A student calculates the potential energy of a roller coaster at the top of a hill.

Question

16.A student calculates the potential energy of a roller coaster at the top of a hill. Then, she uses the kinetic energy equation to calculate the roller coaster's energy as it reaches the bottom of the hill. The calculations show that the roller coaster's potential energy was slightly greater at the top of the hill than its kinetic energy at the bottom of the hill.

Which of the following best explains this difference?

A. Energy in moving systems is not always conserved.

B. The roller coaster's velocity decreases as it moves downhill.

C. The student did not account for energy transformed into heat and sound.

D. The gravitational force is greater at the top of a hill than at the bottom.

I think the answer is either C or D

Answer 1

If energy is conserved, then the kinetic energy at the bottom of the hill should equal the potential energy at the top of the hill.

Assuming that at the top of the hill the roller coaster is momentarily at rest, its kinetic energy at that point is 0. Since total energy E is the sum of the potential energy and the kinetic energy, the total energy is equal to the gravitational potential energy at the top of the hill. This total energy must remain constant according to the conservation of energy principle. As the roller coaster rolls down the hill, potential energy is being converted to kinetic energy until at the bottom of the hill all of the potential energy has been converted to kinetic energy, which is equal to the same constant total energy value.

If one finds that the kinetic energy at the bottom of the hill is less than the potential energy at the top of the hill, then energy must have been lost due to non-conservative forces. This energy may be lost due to friction, air resistance, heat, sound, etc.

Therefore, your best answer is c.

Answer 2

The answer is C. Any time energy is transformed, some of it is always lost to heat and sound. The answer isn't D because the gravitational force between the roller coaster and the Earth is the same whether or not it's at the top of the hill or at the bottom (Note, this is not true in the case of very large distances where the height is significant, but in this case, it isn't).