Answer
The work that has been done on the block by the spring force is $~~-0.36~J$
Work Step by Step
The block will stop when the magnitude of the work done by the applied force is equal in magnitude to the opposing work done on the block by the spring force.
We can find $x$:
$\frac{1}{2}kx^2 = F~x$
$x = \frac{2F}{k}$
$x = \frac{(2)(3.0~N)}{50~N/m}$
$x = 0.12~m$
We can find the work that has been done on the block by the spring force:
$W = -\frac{1}{2}kx^2$
$W = -\frac{1}{2}(50~N/m)(0.12~m)^2$
$W = -0.36~J$
The work that has been done on the block by the spring force is $~~-0.36~J$
