Figure 8-26 shows three situations involving a plane that is not frictionless and a block sliding along the plane. The block begins with the same speed in all three situations and slides until the kinetic frictional force has stopped it. Rank the situations according to the increase in thermal energy due to the sliding, greatest first.

A figure which shows three situations involving a plane that is not frictionless and a block sliding along the plane

As per the law of conservation of energy, the energy cannot be created, nor be destroyed, it can be only transferred from one form to other. The total energy of an isolated system is always constant.

The law of conservation of energy can be used to rank the situations according to the increase in thermal energy due to the sliding.

Forthe first case, initially, the associated kinetic energy is transformed into thermal energy

For the second case, the block has initial kinetic energy and potential energy due to height. This kinetic energy and potential energy is transformed into thermal energy

For the third case, only a part of the initial kinetic energy is transformed into thermal energy, and most of the energy is transformed into gravitational potential energy.

Thus, the rank of the situations according to the increase in thermal energy due to the sliding, greatest first is $2,1,3$.