Finding the Minimum Mass for Plunger-Spring Contact

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SUMMARY

The discussion focuses on determining the minimum mass required for a plunger to maintain contact with a spring. The key equations utilized include the conservation of energy equation (PEf + KEf = PEi) and the force balance equation (kx - mg + N = 0). The derived formula for mass is m = kx² / (2gh + vf²). Participants emphasize the need to analyze the acceleration of the spring-mass system to ensure the plunger remains in contact.

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awiest82
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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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