


1. Name six kinds of simple machines. 1. Name six kinds of simple machines. Give an example of each.Give an example of each.

2. What is the ideal mechanical 2. What is the ideal mechanical advantage of a ramp if its length is advantage of a ramp if its length is 4.0m and its higher end is 0.5m 4.0m and its higher end is 0.5m above its lower end?above its lower end?

IMA = ? IMA = input distanceinput distance = 4.0m output distanceoutput distance = 0.5m IMA = 4.0m = 88

0.5m


3. Tightening a screw with a larger 3. Tightening a screw with a larger spacing between its threads requires spacing between its threads requires fewer turns than a screw with smaller fewer turns than a screw with smaller spacing. What is the disadvantage to spacing. What is the disadvantage to using a screw with a larger spacing using a screw with a larger spacing between threads?between threads?

4. If you want to pry the lid off a pint 4. If you want to pry the lid off a pint can, will it require less force to use a can, will it require less force to use a long or short screwdriver?long or short screwdriver?

Section Assessment 14.4Section Assessment 14.4

5. When the pedals of a bike move 5. When the pedals of a bike move through a distance of 0.25m, the rear through a distance of 0.25m, the rear wheel of the bike moves 1.0m. What wheel of the bike moves 1.0m. What is the ideal mechanical advantage of is the ideal mechanical advantage of the bike?the bike?

input distance = 0.25m IMA = input distanceoutput distance = 1.0m output distanceIMA = ? IMA = 0.25m = 0.250.25

1.0m

THE ENDTHE END

chapter 14: work, power, and machines. sps8. students will determine relationships among force,...

Documents