WorkWork

Work = Force x DistanceWork = Force x Distance

The force must be in the directionThe force must be in the direction

of the motion, or no work is done.of the motion, or no work is done.

W

F D

The unit of work is the The unit of work is the JouleJouleForce x Distance = WorkForce x Distance = Work1 Newton x 1 meter = 1 Newton 1 Newton x 1 meter = 1 Newton

metermeter 1 Newton meter = 1 Joule1 Newton meter = 1 Joule

Example 1:Example 1:

A high jumper weighs 700 newtons. A high jumper weighs 700 newtons. What work does the jumper perform in What work does the jumper perform in jumping over a bar 2.0 meters high?jumping over a bar 2.0 meters high?

Answer: W = F x dAnswer: W = F x d W = 700N x 2.0 m W = 700N x 2.0 m = 1400 nm= 1400 nm = 1400 Joules= 1400 Joules

No work is done if there No work is done if there is no distance!is no distance!

The statue of liberty has The statue of liberty has been holding up her torch been holding up her torch for an awfully long time. for an awfully long time. How much work has she How much work has she done?done?

Answer: 0! Although it Answer: 0! Although it takes a force to hold the takes a force to hold the torch against the force of torch against the force of gravity, there is no motion gravity, there is no motion so no work is doneso no work is done..

Which does more work?Which does more work?

The net work is the force (weight) of the cart X the vertical distance. This is the same in all three cases. In the first, the force is less, but distance is greater to reach the same vertical height.

Example 2Example 2 A force of 200N is required to push a A force of 200N is required to push a

lawn mower. If 4000 J of work is lawn mower. If 4000 J of work is performed on the lawnmower, how far performed on the lawnmower, how far does it move?does it move?

AnswerAnswer

4000Nm 4000Nm ÷ 200N = D ÷ 200N = D == 20m20m

W

F D

4000J

200N D

RememberRemember

For work to happen the force has to be For work to happen the force has to be applied in the SAME direction as the applied in the SAME direction as the motion.motion.

Work done per unit of timeWork done per unit of time

Power =Power = WorkWork

TimeTime

Power =Power = Force x distanceForce x distance

TimeTime

PowerPowerW

P T

PowerPower

An object that has more power than An object that has more power than another object does more work in the another object does more work in the same time.same time. You need more power to You need more power to

run up the stairs than to walk run up the stairs than to walk

because it takes you less time because it takes you less time

to do the same work.to do the same work.

The SI unit of power is The SI unit of power is the WATT (W)the WATT (W)

Power =Power = WorkWork

TimeTime

1 watt 1 watt = = 1 Joule1 Joule

1 Second1 Second

A Watt is small!A Watt is small!

Usually measured in kilowatts(kW)= 1,000WUsually measured in kilowatts(kW)= 1,000W

Another unit of power:Another unit of power: Horsepower (not an SI unit)Horsepower (not an SI unit)

1horsepower= 746 watts1horsepower= 746 watts

Example 3Example 3

A crane lifts a car into a junk pile in 10 seconds. A crane lifts a car into a junk pile in 10 seconds. What is the crane’s power if 120,000 J of work What is the crane’s power if 120,000 J of work are performed?are performed?

Answer: Answer: PowerPower = = WorkWork TimeTime

120,000J 120,000J = = 10 sec10 sec 12,000 Watts12,000 Watts

Example 4Example 4 A 750 N diver does a somersault off a A 750 N diver does a somersault off a

10m platform. It takes her 1.5 seconds to 10m platform. It takes her 1.5 seconds to hit the water. What is her power?hit the water. What is her power?

Since work is Force x distance, the Since work is Force x distance, the power formula can be written aspower formula can be written as

Power =Power = Force x distanceForce x distance

TimeTime

Answer:Answer:

Power =Power = Force x distanceForce x distance Time Time

Power =Power = 750N x 10m750N x 10m 1.5 sec1.5 sec

Power =Power = 7500N m7500N m 1.5 sec1.5 sec

= = 5000 Watts5000 Watts

Other units of powerOther units of power

1 kilowatt = 1000 watts1 kilowatt = 1000 watts 1 horsepower = 746 watts1 horsepower = 746 watts In the previous example, how many In the previous example, how many

kilowatts power was generated? How kilowatts power was generated? How much horsepower?much horsepower?

Answer:Answer: 5000 watts 5000 watts ÷ 1000 kw/w = 5 kilowatts÷ 1000 kw/w = 5 kilowatts 5000 watts ÷ 746 hp/w = 6.7 horsepower5000 watts ÷ 746 hp/w = 6.7 horsepower

What is a Machine?What is a Machine?

A device that allows you to do work A device that allows you to do work in a way that is easier.in a way that is easier.

It changes at least one of 3 factors:It changes at least one of 3 factors:1.1. The amount of The amount of forceforce you exert you exert

2.2. The The distancedistance over which you exert your over which you exert your forceforce

3.3. The The directiondirection in which you exert your in which you exert your force.force.

Input & Output ForceInput & Output Force Input force- Input force- The force you exert on The force you exert on

the machine.the machine. The input force moves the machine a The input force moves the machine a

certain distance, called the input distance.certain distance, called the input distance.

Output force- Output force- The force the machine The force the machine exerts on an object.exerts on an object. The machine does work by exerting a force The machine does work by exerting a force

over another distance, called the output over another distance, called the output distance.distance.

