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 Energy
The energy of motion.
Is the object moving?
1 2
K  mv
2
2
kgm
m
(kg)   2 m  Nm  J
s
s
Gravitational Potential Energy
The energy due to the height of an object.
Does the object have a height?
U g  mgh
m
 kgm 
(kg) 2 (m)   2 m  Nm  J
s 
 s 
Elastic Potential Energy
The energy stored in a stretched or
compressed spring.
Is there a loaded spring?
1 2
U s  kx
2
N 2
 m  Nm  J
m
k = The spring constant
(N/m)
x = distance stretched
or compressed (m)
Internal Energy
The energy transferred to the molecules of
the objects in the due to friction.
HEAT
Is there a force of friction acting?
Eint  fx
f = The force of friction.
∆x = The distance
traveled.
( N )( m)  Nm  J
Chemical Potential Energy
The energy released due to a chemical
reaction.
Is there a chemical reaction
occurring?
Uc  ?
ASK A CHEMISTRY TEACHER
FOR THE FORMULA
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).
Eo  W  E f
Using Pie Charts to understand
Energy transfers
Example 1:
v = 0m/s
A ball is dropped from rest. (Include air friction)
A
B
Eint
A
C
B
Eint
K
Ug
=
Ug
D
=
K
C
Eint
Ug
=
K
D
h=0
Example 2:
A pendulum swings from A to E
(Neglect air resistance)
V=0m/s
E
V=0m/s
A
B
D
h =0
A
Ug
C
B
=
Ug
C
K
=
K
D
=
Ug
E
K
=
Ug
Example 3:
A spring launches a block across a horizontal table.
v=0m/s
v=0m/s
v
A
v
B
A
D
C
C
B
D
Eint
Us
=
K
=
Eint
K
=
Eint
Example 4:
A biker rides up a hill with at a constant speed.
v
D
C
8m
v
B
h=0
A
A
Ug
K
UC
C
B
=
Ug
K
=
UC
D
K
K
=
UC
Ug
UC
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?
E0  W  E f
v = 0m/s
Ug  K
1 2
mgh  mv
2
v  2 gh
m
m
v  2(10 2 )(15m)  17.3
s
s
15m
h=0
v
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)
E0  W  E f
Ug  K
1 2
mgh  mv
2
2
v
h
2g
m 2
(6 )
s
h
 1. 8m
m
2(10 2 )
s
V=0m/s
A
h
C
v = 6m/s
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
E0  W  E f
U s  Eint
1 2
kx  fx
2
5m
2 fx
k 2
x
2 mgx
k
2
x
f  F  mg
N
 600
m
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
v
hill. What is the final velocity of the biker?
E0  W  E f
8m
10m/s
K o  6000  U g  Eint  K f
9500  35v 2  7600
m
1 2
1 2
v  7.37
mv  6000  mv  mgh  2000
s
2
2
1
1
2
(70)(10 )  6000  (70)v 2  (70)(10)(8)  2000
2
2