Set 3 Problem number 24

What is the KE change of an object of mass 4.8 kg as its gravitational PE increases by 48 J if at the same time it also does 62 J of work against the net nongravitational force?

Solution

PE increases when altitude increases, so that work is done BY the object against gravity.

The work done by the object against the net force on it will be at the expense of its KE. The net force on the object is the sum of its gravitational and nongravitational forces.

In order to increase its PE by 48 Joules the object must do 48 Joules of work against gravity.

If the object also does 62 Joules of work against all nongravitational forces, it does a total of 48 J + 62 J = 110 Joules of work against all forces.

This is the same as saying that the object does 110 Joules of work against the net force acting on it.

The net effect will be to decrease kinetic energy by 110 Joules, so the kinetic energy of the object changes by -110 Joules.

An example of such a process might be an object which has been tossed or shot upward, so that its PE is increasing as its upward velocity and hence its KE decreases.

Between two given points its PE might increase by 48 Joules, while it also does 62 Joules of work against air resistance.
This will have the effect of decreasing its KE by 48 J + 62 J = 110 J.