Finding the Minimum Mass for Plunger-Spring Contact

[awiest82]

Homework Statement

A plunger of mass m rests on a spring with constant k. The spring is pressed down a distance x and released from rest. How large does the the mass need to be in order to keep the plunger in contact with the spring?

Homework Equations

PE_f+KE_f=PE_i

kx-mg+N=0

The Attempt at a Solution

Using the Conservation of energy equation and solving for m, I get:

kx²/(2gh+v_f²) = m

I have a suspicion that I somehow have to incorporate the second equation into the answer, but am stumped as to how I proceed.

 

[Filip Larsen]

Perhaps you can find a way through by analyzing the acceleration of the spring-mass and consider what limits this must be within.