D) Law of Conservation of Energy - unless work is done on or by a system, its total mechanical energy does not change.
- Paul Hewitt
1. Total mechanical energy
= PE + KE
Ex 1) Falling object
(w/o friction)
Answer
As the object falls, PE lost equals ....
...KE gained
Ex 2)
KE at A = 0
PE = mgh, g = 10 m/s2
| PE | KE | |
| A | 90 J | 0 |
| B |
30 J |
60 J |
| C |
0 J |
90 J |
| D |
30 J |
60 J |
| E |
0 J |
90 J |
| F |
30 J |
60 J |
| G |
90 J |
0 J |
| H | Never gets there! Doesn't have the energy to go any higher than G | |
Ex 3) Pendulum
If PE at A = 10 J, KE = 0
| PE | KE | |
| A | 10 J | 0 J |
| B | 0 J |
10 J |
| D | 10 J | 0 J |
If PE at C = 3 J, KE = ?
KE = 7 J
All Pendulums
|
PE max. at: Extremes
KE max. at: Bottom
PE at extremes = KE at bottom |
Ex 4) A 1kg pendulum swings to a height of .2m above its lowest point. What's the KE of the pendulum at lowest point?
Ex 4) A 1kg pendulum swings to a height of .2m above its lowest point. What's the KE of pendulum at lowest point?
| PE at A = KE @ B |
PE = mgh
= (1kg)(9.8 m/s2)(.2 m)
PE = 1.96 J
PE = KE @ B = 1.96 J
Ex 5) A
5.00-kg cart at the foot of a hill 10.0 meters high. For the cart to
reach the top of the hill, what is the minimum kinetic energy of the
cart in the position shown? [neglect friction.]
Ex 5) A
5.00-kg cart at the
foot of a hill 10.0 meters high.
For the cart to reach the top of the hill,
what is the minimum kinetic energy
of the cart in the position shown? [neglect friction.]
m = 5 kg
h = 10.0 m
KE = ?
KE at bottom = PE at 10 m
KE = PE = mgh = 5 kg(10 m/s2)10 m
KE = 500 J