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Conservation of Energy

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Conservation of Energy

When working with energy it is necessary to determine where all of the energy you start with comes from and where all of the energy is when you get to your final destination.

The amount of energy you start with must be equal to the amount of energy you end with. Energy can only be transferred not created nor destroyed.

This assumes that there is no energy transferred out of the system.

E is defined to be the total energy of the system, which includes all potential and kinetic energy. We will only focus on mechanical energy at this time.

If energy is transferred out of (or into) the system due to external forces you must include the work done by those forces to remove (or add) energy.

Here the work done corresponds to a loss, which would be negative work.

- Example: A block slides a frictionless hill. The hill has a total height of 10 m and a flat plateau at 6 m. The block has a mass of 10 kg and starts at rest.
- What is the speed of the block along the plateau?
- What is the speed of the block at the bottom of the hill?

a)

m

0

0

0

10 m

6 m

b)

Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Just before hitting the ground, the heavier marble has

1. as much kinetic energy as the lighter one.

2. twice as much kinetic energy as the lighter one.

3. half as much kinetic energy as the lighter one.

4. four times as much kinetic energy as the lighter one.

5. impossible to determine

A block initially at rest is allowed to slide down a frictionless ramp and attains a speed v at the bottom. To achieve a speed 2v at the bottom, how many times as high must a new ramp be?

1. 1

2. 2

3. 3

4. 4

5. 5

6. 6

A spring-loaded toy dart gun is used to shoot a dart straight up in the air, and the dart reaches a maximum height of

24 m. The same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the dart go this time, neglecting friction and assuming an ideal spring?

1. 96 m

2. 48 m

3. 24 m

4. 12 m

5. 6 m

6. 3 m

7. impossible to determine

q = 180o, so cosq = -1

Kinetic Friction

Friction is a non-conservative force that extracts energy from the system it acts on.

The work done by friction is therefore changing the internal energy of the system.

If work is done to decrease the internal energy