Set 3 Problem number 19

If a system does 4.1 Joules of work against non-conservative forces while gravity, which is the only conservative force acting on the system, does 6.6 J of work on the system, then what is the change in the KE of the system?

Solution

The system does 4.1 Joules of work against non-conservative forces.

Since gravity does 6.6 J of work on the system, the system does - 6.6 J of work against gravity, thereby changing its gravitational PE by -6.6 J.

Since `dWnoncons + `dPE + `dKE = 0, we see that

`dKE = - 4.1 J - -6.6 J = 2.5 J

Looking at the situation in an equivalent but slightly different way, we see that the system does total work -2.5 J.

If the total work done by the system is positive, the energy must come from the kinetic energy of the system.
If the total work done by the system is negative, then KE is in fact added to the system.