Question

A 9.6 kg block slides down a 9.9 m long ramp inclined at an angle of 30o above the horizontal. At the bottom of the plane, the block transitions to a flat, smooth table that is 5.0 m in length. There is a spring attached to the wall at the end of the flat portion of the track that has spring constant of 246.2 N/m. What is the compression of the spring when the box has stopped moving forward?

Answer 1

$E_p=E_s$

$E_p=mgh$

$h=l\cdot \sin(30°)$

$E_p=mgl\sin(30°)$

$E_s=\frac{kx^2}{2}$

So,

$\frac{kx^2}{2}=mgl\sin(30°)$

$x=\sqrt{\frac{2mgl\sin(30°)}{k}}=\sqrt{\frac{2\cdot 9.6\cdot 9.8\cdot 9.9\sin(30°)}{243.2}}=1.96 m$