A block of mass m strikes a light pan fitted with a vertical spring after falling through a distance h. If the stiffness of the spring is k, find the maximum compression of the spring.

Explanation

Let the maximum compression in the spring be x. The reference level for potential energy is assumed at the position of maximum compression.
Applying mechanical energy conservation, `DeltaK+DeltaU=0`
As block is released from rest and finally comes to rest. Hence, net change in kinetic energy, `DeltaK=0`.
Net change in potential energy,
`DeltaU=DeltaU_(gr)+DeltaU_(sp)=[-mg(x+h)]+(1/2kx^2)`
`0+[-mg(h+x)]+(1/2kx^2-0)=0`
`x^2-2((mg)/(k))x-2((mg)/(k))h=0`
After solving, we get `x=(mg)/(k)[1+sqrt(1+(2kh)/(mg))]`