Energy conservation with nonconservative forces: Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?

Question

Quizplus · Accepted Answer

The conservation of energy only holds when all forces acting on an object are conservative. In this case, friction is a nonconservative force because it acts in the direction opposite to the direction of motion. Therefore, the conservation of energy principle cannot be applied directly. 
Instead, we can use the work-energy principle, which states that the net work done on an object is equal to its change in kinetic energy. The work done on each block by friction is equal to the force of friction times the distance traveled, which is proportional to the length of the incline. Since the inclines have the same height, the length of the incline for block 1 is shorter than the length of the incline for block 2. Therefore, the work done by friction on block 1 is less than the work done by friction on block 2, resulting in a larger net work being done on block 1. This means that block 1 has a greater increase in kinetic energy and therefore a higher speed at the bottom of the incline.

Energy Conservation with Nonconservative Forces: Block 1 and Block 2