Spring work problem Calculus
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Spring work problem Calculus

[From: ] [author: ] [Date: 12-06-25] [Hit: ]
1 meters to 1.5 meters? The answer is 6/5 N-m.Im not really looking for anyone to solve it, I just want to know how to set up the integral for the work done.k = F/x = (2 N)/(0.......
A force of 2 Newtons will compress a spring from 1 meter (its natural length) to 0.8 meters.
How much work is required to stretch the spring from 1.1 meters to 1.5 meters? The answer is 6/5 N-m.
I'm not really looking for anyone to solve it, I just want to know how to set up the integral for the work done.

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First determine the spring constant

k = F/x = (2 N)/(0.2 m) = 10 N/m

The desired work is then

integral from x=0.1 to x=0.5 (kx) dx

= (1/2)(10 N/m)( (0.5)^2 - (0.1)^2 ) = 1.2 Joules

Note that all x displacements are relative to the 1-meter natural length, since that is where the spring force is zero.

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Nice work solving this on your own. The two solutions are equivalent, of course, via the substitution u=(x-1), which changes both the integrand as well as the limits of integration.

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