The force on the box is:
F = mgsin∅
If we multiply by this with the distance it traveled, we will know the work done by the box.
W = dmgsin∅
This work will be converted to elastic potential energy in the spring which is:
1/2 kx². Equating these and substituting values:
1/2 * 170 * x² = 4 * 13 * 9.81 * sin(30)
x = 1.73 m
The box's maximum speed will at the point right before contact with the spring, when the compression is 0.
