1. Energy and Power

2. Kinetic Energy Kinetic Energy is the energy of motion KE = ½mv2
m = mass of object
v = speed of object
KE is always zero or positive, never negative
Net work done on an object results in a change in kinetic energy:
Wnet = KE

3. Potential Energy Potential energy is stored energy
An object has potential energy because of its relative position to other objects
Only a change in potential energy matters
Gravitational potential energy is stored energy because of an objects position relative to earth
PEg = mgh
h = height above zero level
The zero level is arbitrary

4. Potential Energy (cont.)
Elastic potential energy is energy stored in a compressed or stretched object
Classic example is a spring:
PEelastic = ½ kx2
k = the spring constant
x = distance object is stretch or compressed
Spring constant (units = N/m) is a measure of how stiff the spring is

5. Example of Potential Energy
How high can a dart gun (k = 100 N/m) shoot a 3.1 g dart, given that the spring is compressed 4.0 cm?
Answer: At the highest point, the energy of the compressed spring becomes PEg:
½ kx2 = mgh
h = kx2/(2mg) = (100 N/m)(.040 m)2/
[2(.0031 kg)(9.8 m/s2)]
= 2.6 m

6. Conservation of Mechanical Energy
Kinetic and potential energy are the two types of mechanical energy
The total mechanical energy of an object or group of objects is
ME = KE + PE
If there is no friction, then ME is conserved:
MEi = MEf
KEi + PEi = KEf + PEf
½mvi2 + mghi = ½mvf2 + mghf (PEelastic = 0)

7. Example of Conservation of Mechanical Energy
Tarzan is running through the jungle. He grabs a vine to get over a chasm, but the other side is 1.8 m higher. How fast does he need to be running to make it?
1.8 m
vi = ?

8. Power Power is the rate that work is done or energy transferred
P = W/t (work per time) or
P = Fv (force  speed)
The SI unit for power is the watt (W)
1 W = 1 J/s

9. Example
A 120-kg backpacker climbs a 1400-m high mountain in 6.3 hours. What is his power output?
W = Fd = mgd
P = W/t = mgd/t
= (120 kg)(9.80 m/s2)(1400 m)
(6.3 h)(3600 s/h)
= 73 W

10. Example
A woman lifts a bucket of water out of a well at a speed of 1.75 m/s. The bucket plus water has a total mass of 9.30 kg. What is her power output?
P = Fv = mgv = (9.30 kg)(9.80 m/s2)(1.75 m/s)
= 159 W