Answer:
19.62mh or 2mgh
Explanation:
the mass of the cat = m
height of the inclined plane = h
NB: The work made by the gravitational force applied onto the cat by the Earth will be equal to the work done by the cat to overcome this force.
a) For climbing (directly) up the inclined plane, the work done by the cat against gravity will be
work = weight x distance
weight = mg = mass x acceleration due to gravity
where g acceleration due to gravity = 9.98 m/s^2
work = -mgh = -9.81mh
the negative sign indicates that the work is done against gravity
b) while climbing down the vertical side of the inclined plane, work done by the cat is the same amount of work the cat does in climbing (directly) up the inclined plane, if we disregard losses due to friction. The only advantage of the inclined plane is that the inclined plane allows the same work to be done with a smaller force exerted over a greater distance; by spreading the distance (now the length of the inclined plane), and reducing the force (weight of the cat) by resolving it into a smaller force that is normal to the inclined plane. All in all the work done is equal and is in accordance with the conservation of energy.
the work done by gravity on the cat on climbing down is
work = mgh = 9.81mh
c) total work done = final work - initial work = 9.81mh - (-9.81mh) = 19.62mh
