Equilibrium Shift and Magnitude in Non-Intertial Frame?

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SUMMARY

The equilibrium of a mass M hanging from a spring in an accelerating elevator shifts downward when the elevator accelerates upwards at g/5. The force equation for the moving scenario is F = -kx = m(g + g/5), leading to a new equilibrium position calculated as x = -(mg/k) - (mg/5k). The magnitude of the shift is definitively -(mg/5k), indicating that the mass displaces downward from its initial equilibrium position.

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Homework Statement



A particle of mass M is hanging from one end of a massless spring, while the other is attached to the ceiling of an elevator.

The elevator then starts to move upwards at an acceleration equal to g/5.

Which way does the equilibrium shift, and what is the magnitude of the shift?

Homework Equations



F=-kx, F=ma

The Attempt at a Solution



Equilibrium when not moving...

F=-kx=mg, so x=-(mg/k)

When moving...

F=-kx=m(g+(g/5))

x= -(mg/k) - (mg/5k)

Where the magnitude of the shift is -(mg/5k), and the equilibrium would shift downwards.

Is this correct? I am a bit confused because i though x was displacement from equilibrium.
 
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Yes, that looks correct. The mass will displace downward an additional mg/5k units from it's initial at rest equilibrium position, and the mass will be in its new state of dynamic equilibrium (not moving with respect to the elevator, but accelerating with respect to the ground).
 
Great, thanks.
 

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