I need help calculation the work done stretching
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I need help calculation the work done stretching

[From: ] [author: ] [Date: 11-07-09] [Hit: ]
-It should be 3J.The energy involved in a spring is proportional to the square of the displacement.So if you double the displacement ( from 0.10 m to0.20 m ), you quadruple the stored energy.......
Supposed 1J is the energy transferred stretching a spring from 0 to 0.10m. The amount of working done stretching the same spring from 0.10 m to 0.20 m is?

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It should be 3J.

The energy involved in a spring is proportional to the square of the displacement. So if you double the displacement ( from 0.10 m to 0.20 m ), you quadruple the stored energy. So the additional amount of work you need to do is 4J - 1J = 3J



Potential energy of a spring:
U = ½kx²


Ratio of the potential energies:
U2 / U1 = ½k( 0.20 )² / ½k( 0.10 )²

U2 / U1 = ( 0.2 / 0.1 )²

U2 / U1 = 4

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3 J

The total needed to stretch the spring 0.2 m is 4 J ( since energy is proportional to extension squared )

1 J does the 0 to 0.1 m so 3 more J is needed to go from 0.1 to 0.2 m
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