Question

The spring is now compressed so that the unconstrained end moves from x=0 to x=L. Using the work integral W=∫xfxiF⃗ (x⃗ )⋅dx⃗ , find the work done by the spring as it is compressed. Express the work done by the spring in terms of k and L?

Answer 1

solution:

the spring force exerted by spring with spring constant k is given by

$F(x)=-kx$

where k is spring constant

and x is deformation of spring

in order to calculate word done by the spring

$W=\int\limits^L_0 {} \, dW$

the work done by the spring as it is compressed from x=0 to x=L

$W=-kx^2/2$

inserting the limits x=0 and x=L

we get work done in terms of k and L

$ANSWER$

$W=-kL^2/2$