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Work, Power, and Work, Power, and MachinesMachines

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What’s work?What’s work? A scientist delivers a speech to an A scientist delivers a speech to an

audience of his peers. audience of his peers. A body builder lifts 350 pounds above his A body builder lifts 350 pounds above his

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

room. room. A father pushes a baby in a carriage.A father pushes a baby in a carriage. A woman carries a 20 kg grocery bag to A woman carries a 20 kg grocery bag to

her car.her car.

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What’s work?What’s work? A scientist delivers a speech to an A scientist delivers a speech to an

audience of his peers. audience of his peers. NoNo A body builder lifts 350 pounds above his A body builder lifts 350 pounds above his

head. head. YesYes A mother carries her baby from room to A mother carries her baby from room to

room. room. NoNo A father pushes a baby in a carriage. A father pushes a baby in a carriage. YesYes A woman carries a 20 km grocery bag to A woman carries a 20 km grocery bag to

her car? her car? NoNo

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What IS work?What IS work?

Transfer of energy to an object by applying Transfer of energy to an object by applying force that causes the object to move in the force that causes the object to move in the direction of the force. direction of the force.

VS.VS.

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The only lifter doing any work is…The only lifter doing any work is…

Because work is 0, when an object is not Because work is 0, when an object is not moving!moving!

Work = force x distanceWork = force x distanceW = FdW = Fd

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Work = Force x DistanceWork = Force x Distance

Unit of force is newtonsUnit of force is newtons

Unit of distance is metersUnit of distance is meters

Unit of work is newtons times metersUnit of work is newtons times meters

One newton-meter is equal to one jouleOne newton-meter is equal to one joule

So… the So… the unit of workunit of work is a is a joule (J)joule (J)

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Unit relationships…Unit relationships…

1 N m = 1 J = 1 kg m1 N m = 1 J = 1 kg m22/s/s22

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W=FdW=Fd

Work = Force x Work = Force x DistanceDistance

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

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W=FdW=Fd

Work = Force x Work = Force x DistanceDistance

Calculate: If a man Calculate: If a man pushes a concrete pushes a concrete block 10 meters with block 10 meters with a force of 20 N, how a force of 20 N, how much work has he much work has he done? done? 200 joules200 joules

(W = 20N x 10m)(W = 20N x 10m)

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Practice!Practice!1.Imagine a father playing with his daughter by lifting her 1.Imagine a father playing with his daughter by lifting her

repeatedly in the air. How much work does he do repeatedly in the air. How much work does he do with each lift if he lifts her 2.0m and exerts an with each lift if he lifts her 2.0m and exerts an average force of 190 N?average force of 190 N?

2. A crane uses an average force of 5200N to lift a girder 2. A crane uses an average force of 5200N to lift a girder 25m. Calculate its work.25m. Calculate its work.

3. An apple weighing 1N falls a distance of 1m. How 3. An apple weighing 1N falls a distance of 1m. How much work is done on the apple by the force of much work is done on the apple by the force of gravity?gravity?

4. A bike’s brakes apply 125N of frictional force to the 4. A bike’s brakes apply 125N of frictional force to the wheels as the bike moves 14.0m. How much work is wheels as the bike moves 14.0m. How much work is done by the brakes?done by the brakes?

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Think about this…Think about this…

Running up a flight of stairs does not Running up a flight of stairs does not require more WORK than walking up require more WORK than walking up

slowly does, but its more tiring.slowly does, but its more tiring.

Why? Why?

You are doing the work in a shorter time!You are doing the work in a shorter time!

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PowerPower Power is: the rate at which work is done Power is: the rate at which work is done

OR how much work is done in a given OR how much work is done in a given amount of time.amount of time.

Power = WorkPower = Work**/Time/Time **(force x distance)(force x distance)

The unit of power is the watt (W). 1 W The unit of power is the watt (W). 1 W equals the amount of power needed to do equals the amount of power needed to do 1 J of work in 1s.1 J of work in 1s.

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Check for UnderstandingCheck for Understanding

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

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

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

Explain your answers. Explain your answers.

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Ben and Bonnie do Ben and Bonnie do the same amount of work; the same amount of work; they apply the same force they apply the same force to lift the same barbell the to lift the same barbell the same distance above same distance above their heads. their heads.

Yet, Ben is the Yet, Ben is the most powerful since he most powerful since he does the same work in does the same work in less time. less time.

Power and time Power and time are are inversely inversely proportionalproportional..

