Download Mechanical Energy Conservation

Day #6
Mechanical Energy Conservation
What are the two main types of energy we will learn about in this chapter?
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Together, these two types of energy are referred to as ___________________________.
Write three (3) equations for energy that we will use in this chapter.
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When will the energy of a system be conserved?
When will the energy NOT be conserved?
What is the Work/Energy Equation?
4 key examples:
 Ball being dropped.
 Sliding down an incline.
 Swinging Pendulum.
 Roller Coaster.
Conservation of Energy Problems
1.
Energy cannot be (a) transferred (b) conserved (c) created (d) in different forms.
2.
If a non-conservative force acts on an object, and does work, then (a) the object’s KE is conserved (b) the object’s PEg
is conserved (c) the mechanical energy is conserved (d) the mechanical energy is not conserved.
3.
The speed of a swinging pendulum is greatest (a) when the pendulum’s KE is a minimum (b) when the pendulum’s
acceleration is a maximum (c) when the pendulum’s PEg is a minimum (d) none of the preceding.
4.
When you throw an object up into the air, its initial speed is the same as the speed that it has just as it returns to your
hand. Explain using the concepts of conservative forces and the conservation of energy.
5.
Use the conservation of mechanical energy to find the height attained by a 4 kg ball that is thrown upward with an initial
vertical speed of 20 m/s.
6.
A 60 kg object is dropped from a height above the ground at which it has 50,000 J of PEg. Find the speed at which the
object will hit the ground.
7.
A skier coasts down a VERY smooth, 10 meter high slope. If the speed of the skier at the top of the slope is 5 m/s, find
his speed at the bottom of the slope.
8.
A golf ball dropped from a height of 1.0 m rebounds from a concrete floor to a height of 0.80 m. Was energy
destroyed? Account for this “apparent” failure of energy conservation by explaining where the energy might have gone.
9.
A car of mass 1000 kg starts from rest and rolls from the top of one hill to the bottom and ascends a second hill. The
height of the first hill is 70 meters and the second 50 meters. What is the car’s speed at the top of the second hill?
10. A baseball is thrown vertically upward with a velocity of 50 m/sec. How high will it rise? (Find your answer two
different ways. First, use the equations of motion. Second, use the conservation of energy).
11. A 250 kg go cart is traveling at a constant velocity of 20 m/s on a flat road. It slows down to a speed of 10 m/s. If the
brakes exerted a constant force of -4000N on the car during this acceleration, find the distance the car traveled while
slowing down.
12. A 40 kg rocket blasts off from the earth. Find the work done by the rocket fuel on the rocket if the rocket reaches a
maximum height of 1200m. Neglect air resistance, friction, etc.
13. A 10,000 kg plane is flying at a steady speed of 50 m/s at an altitude of 250 m above the ground. Moments later, the
plane is flying at a steady speed of 70 m/s at an altitude of 200 m. How much total work was required to change the
plane’s flying conditions?
14. A rollercoaster car sits at the top of a 30m tall hill. It begins descending.
a) What will be its speed at the bottom?
b) At what height (above the bottom of the hill) will it reach a speed of 15 m/s?
2m
15. A pendulum (shown at the right) with a string 2 m long is pulled to one side. How much work
needs to be done in order to pull the pendulum bob, of mass 4 kg, through an angle of 45o?
16. A pendulum with a string 2 m long is pulled to one side, making an angle of 30 o with the
vertical. Find the maximum speed that this pendulum will reach.
17. A block is held motionless on a frictionless ramp. The angle between the ramp and the horizontal is 45 o. Find the
speed of the block after it has traveled 3 m down the ramp (parallel to the ramp surface).
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