Final answer:
The total mechanical energy of a system does not stay constant when work is done on it by external non-conservative forces. It changes according to the work-energy theorem, where the change in mechanical energy is equal to the work done by these forces.
Step-by-step explanation:
If work is done on a system by external non-conservative forces, the total mechanical energy (kinetic plus potential) of a system does not stay constant. The total mechanical energy is the sum of kinetic energy (KE) and potential energy (PE) within a system. According to the conservation of mechanical energy principle, KE + PE remains constant if only conservative forces, like gravity or spring forces, are acting within the system, without any external work being done.
However, when non-conservative forces do work on a system, they change the total mechanical energy of that system. The work-energy theorem states that the change in the mechanical energy of a particle equals the work done on it by non-conservative forces. This is mathematically represented as the change in total mechanical energy (ΔKE + ΔPE) being equal to the work done by non-conservative forces minus any work done by friction or other dissipative forces.