Equilibrium Shift and Magnitude in Non-Intertial Frame?

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The equilibrium of a mass hanging from a spring in an accelerating elevator shifts downward when the elevator accelerates upwards at g/5. The initial equilibrium position is determined by the force balance F = -kx = mg, leading to x = -(mg/k). When the elevator accelerates, the new force equation becomes F = -kx = m(g + g/5), resulting in a downward shift of -(mg/5k). This indicates that the mass displaces downward an additional mg/5k from its original equilibrium position. The system reaches a new dynamic equilibrium while accelerating with respect to the ground.
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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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