A block is projected with speed v across a horizontal surface and slides to a stop due to friction.The same block is then projected with the same speed v up an incline where is slides to a stop due to friction.In which case did the total mechanical energy of the block decrease the least?
A)This problem cannot be solved since it was not indicated whether the horizontal surface and the incline both had the same coefficient of kinetic friction.
B)The case on the horizontal surface had the least decrease in total mechanical energy.
C)The case on the inclined surface had the least decrease in total mechanical energy.
D)In both cases the decrease in mechanical energy was the same.

Question

Quizplus · Accepted Answer

The total mechanical energy of an object is given by the sum of its kinetic energy and potential energy. When the block is projected across the horizontal surface, it stops due to friction alone, which means that all of its initial kinetic energy is converted into heat energy, and thus the total mechanical energy decreases significantly. However, when projected up the incline, some of the block's initial kinetic energy will be converted into potential energy as it gains height, and only part of the initial kinetic energy will be lost due to friction. Therefore, the decrease in total mechanical energy will be less in the case of the incline than the horizontal surface. Option C is the best choice. Option A is not correct because the question only asks for a comparison between the two cases, regardless of the coefficients of friction. Option B is not correct, as explained above. Option D is not correct because, as explained above, the decrease in mechanical energy is not the same in both cases.

A Block Is Projected with Speed V Across a Horizontal