Directions: Consider a 2-kg bowling ball sits on top of a building that is 40 meters tall. It falls to the ground. Think about the amounts of potential and kinetic energy the bowling ball has:
• as it sits on top of a building that is 40 meters tall.
• as it is half way through a fall off a building that is 40 meters tall and travelling 19.8 meters per second.
• as it is just about to hit the ground from a fall off a building that is 40 meters tall and travelling 28 meters per second.


4. What is the potential energy of the bowling ball as it sits on top of the building?

5. What is the potential energy of the ball as it is half way through the fall, 20 meters high?

4) Potential energy: 784 J

5) Potential energy: 392 J

Explanation:

4)

The potential energy of an object is the energy possessed by the object due to its position in the gravitational field. It is given by

where

m is the mass of the object

g is the acceleration of gravity

h is the height of the object from the ground

Here, for the ball sitting on top of the building, we have:

m = 2 kg (mass)

(acceleration of gravity)

h = 40 m (height of the builiding)

So, the potential energy is

5)

As the ball is half way through the fall, the height of the ball is

h = 20 m

The potential energy of the ball now is

where

m = 2 kg is the mass  of the ball

is  the acceleration of gravity

Therefore, the potential energy now is

And we see that the potential energy has halved: this is because part of the potential energy, during the fall, has been converted into kinetic energy, increasing the speed of the ball (which is in fact accelerating).

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