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For a rope obeying Hooke's law show that the elastic potential energy stored in the rope is given by E=1/2kx^2 where k is the elastic spring constant and x is the extension.
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For a rope obeying Hooke's law show that the elastic potential energy stored in the rope is given by

E=1/2kx^2

where k is the elastic spring constant and x is the extension.

User Ricky Smith
by
9.1k points

1 Answer

5 votes
The average force can be calculated as F/2, where

F = kx

Therefore, substituting this in to the equation for energy:

Energy = Force * Distance
Energy = F/2 * x
Energy = kx/2 * x
Energy = 1/2 kx^2
User Amarnath Chatterjee
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8.3k points
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