Final answer:
Yes, a non-conservative force can increase the mechanical energy of a system when it performs work on the system, such as an external force pushing an object, resulting in increased kinetic energy.
Step-by-step explanation:
Can a non-conservative force increase the mechanical energy of the system? The answer is yes. A non-conservative force, such as work done by an external force like pushing a box along a surface, can add energy to a system, increasing its mechanical energy. This contrasts with conservative forces, which preserve the total mechanical energy within a closed system. An example of a non-conservative force at work is when a car accelerates due to the force exerted by the engine, which increases the vehicle's kinetic energy.
It's also important to note that non-conservative forces typically convert mechanical energy into other forms, such as thermal energy due to friction. However, when these forces perform work on a system (as opposed to removing energy from it), they result in an increase in mechanical energy.