Input & Output WorkInput & Output Work

Input work= input force x input Input work= input force x input distancedistance

Output work= Output force x Output work= Output force x Output Output distancedistance

The amount of output work can The amount of output work can never be greater than the amount never be greater than the amount of input work.of input work.

Changing ForceChanging Force

In some machines, the output force In some machines, the output force is greater than the input forceis greater than the input force This is possible by increasing the This is possible by increasing the

distance.distance. What kind of machine allows you to What kind of machine allows you to

exert a smaller input force?exert a smaller input force? Ramp, faucet knob.Ramp, faucet knob.

Changing DistanceChanging Distance

In some machines, the output force In some machines, the output force is less than the input forceis less than the input force Why would you use a machine like Why would you use a machine like

this?this? Hockey stick, chopsticks, riding a bike on a Hockey stick, chopsticks, riding a bike on a

high gear.high gear.

Changing DirectionChanging Direction

Some machines don’t change either Some machines don’t change either the force of the distance.the force of the distance. What is the advantage of using a What is the advantage of using a

machine like this?machine like this? It is easier to pull down then to push up.It is easier to pull down then to push up.

Mechanical AdvantageMechanical Advantage

A machine's mechanical advantage A machine's mechanical advantage is the number of times a machine is the number of times a machine increases a force.increases a force. Formula:Formula:

mechanical advantage (MA) = mechanical advantage (MA) = Output Output ForceForce

Input ForceInput Force

There is no unit for MA. There is no unit for MA.

Mechanical AdvantageMechanical Advantage

(IMA) Ideal MA: (IMA) Ideal MA: This is the MA of a This is the MA of a machine in a world with no friction, and no machine in a world with no friction, and no force is lost anywhere.force is lost anywhere.

(AMA) Actual MA: (AMA) Actual MA: This is simply the MA This is simply the MA of a machine in the world as we know it.of a machine in the world as we know it.

- Force is lost due to friction.- Force is lost due to friction.

- It is transferred into thermal - It is transferred into thermal energy. energy.

Can we have an ideal machine?Can we have an ideal machine?

Increasing ForceIncreasing Force

When the output force is greater than the When the output force is greater than the input force, the MA is greater than 1.input force, the MA is greater than 1. Suppose you exerted a force of 10 N on a hand-Suppose you exerted a force of 10 N on a hand-

held can opener and the can-opener exerts a held can opener and the can-opener exerts a force of 30 N on the can. What is the MA of the force of 30 N on the can. What is the MA of the can opener?can opener?

MA= MA= Output forceOutput force

Input ForceInput Force MA= MA= 30N30N

10N10N MA= 3MA= 3

Increasing DistanceIncreasing Distance For a machine to increase distance, the output For a machine to increase distance, the output

force is less than the input force. The MA is less force is less than the input force. The MA is less than 1than 1 Suppose you applied a force of 20N and the machine Suppose you applied a force of 20N and the machine

applied a force of 10 N. What is the MA?applied a force of 10 N. What is the MA? MA= MA= Output forceOutput force

Input ForceInput Force MA= MA= 10N10N

20N20N MA= 0.5MA= 0.5

The MA is less but the machine would exert the force The MA is less but the machine would exert the force over a longer distance.over a longer distance.

Changing DirectionChanging Direction

What can you predict about the MA of a What can you predict about the MA of a machine that changes the direction of the machine that changes the direction of the force?force? If ONLY the direction is change the input If ONLY the direction is change the input

force will be the same as the output force so force will be the same as the output force so the MA will always be 1the MA will always be 1

EfficiencyEfficiency

In real world situations, the output work is In real world situations, the output work is always less than the input work because always less than the input work because some work is wasted overcoming friction.some work is wasted overcoming friction.

Efficiency compares the output work to Efficiency compares the output work to the input work.the input work. Efficiency= Efficiency= Output workOutput work x100% x100%

Input workInput work

Efficiency is expressed as a percentEfficiency is expressed as a percent

Try it outTry it out

You do 20 J of work while using a hammer. You do 20 J of work while using a hammer. The hammer does 18J of work on the nail. The hammer does 18J of work on the nail. What is the efficiency of the hammer?What is the efficiency of the hammer? Efficiency= Efficiency= Output workOutput work x100% x100%

Input workInput work Efficiency= Efficiency= 18J18J x100% x100%

20J20J Efficiency= .9 x100% = 90%Efficiency= .9 x100% = 90%

You do 250,000J of work to cut a lawn with a You do 250,000J of work to cut a lawn with a hand mower. If the work done by the mower hand mower. If the work done by the mower is 200,000J, what is the efficiency of the is 200,000J, what is the efficiency of the lawn mower?lawn mower? Efficiency= Efficiency= Output workOutput work x100% x100%

Input workInput work Efficiency= Efficiency= 200,000J200,000J x100% x100%

250,000J250,000J Efficiency= .8 x100% = 80%Efficiency= .8 x100% = 80%

Is there a machine with Is there a machine with 100% efficiency?100% efficiency?

Unfortunately, there is no such machine. Unfortunately, there is no such machine. In all machines some work is transferred In all machines some work is transferred into thermal energy due to friction.into thermal energy due to friction. Ideal vs. ActualIdeal vs. Actual

All machines have an efficiency of less All machines have an efficiency of less than 100%than 100%