1. Energy
Chapter 11

2. Energy and Work Throwing a ball. KEbefore + W = KEafter 0 + ==
Catching a ball
= 0

3. Kinetic Energy Again KE = 1/2 mv2
An 875 kg car travels 22m/s. Find the KE of the car.
KE = 2.12x105J
The car speeds up to 44m/s Find the KE.
KE = 8.47x105J
How much work is done on the car to speed it up?
∆KE = W
W = 6.35x105J

4. Stored Energy Energy does not have to be in the form of movement.
Energy can be stored based on an objects position or its chemical makeup.
This is called Potential Energy. (Either PE or U)
Matter is a form of potential energy - can be converted to energy by nuclear reactions. (E=mc2)

5. Gravitational Potential Energy
Stored energy based on an objects height above the ground.
W = Fd
Fg = mg
Wgravity = mgd
d we call the height (h) from our zero point
Wgravity = mgh
∆PE = mg∆h
- does not come from g but from h

6. Practice
A 50 kg mountain climber ascends from 10m above the base of a mountain to 100m above the base. What is the change in the PE of the mountain climber?
∆PE = mg∆h
= 50kg x 9.8m/s2 x 90m
= 4.41x104J

7. Elastic Potential Energy
Energy can be stored elastically in a pulled bow, rubber band, a bent object or a spring.
For a spring: PE = 1/2 kx2
k is the spring constant
x is the displacement from the reference point.

8. Building the Work Energy Theorem
Work also affects and is affected by potential energy.
Initial Energy + Work = Final Energy
KEi + PEgi +PEsi + Uint + W = KEf + PEgf + PEsf + Uint

9. Conservation of Energy
Energy is neither created nor destroyed but rather is converted from one form of energy to another.
Therefore the initial energy of a system must be equal to the final energy of a system.
The universe is a system so the amount of energy in the universe is finite.
Possible forms of energy include: mechanical, electrical, thermal, sound, nuclear, chemical, and electromagnetic.

10. Ball in the Air
Throwing a ball straight up into the air contains interactions of kinetic and gravitational potential energy.
Start
End
Middle

11. Mechanical Energy
Mechanical energy is the sum of the KE and PE in a system.
MEinitial = MEfinal
PEi + KEi = PEf + KEf
A large chunk of ice with a mass of 15.0kg falls to the ground from an 8.0m roof.
What is the KE of the ice just before it reaches the ground?
KE = PE = mgh = 1.18x103J
How fast is it moving just before it reaches the ground?
KE = 1/2mv2
v = 12.5m/s

12. Loss of ME
A pendulum will not swing forever. Friction and air resistance will turn some mechanical energy into thermal energy.

13. Practice
A 35kg roller skater is on top of a 45m hill. How fast is the roller skater traveling at the bottom of the hill?
PEi + KEi = PEf + KEf
mgh + 0 = 0 + 1/2mv2
mgh = 1/2mv2
v =29.7m/s

14. The skater proceeds up the next hill
The skater proceeds up the next hill. If a total work done by friction on the roller skates and air resistance is 5000J, how far up the next hill will the skater go?
PEi + KEi + Wf = PEf + KEf
mgh J = mgh + 0
15435J J = mgh
10435J = (35kg)(9.8m/s2)h
h = 30.4m