Use the scenario to answer the following question.

Question

A person is riding their mountain bike along a trail with multiple hills. At the bottom of the second hill, the biker has 3200 J of kinetic energy. At the top of the third hill, when the biker is going the slowest, the potential energy measures 1650 J.

Which statement is true?

Question 5 options:

The total amount of energy at the bottom of the hill cannot equal the amount at the top, because some of the energy is destroyed.

The total amount of energy at the bottom of the hill is equal to the amount at the top of the hill, but some energy was converted into other forms of energy due to friction.

The total amount of energy at the top of the hill is equal to the amount at the bottom of the hill, but the biker gained some energy as they traveled due to a higher speed going down the first two hills.

The total amount of the energy at the bottom of the hill cannot equal the amount at the top, because some of the energy is gained.

Answer 1

The correct statement is:

The total amount of energy at the bottom of the hill is equal to the amount at the top of the hill, but some energy was converted into other forms of energy due to friction.

In this scenario, the biker has kinetic energy (KE) at the bottom of the second hill and potential energy (PE) at the top of the third hill. Energy is conserved, so the total mechanical energy (the sum of potential and kinetic energy) should remain constant in the absence of non-conservative forces like friction. However, in real-world situations, some energy is lost to friction and other forms of dissipation. At the top of the third hill, the biker is slowest due to this energy loss. Thus, while the total amount of energy is conserved theoretically, practical energy transformations (like friction turning kinetic energy into thermal energy) account for the differences observed between the two points.