Section 11.2Conservation of Energy

Conservation of Energy

How can I solve problems using the law of conservation of energy?

Conservation of Energy

Law of Conservation of Energy: in a closed, isolated system, energy cannot be created or destroyed

Energy can be changed from one form to another, but the total amount of energy stays the same

E1 = E2

Mechanical Energy

We will consider only mechanical energy

Potential and Kinetic

E = PE + KE

Ignore other forms (air resistance, etc…)

Conservation

E1 = E2

KEi + PEi = KEf + PEf

Conservation Of Mechanical Energy

Suppose you a at the top of a ski slope

What kind of energy do you have?

Once you start skiing, what happens to your energy?

What kind of energy do you have at the bottom of the slope?

Change in Form of Energy

Example

You are holding a ball 2.0 m above the ground. What is the PE of the ball?

You drop the ball, what is the PE after it falls 1.0 m?

What is KE after it falls 1.0 m?

What is PE when it reaches the ground?

What is KE just before it reaches the ground?

Hints

Look for the word rest, that means v = 0

When an object is at the peak of its trajectory, v = 0

Example

During a hurricane, a large tree limb, with a mass of 22.0 kg and a height of 13.3 m above the ground, falls on a roof that is 6.0 m above the ground.a. Ignoring air resistance, find the kinetic

energy of the limb when it reaches the roof.

b. What is the speed of the limb when it reaches the roof?

Homework

Page 297, # 15 - 18

Page 308, # 73 - 77

Conservation of Energy

The largest apple ever grown was 1.47 kg. Suppose you hold such an apple in your hand 1.50 m above the ground. You accidentally drop the apple, then manage to catch it when it is 0.5 m above ground. a. What was the apples KE at this point?b. What was its velocity?

What about Friction?

In the real world, there is friction

How do we account for it in our conservation of energy equation?

E1 + Wf = E2

Example

A 36.0 kg child slides down a slide that is 2.5 m high. At the bottom of the slide, she is moving at 3.0 m/s. How much energy was lost as she slid down the slide?

Homework

Worksheet

Collisions

How can we analyze collisions to find the change in kinetic energy?

Analyzing Collisions

We will analyze collisions just before and just after the actual collision

If the system is isolated, then momentum and energy are conserved

Energy can be converted to other forms› Potential, thermal and sound energy› Can increase, stay the same or decrease

Kinetic Energy

Cannot predict whether kinetic energy is conserved

Strategy:› Conservation of momentum first› Conservation of kinetic energy second

Change In KE?

KE increases: superelastic or explosive› A compressed spring was released

KE remains the same: elastic collision› Hard elastic items such as marbles

KE decreases: Inelastic› Energy is converted to other forms› Soft items, car crashes, when items stick

together after the collision

Analyzing Collisions

Momentum and energy are different

Momentum is (almost) always conserved

Energy is only conserved in elastic collisions

Momentum is what makes objects stop

Example

In an accident on a slippery road, a compact car with a mass of 575 kg moving at 15.0 m/s smashes into the rear end of a car with mass 1575 kg moving at 5.00 m/s in the same direction.a. What is the final velocity if the cars stick

together?b. How much kinetic energy was lost in the

collision?c. What fraction of the original kinetic energy

was lost?

Homework

Page 300, # 19 – 21 Page 309, # 78 – 82, 85