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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