  

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While rowing across the lake during a While rowing across the lake during a race, John does 3960 J of work on the race, John does 3960 J of work on the oars in 60.0s. What is his power output oars in 60.0s. What is his power output

in watts?in watts?

How does his power output change if it How does his power output change if it takes him 30s? 120.0s?takes him 30s? 120.0s?

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How much power will it take to move a 10 How much power will it take to move a 10 kg mass at an acceleration of 2 m/s/s a kg mass at an acceleration of 2 m/s/s a distance of 10 meters in 5 seconds? This distance of 10 meters in 5 seconds? This problem requires you to use the formulas problem requires you to use the formulas for force, work, and power all in the correct for force, work, and power all in the correct order.order.

Force=Mass x Acceleration Force=Mass x Acceleration

Work=Force x DistanceWork=Force x Distance

Power = Work/TimePower = Work/Time

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How much power will it take to move a 10 kg How much power will it take to move a 10 kg mass at an acceleration of 2 m/s/s a distance of mass at an acceleration of 2 m/s/s a distance of 10 meters in 5 seconds? This problem requires 10 meters in 5 seconds? This problem requires you to use the formulas for force, work, and you to use the formulas for force, work, and power all in the correct order.power all in the correct order.

Force=Mass x Acceleration Force=Mass x Acceleration Force=10 x 2Force=10 x 2Force=20 NForce=20 N

Work=Force x DistanceWork=Force x DistanceWork = 20 x 10Work = 20 x 10

Work = 200 JoulesWork = 200 Joules

Power = Work/TimePower = Work/TimePower = 200/5Power = 200/5

Power = 40 wattsPower = 40 watts

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Simple MachinesSimple Machines

Ancient people invented simple Ancient people invented simple machines that would help them overcome machines that would help them overcome resistive forces and allow them to do the resistive forces and allow them to do the desired work against those forces. desired work against those forces.

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Simple MachinesSimple Machines

The six simple machines are:The six simple machines are: Lever Lever Wheel and Axle Wheel and Axle Pulley Pulley Inclined Plane Inclined Plane Wedge Wedge Screw Screw

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Simple MachinesSimple Machines

A machine is a device that helps A machine is a device that helps make work easier to perform by make work easier to perform by accomplishing one or more of the accomplishing one or more of the following functions: following functions: transferring a force from one place to transferring a force from one place to

another, another, changing the direction of a force, changing the direction of a force, increasing the magnitude of a force, or increasing the magnitude of a force, or increasing the distance or speed of a increasing the distance or speed of a

force. force.

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Mechanical AdvantageMechanical Advantage

It is useful to think about a machine It is useful to think about a machine in terms of the in terms of the input forceinput force (the (the force you apply) and the force you apply) and the outputoutput forceforce (force which is applied to the (force which is applied to the task).task).

When a machine takes a small input When a machine takes a small input force and increases the magnitude of force and increases the magnitude of the output force, a the output force, a mechanical mechanical advantageadvantage has been produced. has been produced.

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Mechanical AdvantageMechanical Advantage Mechanical advantage is the ratio of output force Mechanical advantage is the ratio of output force

divided by input force. If the output force is divided by input force. If the output force is bigger than the input force, a machine has a bigger than the input force, a machine has a mechanical advantage greater than one.mechanical advantage greater than one.

If a machine increases an input force of 10 If a machine increases an input force of 10 pounds to an output force of 100 pounds, the pounds to an output force of 100 pounds, the machine has a mechanical advantage (MA) of 10. machine has a mechanical advantage (MA) of 10.

In machines that increase distance instead of In machines that increase distance instead of force, the MA is the ratio of the output distance force, the MA is the ratio of the output distance and input distance.and input distance.

MA = output/input MA = output/input

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No machine can increase No machine can increase bothboth the magnitude and the magnitude and the distance of a force at the distance of a force at the same time.the same time.

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The LeverThe Lever

A lever is a rigid bar A lever is a rigid bar that rotates around a that rotates around a fixed point called the fixed point called the fulcrum.fulcrum.

The bar may be either The bar may be either straight or curved.straight or curved.

In use, a lever has In use, a lever has both an effort (or both an effort (or applied) force and a applied) force and a load (resistant force). load (resistant force).

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The 3 Classes of LeversThe 3 Classes of Levers

The class of a lever The class of a lever is determined by is determined by the location of the the location of the effort force and the effort force and the load relative to the load relative to the fulcrum. fulcrum.

