A horse whose mass is M gallops at constant speed v up a long hill whose vertical height is h, taking an amount of time t to
reach the top. The horse's hooves do not slip on the rocky ground, so the work done by the force of the ground on the
hooves is zero (no displacement of the force). When the horse started running, its temperature rose quickly to a point at
which from then on, heat transferred from the horse to the air keeps the horse's temperature constant.
(a) First consider the horse as the system of interest. In the initial state the horse is already moving at speed v. In the
final state the horse is at the top of the hill, still moving at speed v. Write out the Energy Principle ΔEsys = W + Q
for the system of the horse alone. The terms on the left-hand side should include only energy changes for the
system, while the terms on the right-hand side should relate to the surroundings (everything else).
Which of the terms are equal to 0? Which of the terms should go on the system (left) side (ΔEsys)? Which of the
terms should go on the surroundings (right) side?
(b) Next consider the Universe as the system of interest. Write out the energy principle for this system. Remember that
terms on the left-hand side should include all energy changes for the system, while the terms on the righthand side
should relate to the surroundings.
Which of the terms are equal to 0? Which of the terms should go on the system (left) side (ΔEsys)? Which of the
terms should go on the surroundings (right) side?