A block of mass m has a spring –spring constant k and length L –connected, vertically, to the bottom.

Question

The block is dropped from height h, towards the floor. Assuming the spring is stiff enough that it does not
compress fully at the floor, what is the closest distance, z, the block gets to the floor? (Note that the quadratic
equation might seem ugly but things like k, L, h, m, g are all given so there’s really only one unknown in
there.)

Answer 1

mgh=kx²/2

x=sqrt{2mgh/k}

Z=L- sqrt{2mgh/k}