Question

A ball was positioned in the middle of a smooth ramp and allowed to roll downward. How does the total mechanical energy of the ball before it is released compare to its total mechanical energy at the bottom of the ramp? Assume there is no friction.

A. The total mechanical energy is zero before it is released and
increases until it reaches the bottom of the ramp.
B. The total mechanical energy at the bottom of the ramp is twice
what it was before the ball was released.
C. The total mechanical energy is the same before it was released
and at the bottom of the ramp.
D. The total mechanical energy before it was released is less than
what it is at the bottom of the ramp.

Answer 1

Answer: C

In the absence of friction, the total mechanical energy of the ball is conserved throughout its motion. This conservation is known as the principle of conservation of mechanical energy. Mechanical energy is the sum of the ball's kinetic energy (KE) and potential energy (PE).

Before the ball is released, it has potential energy due to its position on the ramp, but it has no kinetic energy because it is stationary. At this point, its total mechanical energy is equal to its potential energy.

As the ball rolls downward, it gains speed and its potential energy decreases. However, this decrease in potential energy is accompanied by an increase in kinetic energy. The ball's total mechanical energy remains constant throughout the motion.

Therefore, the correct answer is:

C. The total mechanical energy is the same before it was released and at the bottom of the ramp.