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To find the MA of a lever, divide the output force by the input force, or divide the length of the resistance arm by the length of the effort arm.

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First Class LeverFirst Class Lever

In a first-class lever the fulcrum is In a first-class lever the fulcrum is located at some point between the located at some point between the effort and resistance forces.effort and resistance forces. Common examples of first-class levers Common examples of first-class levers

include crowbars, scissors, pliers, tin include crowbars, scissors, pliers, tin snips and seesaws. snips and seesaws.

A first-class lever always changes the A first-class lever always changes the direction of force (I.e. a downward effort direction 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).

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Fulcrum is between EF (effort) and RF (load)Fulcrum is between EF (effort) and RF (load)Effort moves farther than Resistance.Effort moves farther than Resistance. Multiplies EF and changes its direction Multiplies EF and changes its direction

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Second Class LeverSecond Class Lever

With a second-class lever, the load is With a second-class lever, the load is located between the fulcrum and the effort located between the fulcrum and the effort force.force.

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

A second-class lever does not change the A second-class lever does not change the direction of force. When the fulcrum is direction 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 increase in force (mechanical force, an increase in force (mechanical advantage) results. advantage) results.

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RF (load) is between fulcrum and EF RF (load) is between fulcrum and EF Effort moves farther than Resistance.Effort moves farther than Resistance.

Multiplies EF, but does not change its directionMultiplies EF, but does not change its direction

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Third Class LeverThird Class Lever

With a third-class lever, the effort With a third-class lever, the effort force is applied between the fulcrum force is applied between the fulcrum and the resistance force.and the resistance force. Examples of third-class levers include Examples of third-class levers include

tweezers, hammers, and shovels.tweezers, hammers, and shovels. A third-class lever does not change the A third-class lever does not change the

direction of force; third-class levers direction of force; third-class levers always produce a gain in speed and always produce a gain in speed and distance and a corresponding decrease distance and a corresponding decrease in force. in force.

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EF is between fulcrum and RF (load) EF is between fulcrum and RF (load) Does not multiply force Does not multiply force

Resistance moves farther than Effort.Resistance moves farther than Effort.

Multiplies the distance the effort force travelsMultiplies the distance the effort force travels

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Wheel and AxleWheel and Axle The wheel and axle is The wheel and axle is

a simple machine a simple machine consisting of a large consisting of a large wheel rigidly secured wheel rigidly secured to a smaller wheel or to a smaller wheel or shaft, called an axle. shaft, called an axle.

When either the wheel When either the wheel or axle turns, the or axle turns, the other part also turns. other part also turns. One full revolution of One full revolution of either part causes one either part causes one full revolution of the full revolution of the other part. other part.

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PulleyPulley A pulley consists of a grooved wheel A pulley consists of a grooved wheel

that turns freely in a frame called a that turns freely in a frame called a block.block.

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

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 direction of a force; however, it does direction of a force; however, it does not create a mechanical advantage. not create a mechanical advantage.

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

The mechanical advantage of a The mechanical advantage of a moveable pulley is equal to the moveable pulley is equal to the number of ropes that support the number of ropes that support the moveable pulley. moveable pulley.

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Inclined PlaneInclined Plane

An inclined plane is An inclined plane is an even sloping an even sloping surface. The surface. The inclined plane inclined plane makes it easier to makes it easier to move a weight move a weight from a lower to from a lower to higher elevation.higher elevation.

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Inclined PlaneInclined Plane The mechanical The mechanical

advantage of an advantage of an inclined plane is equal inclined plane is equal to the length of the to the length of the slope divided by the slope divided by the height of the inclined height of the inclined plane. plane.

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

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Although it takes less force for car A to get to the top of the ramp, Although it takes less force for car A to get to the top of the ramp, all the cars do the same amount of work.all the cars do the same amount of work.

A B C

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Inclined PlaneInclined Plane A wagon trail on a A wagon trail on a

steep hill will often steep hill will often traverse back and forth traverse back and forth to reduce the slope to reduce the slope experienced by a team experienced by a team pulling a heavily loaded pulling a heavily loaded wagon.wagon.

This same technique is This same technique is used today in modern used today in modern freeways which travel freeways which travel winding paths through winding paths through steep mountain passes. steep mountain passes.

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WedgeWedge The wedge is a The wedge is a

modification of the inclined modification of the inclined plane. Wedges are used as plane. Wedges are used as either separating or either separating or holding devices. holding devices.

