Physics: Work and Power

This presentation was developed at Oak Ridge High School

There are many ways to look at the application of a force. Rather than considering the time, we could look at the distance over which a force is applied.

The product of the force applied over a distance is called WORK.

W = F d

Describing Work

There are three requirements for work:

1. A force must be applied2. Something must be moved by the

force.3. The force and the motion must be

in the SAME direction.

No Direction

• Acceleration has a direction• Velocity has a direction• Force has a direction• Momentum has a direction

• Work has no direction – scalar!• Temperature has no direction• Gallons of gas in my car has no

direction.

Thinking about work…

A person carrying a backpack up four flights of stairs does ___________ the work as a person climbing two flights of stairs

a) half

b) twice

c) four times

d) the same

Thinking about work…

A person carrying a backpack up four flights of stairs does ___________ the work as a person climbing two flights of stairs

a) half

b) twice

c) four times

d) the same

Since W = F d, if youDOUBLE the distance,you DOUBLE the work

Thinking about work…

A weightlifter holding 500lbs over his head is doing no work.

True or False?

True! The weightlifter is notmoving the barbell overany distance. Therefore he is not doing any work.

Which picture?

• Which picture illustrates Which picture illustrates work being done?work being done?

Neither one by Neither one by themselvesthemselves!

A better question…

• How much work did How much work did the weightlifter do to the weightlifter do to move the weights move the weights distance Y?distance Y?

DistanceDistance Y

Question?

If the distance is If the distance is doubled, how doubled, how does that affect does that affect the work?the work?

DistanceDistance DistanceDistance

DistanceDistance

Doubled!Doubled!

What if…

• the weights were twice as heavy?the weights were twice as heavy?– Twice the workTwice the work

• the weights were twice as heavy the weights were twice as heavy and they were lifted twice as far?and they were lifted twice as far?– Four times as much workFour times as much work

Another thing about work…

The definition of work requires that the force you are exerting be in the SAME direction you are moving an object.

Thinking Physics

• Guy has to get a piano onto a 2.0 m high platform. He can use a 3.0 m long, frictionless ramp or a 4.0 m long, frictionless ramp.

– Which ramp will Guy use if he wants to do the least amount of work?

Work – a review

• What is work?– Work is the force applied over a

distance

• Does work have a direction?– Work is a SCALAR and does NOT have a

direction.

• What is the relationship between the force applied and the work done on an object?

– Work is directly proportional to force.

Calculating work

How much work does a student do when she carries 30 kg of books up a 5 meter staircase?

Knowns Unknowns

m = 30 kg

d = 5 m

a = g = 9.8 m/s2

W = ???

F = ???

Relationships

F = m g

W = F d

Knowns Unknowns

m = 30 kg

d = 5 m

a = g = 9.8 m/s2

W = ???

F = ???

Now that you have your information organized, decide what relationships are important to solving the problem.

Step 1: Find the force

The force you must find is the weight of the books.

F = m g

F = (30 kg) (9.8 m/s2)

F = 294 N

Step 2 : Find the work

Work is the product of the force applied over a distance. In this case, she carries 294 N up 5 meters of stairs.

W = F d

W = (294 N) (5 m)

W = 1470 N m = 1470 J

Try this…

A net force of 20 N is needed to push a rock 1.5 m with a constant velocity.

• How much work is done on the rock?

30 J• What does this look like graphically?

Work = area under the curve

0 1.0 2.0 3.0

10

20

Displacement (m)

For

ce (

N)

4.0 5.0

40

Work can be calculated by the area under the curve.

The area of a rectangle = base * height

Area = (1.5 m)(20 N) = 30 J

Force vs. Displacement

Problem?

• If Jane pushes the lawn mower with 120 N of force over a distance of 5 meters, how much work is done?

W = F d

W = (120 N)(5 m)

W = 600 JX

Work and Direction of Force

• Which direction is the force applied?

• Which direction is the mower going?

Break Force into Components

W = F d W = F d (cos 60(cos 60oo))

W = (120 N)(5 m) W = (120 N)(5 m) (cos 60(cos 60oo))

W = 300 Nm or 300 JW = 300 Nm or 300 J

60o

F =

120

N

F =

120

N

Fh

Fv

Only the horizontalcomponent of the forcedoes work!!!

Practice Problem

A rope is used to pull a metal box 15.0 m across the floor. The rope is held at an angle of 30.0o with the floor using a force of 628 N.

• How much work does the force on the rope do?

W = F d (cos θ)

W = (628 N) (15.0 m) (cos 30o)

W = 8157.96 J ~ 8160 J

What is work?

• Work is the transfer of energy by mechanical means.

Needing something more…

Impulse does a good job of helping you to know the time over which a force is applied.

Work does a good job of telling you the distance over which a force is applied.

Wouldn’t it be nice to find a way to combine force, time, and distance into one relationship?

I’ve got the POWER!!!

We invent POWER as a combination of WORK (force x distance) and TIME.

Power = Work done time interval

P = W / t

Units of Power

Power is measured in joules per unit time.

This is often rewritten as WATTS, in honor of James Watt, the developer of the steam engine.

• 1 Watt = 1 Joule/second = 1 N m/s

• Because a Watt is small, it is usually written in terms of kW or kilo-Watts.

• 750 Watts = 1 Horse Power

Practice Problem

An electric motor lifts an elevator that weighs 12 000 N a distance of 9.00 m in 15.0 s.

• What is the power of the motor in watts?

• What is the power in kilowatts?

P = 7200 W

P = 7.2 kW

Try this• If little Nellie Newton lifts her 40-kg

body at a velocity of 0.125 m/s then what is the power delivered by little Nellie's biceps?

P = W/t

P = (Fd)/t

P = F(d/t)

P = F v

P = (40*9.81)(0.125 m/s)

P = 49 Watts

I Rock…!