Final answer:
A woman on a trampoline uses the force of her muscles to increase her mechanical energy, converting it from kinetic to gravitational potential energy during a jump, which allows her to bounce higher with each exertion.
Step-by-step explanation:
A woman increases the total mechanical energy while bouncing on a trampoline by applying a force against the trampoline surface. When she pushes down on the trampoline, it compresses and then the trampoline exerts an upward force, propelling her into the air. During this phase, the chemical potential energy in her muscles is converted into kinetic energy as she accelerates upwards, and then into gravitational potential energy at the peak of her bounce.
By repeatedly adding energy with each jump, she can increase her gravitational potential energy with each subsequent bounce, reaching higher altitudes. Non-conservative forces, such as the work done by her muscles, add energy to the system, which is evident from the increase in the total mechanical energy of the system.