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.
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.
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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