What happens to the sum of the ball’s kinetic energy and potential energy as the ball rolls from point a to point e? assume there’s no friction between the ball and the ground.

a. the sum decreases.

b. the sum increases.

c. the sum remains the same.

d. the sum always equals zero.

C. The sum remains the same.

Explanation:

The mechanical energy of an object is defined as the sum of its kinetic energy (K) and its potential energy (U):

E = K + U

The law of conservation of energy states that in absence of friction, the mechanical energy E is conserved, so it does not change.

This law can be applied to this situation, since there is no friction. Therefore, we can say that the mechanical energy (sum of kinetic and potential energy) remains the same. During the motion, the individual values of K and U changes (in fact, when the ball goes down, the kinetic energy increases while the potential energy decreases, and when the ball goes up, the kinetic energy decreases while the potential energy increases); however, their sum still remains the same, since no energy is lost in the motion.

Therefore, the correct answer is

C. The sum remains the same.