Finding the Minimum Mass for Plunger-Spring Contact

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To determine the minimum mass required for a plunger to remain in contact with a spring, the conservation of energy equation is applied, leading to the relationship m = kx²/(2gh + vf²). The discussion highlights the need to integrate the equation involving forces, specifically kx - mg + N = 0, to fully understand the dynamics at play. Participants suggest analyzing the acceleration of the spring-mass system to identify necessary limits for mass. The conversation emphasizes the importance of combining both energy and force equations for a comprehensive solution. Ultimately, the goal is to ensure the plunger maintains contact with the spring throughout its motion.
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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



PEf+KEf=PEi

kx-mg+N=0

The Attempt at a Solution



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

kx2/(2gh+vf2) = 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.
 
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Perhaps you can find a way through by analyzing the acceleration of the spring-mass and consider what limits this must be within.
 

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