Two objects of the same mass slide down two different inclin...

Question

Two objects of the same mass slide down two different inclined planes, AC and BC, starting from rest at the top. The coefficient of kinetic friction between the objects and the inclined planes is the same for both planes. When the objects reach the bottom of the planes (at point C), their kinetic energies are and respectively. The work done by friction during the descent is and respectively. Which of the following statements is true?

1. Work - Energy Theorem Analysis

According to the work - energy theorem, the net work done on an object is equal to the change in its kinetic energy, i.e., .

For both objects, the initial kinetic energy is zero (starting from rest). The work done by gravity is , where is the height of the starting point above the bottom point (in this case ).

The work done by the friction force is , where is the coefficient of kinetic friction, is the angle of the incline, and is the distance traveled along the incline.

Regardless of the length of the incline (L), L multiplied by cosθ is equal to the length of OC. (Let x represent the length of OC)

Thus, the work done by friction can be written as

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