Question

A ball is dropped from the top of an eleven-story building to a balcony on the ninth floor. In which case is the change in the potential energy associated with the motion of the ball the greatest?

A. It is greatest when y = 0 is set level with the ninth floor balcony.
B. The change in potential energy is the same in all three cases.
C. It is greatest when y = 0 is set at ground level.
D. It is greatest when y = 0 is set level with the top of the building.

Answer 1

The change in potential energy is the same no matter where y=0 is set, since it only depends on the change in height, making the correct answer B. The change in potential energy is the same in all three cases.

Step-by-step explanation:

The change in potential energy of a falling object is determined by its change in height and does not depend on the choice of the zero level. Regardless of where we set y=0, the change in potential energy is given by the mass of the ball multiplied by the acceleration due to gravity and the change in height (U=mgh). Whether y=0 is set at the ground level, the ninth floor, or the top of the building, the change in height from the top of the building to the ninth floor remains the same, hence, the change in potential energy is identical in all cases.

Therefore, the correct answer to the student's question is: B. The change in potential energy is the same in all three cases.