1

Work and Energy

2

Work

In science, commonly used terms may have slightly different definitions from normal usage.

The quantity work, is a perfect example of this.

3

Work DefinitionWork = Force x Distance

W = FdThus, work depends on force applied, and

distance moved.

4

Example of Work?

The weightlifter holding the bar in a stationary position does NO work since

distance equals zero.

5

UnitsSince W = F d

Work is measured in N• mOne N• m is also called 1 Joule.

6

More Work?

Q: If one person lifts a 100 kg mass a distance of 1m up in 3 seconds, and

another person does the same task in only 1 second, who does more work?

A: Neither. Work is not dependent of time. However, power is dependent on

time.

7

Which does more work?

8

Which path will require more work?

9

Energy

When you do work on an object and lift it upwards, you change the state of the

object. Since the object is higher now, it could

fall and do work for you.Thus, the work you did increased the

energy of the object.

10

Energy is the ability to causechange and perform work.

Work involves movement but energydoes not require movement.

The unit for energy is a JOULE orN-m (Newton-meter)

11

Forms of Energy:

1. Heat energy2. Chemical energy3. Electrical energy4. Radiant energy5. Nuclear energy

12

Potential Energy: stored energy.There are many ways that energy can be stored and then released. It’s a lot

like saving money in the bank so that it can be used later.

13

Chemical Potential Energy

The chemical bonds between atoms can store energy. This can be released

when the bonds are broken in chemical reactions.

14

Gravitational Potential Energy

When an object is lifted to a particular height, the stored energy due to its

elevated position increases. A dam is a good example of this.

15

Gravitational potential energy, PE, will be the main type considered.

PEgrav = weight x heightPEgrav = mg h

Remember that you only increase PE when you work against gravity. Moving an object horizontally doesn’t change its

PE.

16

PE Example:A crane lifts a steel

beam with a mass of 2500 kg to a height

of 20 m. How much potential energy was given to

the beam?

17

Potential Energy Example• The crane is lifting against gravity, so we

find the gravitational potential energy.• h= 20 m; g= 9.8 m/s2; m = 2500kg

• PEgrav= m g h• 2500kg * 9.8 m/s2 * 20 m• 490000 J

18

Reference Point, Base Level

When measuring an “h” to calculate PE, its important to know where you are measuring

from.

Any point can be used as a base level because the energy amount you calculate will be relative.

However, you must be consistent.

19

Elastic Potential Energy

If you compress a spring, or stretch a rubber band, the work you do can be

returned later when the spring or rubber band bounces back.

20

Elastic potential energy (PEelast )is stored as a result of deformation of an elastic object, such as the stretching of a spring. It is equal to the work done to stretch the spring, which depends upon the spring constant k!

21

The Force required to stretch the spring will be directly proportional to the amount of stretch.

F = kxthen the work done to stretch the spring a distance x is

22

23

Kinetic EnergyKinetic Energy, KE: energy of

motion

KE = 1/2 m v2

m = mass v = velocityAny object in motion has kinetic

energy.

24

Objects with a small mass can have high kinetic energy if their velocity is

high.(Example: a cannonball)

BOOM

25

Objects moving at slow speed can have great kinetic energy if their mass is

great.(Example: a freighter)

26

KE Example:Ex: A 80 kg sprinter may average about 10 m/s during a 100m dash.

What would his KE be?m=80 kg; v = 10m/s; d = 100 m

KE = 1/2 mv2

KE = 1/2 (80kg) (10m/s)2

KE = 4000 kgm2/s2 or 4000 J

27

Work Energy Theorem

Work = ΔEWork is equivalent to the change in

energy.Work and energy both have the

same unit, Joule.

28

Ex: You could do work by pushing an object to slide it across the floor. This work you do goes

into increasing the KE of the object.

29

Ex: You lift an object and do work. This work goes into increasing the PE of the object.

30

The archer does work to draw the bow back. This is temporarily stored as PE in the bow.

When the arrow is released, it is changed to KE in the form of the flying arrow.

31

Conservation of Energy:

Energy cannot be created or destroyed; it may be transformed

from one form into another, but the total amount of energy never

changes.

32

Often, it may seem like energy is lost, but it merely is transformed into another type of KE or

PE.Just look closely and consider where energy may

be transferred.

33

At the top, the diver has all PE

As he falls, PE is changed to KE.

Before he hits, all the PE has changed to KE.

Notice that the total amount of energy remains constant.

34

Example:

Question: If a 2 kg brick were to fall from a building 20m high, how fast would it be traveling

just before it hits the ground?

m= 2 kg; h = 20m; g = 9.8 m/s2

2kg

35

Solution: PEtop = KEbottom

mgh = ½ mv2

(2kg) (9.8m/s2) (20m) = ½ (2kg) v2

solve for “v” (notice “m” cancels out)(2kg) (9.8m/s2) (20m) = ½ (2kg) v2

(392 m2/s2) = v2

(392 m2/s2) = vv= 19.8 m/s

In a previous chapter, we could solve this a different way but would get the same answer.

36

Total Mechanical Energy = KE + PE

PE = mghKE = 1/2 mv2

#1 - Tot E = all PE

#2 - Tot E = mostly KE+ some PE

#3 - Tot E = mostly PE+ some KE

#4 - Tot E = all KE

37

PowerPower = Work / time

P = W / t = F x d / tPower is a measure of how quickly

work is done.

38

Units:Since work has units of Joules, power must be in

units of Joules per second.

1 J/s = 1 Watt, WJames Watt invented the steam engine.

39

A watt is not exclusively used for electrical measurements, although that is common.

Since 1 watt is relatively small, kilowatts 103 W or megawatts 106 W

are often used.

40

Power Example:Ex: A 50 kg boy wants to escape the

monster beneath his steps. He climbs the 5m high steps in 2.0 seconds. How much power did he generate during his

run?

5m high

m= 50kgh= 5mt= 2sg = 9.8m/s2

41

P = W / t = Fd / t(notice the force needed is the boy’s weight)

= (mg)d / t

= (50kg) ( 9.8m/s2) ( 5.0 m) / (2.0s)

= 1225 J/s = 1225 Watts= 1.225 kilowatts

42

43

44