QUESTION 4 Compare the case of an object sliding down a ramp and the same object

Question

QUESTION 4 Compare the case of an object sliding down a ramp and the same object rolling without slipping down a ramp with the same slope, and from the same height. Which of the following is true? a. The sliding object reaches the bottom faster, but the increase in total kinetic energy is the same b. Both objects reach the bottom at the same time, but the rolling one has more kinetic energy .The sliding object takes longer to reach the bottom, and has less kinetic energy d. Both objects reach the bottom at the same time, and have the same kinetic energy

Explanation / Answer

Ans: (a) The sliding object reaches the bottom faster, but the increase in total kinetic energy is the same.

No energy is dissipated by static friction, so, if you consider a system that includes the Earth, the final kinetic energy just equals the initial potential energy, which is the same in both cases. However, the rolling object has to split this total kinetic energy into a translational part and a rotational part, so its translational kinetic energy has to be smaller than the sliding object’s, which means its center of mass moves more slowly.

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