Why is the calculated change in PE for a mass on a spring incorrect?

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The discussion focuses on calculating the change in potential energy (PE) for a mass hanging from a spring. The extension of the spring is correctly calculated as 0.123m using the formula x = (mg)/k. However, the calculated change in PE of 0.30J is deemed incorrect because it represents the energy stored in the spring rather than the actual change in gravitational potential energy of the mass. The misunderstanding arises from the fact that energy is not conserved as the mass moves through the equilibrium position. Therefore, the calculated value does not reflect the true change in potential energy for the mass.
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Homework Statement


A spring of length 75cm has a mass of 0.5kg hanging from it.
If the spring constant = 40N/m calculate:
a) the extension of the spring
b) The change in PE of the mass


Homework Equations


Part (a) is easy x = (0.5 x 9.81)/40 = 0.123m
Part (b) energy = 0.5kx^2 gives 0.30J which is WRONG !

WHY ?


The Attempt at a Solution


 
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Hi Emilyjoint! :smile:
Emilyjoint said:
A spring of length 75cm has a mass of 0.5kg hanging from it.
If the spring constant = 40N/m calculate:
…
b) The change in PE of the mass
…
part (b) energy = 0.5kx^2 gives 0.30J which is WRONG !

that's the energy of the spring

(energy is not conserved … if you released the mass from rest, it would sail through that equilibrium position at high speed, wouldn't it? :wink:)
 

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