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
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
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