Question

Compare the potential energy of a 5 lb ball at the top of a 5 foot hill and a 5 lb ball at the top of a 10 foot hill. Question 4 options: Their potential energies are the same because they have the same mass. Potential energy doesn't depend on a object's relative height. The ball at the top of the 5 foot hill has more potential energy. The ball at the top of the 5 foot hill has less potential energy.

Answer 1

I'll firstly separate the options for the answer so the question is more clear:

a) Their potential energies are the same because they have the same mass.
b) Potential energy doesn't depend on an object's relative height.
c) The ball at the top of the 5 foot hill has more potential energy.
d) The ball at the top of the 5 foot hill has less potential energy.

If we look at the equation for gravitational potential energy:

GPE = mgh

GPE = gravitational potential energy
m = mass of the object
g = gravitational constant
h = height of the object

We can see that GPE and height have a direct linear relationship. Therefore, as the height increases, the potential energy increases. This relationship suggests that since the mass is equal, the ball at the top of the 10 ft hill will have more potential energy than the ball at the top of the 5 ft hill.

The answer we are looking for is d) The ball at the top of the 5 foot hill has less potential energy.