Work and Energy

Work is done when an external force is used to change the energy of the system.

Energy is the ability to create change or do work.

• Energy and work are both measured in Joules (J =Nm).

• Energy and work are scalar quantities. They only have magnitude, no direction

There are many different forms of Energy:

Kinetic EnergyThe energy of motion.

Is the object moving?

2

2

1mvK

JNmms

kgm

s

mkg

2

2

)(

Gravitational Potential Energy

The energy due to the height of an object.

Does the object have a height?

mghU g JNmm

s

kgmm

s

mkg

22)()(

Elastic Potential Energy

The energy stored in a stretched or compressed spring.

Is there a loaded spring?

2

2

1kxU s

k = The spring constant (N/m)

x = distance stretched or compressed (m)

JNmmm

N

2

Internal EnergyThe energy transferred to the molecules of

the objects in the due to friction.HEAT

Is there a force of friction acting?

xfE intf = The force of friction.

∆x = The distance traveled.

JNmmN ))((

Chemical Potential Energy

The energy released due to a chemical reaction.

Is there a chemical reaction occurring?

ASK A CHEMISTRY TEACHER

FOR THE FORMULA

?cU

Conservation of Energy

For a closed system the sum of the original energy (Eo) and the work (W) done is equal to the final energy (Ef).

fo EWE

Using Pie Charts to understand Energy transfers

Example 1:

A ball is dropped from rest. (Include air friction)

===

BA DC

v = 0m/s A

C

B

D

Ug

Ug

K

Eint

UgK

Eint Eint

K

h = 0

Example 2:

A pendulum swings from A to E

(Neglect air resistance)

===

BA DC

=

E

E

C

V=0m/s

DB

A

V=0m/s

h =0

Ug Ug K K KUg Ug

Example 3:

A spring launches a block across a horizontal table.

===

BA DC

v=0m/s v=0m/s

vv

Us K

Eint

EintKEint

A B C D

Example 4:

A biker rides up a hill with at a constant speed.

v

v

8m

v

v

===

BA DC

h = 0

K KKKUg Ug

UgUC UCUCUC

A

B

C

D

Let’s do some quantitative problems:

Example 1:

A ball is dropped from a height of 15 meters. What is its velocity just before it hits the ground?

v = 0m/s

v

15m

fEWE 0KU g

2

2

1mvmgh

ghv 2

s

mm

s

mv 3.17)15)(10(2

2 h = 0

Example 2:

A pendulum is released from rest at point A and has a velocity of 6 m/s at point C. Find the initial height (h) from which the pendulum was released. (Neglect air resistance)

C

A

V=0m/s

v = 6m/s

h

fEWE 0KU g

2

2

1mvmgh

g

vh

2

2

m

smsm

h 8.1)10(2

)6(

2

2

Example 3:

A spring is compressed 20cm and launches a 400 gram block across a horizontal table. The block comes to rest after traveling 5 meters. The coefficient of friction is 0.6. What is the spring constant (k)?

v=0m/s v=0m/s

5m

fEWE 0

intEU s

xfkx 22

1

2

2

x

xfk

mgFf

2

2

x

xmgk

m

N600

Example 4:

A 70kg biker has a velocity of 10m/s at the bottom of a 8 meter hill. The biker does 6000J of work in climbing the hill and 2000J is transferred to internal energy as he climbs the hill. What is the final velocity of the biker? v

10m/s

8mfEWE 0

fgo KEUK int6000

20002

16000

2

1 22 mghmvmv

2000)8)(10)(70()70(2

16000)10)(70(

2

1 22 v

7600359500 2 v

s

mv 37.7