Question

1. a. Which has more potential energy, a 10-kg box on a shelf or a 5-kg box on a shelf that’s twice as high? Explain.

   b. Which has more kinetic energy, a 2000-kg car traveling down the road or a 1000-kg car traveling twice as fast? Explain.

2. If your friend pushes a lawnmower six times as far as you do while exerting one half as much force, which one of you does more work? How much more? Explain.

3. a. A car has a certain amount of kinetic energy when it’s moving at 40 mph. If it speeds up until it’s going at 80 mph (two times faster), how many times more kinetic energy does it have? Explain.

   b. If the stopping distance for the car at 40 mph was about 75 ft, what is the stopping distance when it’s going two times faster? (Assume the stopping force stays the same. Keep in mind that Work, which is force × distance, is equal to the change in kinetic energy.)

4. An apple hanging from a limb has potential energy relative to the ground because of its height. If it falls, what has become of this energy just before it hits the ground? What has become of this energy after it hits the ground? Explain.

5. A roller coaster car has a potential energy of 10,000 J (relative to the ground) at the top of a certain hill, where it’s almost motionless. Then it rolls down the track. Explain your answers to these questions, assuming friction and air resistance can be neglected.

   1. The bottom of the hill is right at ground level. When the car gets there, how much potential energy and how much kinetic energy will it have?

   2. The car goes up another hill which is 3/4 as high as the original hill. How much potential energy and kinetic energy will the car have at the top of this second hill?

   3. The car goes down the second hill, where once again the track reaches ground level. How much potential energy and kinetic energy will the car have there?

Answer 1

1.

(a)

They have the same potential energy.

(b)

The second car has more kinetic energy.

(c)

The second guy would do more work.

2.

(a)

Now the car has 4 times as much kinetic energy as it was earlier.

(b)

The stopping distance would be 4 times greater than earlier.

(c)

Its potential energy is converted into the kinetic energy just before hitting the ground. After it hits the ground the kinetic energy gets converted into the sound energy and other forms of energy and finally, it stops because of the dissipation of energy.

3.

(a)

Its potential energy is zero and kinetic energy is 10,000 J.

(b)

(d)