A spring with force constant 327 N/m is in a compressed state, 0.401 m shorter t

Question

A spring with force constant 327 N/m is in a compressed state, 0.401 m shorter than its relaxed length. In this condition, the spring serves a vital purpose in a device for detecting impending earthquakes. A curious physicist releases the spring and, moreover, stretches it until it is 0.143 m longer than its relaxed length. That renders the earthquake detector useless, and it fails to warn of a very strong earthquake that subsequently shatters all the lawn sculptures in the area–fortunately with no other damage or injury. Although some might consider this to be beneficial, the physicist's boss does not. She had some extremely unattractive plaster gnomes around her yard and loved them dearly. So she imposes a punishment on the physicist and requires him to calculate the change of elastic potential energy that he caused by his meddling. What does he find?

Explanation / Answer

Change in potential energy = 0.5*k*(x2^2 - x1^2) (here X1 is initial compression and x2 is final extension)

= 0.5*327*(0.143^2 - 0.401^2)

= -22.94 J

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