If an actuator is used to raise and lower a mirror how does

If an actuator is used to raise and lower a mirror, how does required force scale? Hint: How does actuation work (force x distance) scale relative to the required poteneital energy needed to raise and lower the mirror (mgh)?

This question is asking for the scaling for the required force (not the general force to deform the mechanical structure). The force can be expressed by other variables, and from the scaling of these variables, you can find the required force.

We have been working with a scaling factor of L^exponent, but I am not sure if this applies to this problem.

Solution

Actuation force = Fx

Change in potential energy = mg(change in elevation) = mg(h₂ - mgh₁) = mg(h₂ - h₁) =mgx

Equating , Fx = mgx or F =mg

Required force F varies as g times mass