A wedge can either be A wedge can either be composed of one or two composed of one or two inclined planes. A double inclined planes. A double wedge can be thought of wedge can be thought of as two inclined planes as two inclined planes joined together with their joined together with their sloping surfaces outward. sloping surfaces outward.

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ScrewScrew

The screw is also a The screw is also a modified version of modified version of the inclined plane. the inclined plane.

While this may be While this may be somewhat difficult somewhat difficult to visualize, it may to visualize, it may help to think of the help to think of the threads of the threads of the screw as a type of screw as a type of circular ramp (or circular ramp (or inclined plane). inclined plane).

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MA of an screw can be calculated by dividing the number of turns per inch.

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EfficiencyEfficiency We said that the input force times the distance equals We said that the input force times the distance equals

the output force times distance, or:the output force times distance, or:

Input Force x Distance = Output ForceInput Force x Distance = Output Force x Distancex Distance

However, some output force is lost due to friction.However, some output force is lost due to friction.

The comparison of work input to work output is called The comparison of work input to work output is called efficiency. efficiency.

No machine has 100 percent efficiency due to friction. No machine has 100 percent efficiency due to friction.

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Practice QuestionsPractice Questions1. Explain who is doing more work and why: a bricklayer 1. Explain who is doing more work and why: a bricklayer carrying bricks and placing them on the wall of a building carrying bricks and placing them on the wall of a building being constructed, or a project supervisor observing and being constructed, or a project supervisor observing and recording the progress of the workers from an observation recording the progress of the workers from an observation booth. booth.

2. How much work is done in pushing an object 7.0 m across 2. How much work is done in pushing an object 7.0 m across a floor with a force of 50 N and then pushing it back to its a floor with a force of 50 N and then pushing it back to its original position? How much power is used if this work is original position? How much power is used if this work is done in 20 sec?done in 20 sec?

3. Using a single fixed pulley, how heavy a load could you 3. Using a single fixed pulley, how heavy a load could you liftlift??

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Practice QuestionsPractice Questions

4.4. Give an example of a machine in which friction is Give an example of a machine in which friction is both an advantage and a disadvantage.both an advantage and a disadvantage.

5. Why is it not possible to have a machine with 5. Why is it not possible to have a machine with 100% efficiency?100% efficiency?

6. What is effort force? What is work input? Explain 6. What is effort force? What is work input? Explain the relationship between effort force, effort the relationship between effort force, effort distance, and work input. distance, and work input.

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Practice QuestionsPractice Questions1. Explain who is doing more work and why: a bricklayer carrying 1. Explain who is doing more work and why: a bricklayer carrying bricks and placing them on the wall of a building being bricks and placing them on the wall of a building being constructed, or a project supervisor observing and recording the constructed, or a project supervisor observing and recording the progress of the workers from an observation booth. progress of the workers from an observation booth. Work is defined as a force applied to an object, moving that object a distance in the direction of the applied force. The bricklayer is doing more work.

2. How much work is done in pushing an object 7.0 m across a 2. How much work is done in pushing an object 7.0 m across a floor with a force of 50 N and then pushing it back to its original floor with a force of 50 N and then pushing it back to its original position? How much power is used if this work is done in 20 sec? position? How much power is used if this work is done in 20 sec? Work = 7 m X 50 N X 2 = 700 N-m or J; Power = 700 N-m/20 sec = 35 W

3. Using a single fixed pulley, how heavy a load could you lift?3. Using a single fixed pulley, how heavy a load could you lift?Since a fixed pulley has a mechanical advantage of one, it will only change the direction of the force applied to it. You would be able to lift a load equal to your own weight, minus the negative effects of friction.

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Practice QuestionsPractice Questions4. 4. Give an example of a machine in which friction is both an Give an example of a machine in which friction is both an

advantage and a disadvantage. advantage and a disadvantage. One answer might be the use of a car jack. Advantage of friction: It allows a car to be raised to a desired height without slipping. Disadvantage of friction: It reduces efficiency.

5. Why is it not possible to have a machine with 100% efficiency? 5. Why is it not possible to have a machine with 100% efficiency? Friction lowers the efficiency of a machine. Work output is always less than work input, so an actual machine cannot be 100% efficient.

6. What is effort force? What is work input? Explain the relationship 6. What is effort force? What is work input? Explain the relationship between effort force, effort distance, and work input. between effort force, effort distance, and work input. The effort force is the force applied to a machine. Work input is the work done on a machine. The work input of a machine is equal to the effort force times the distance over which the effort force is exerted.