Engineering Physics
posted by M .
A 1.0kg block is released from rest at the top of a frictionless incline that makes and angle of 37 degrees with the horizontal. An unknown distance down the incline from the point of release, there is a spring with k=200 N/m. It is observed that the mass is brought momentarily to rest after compressing the spring .20m. What distance does the mass slide from the point of release until it is brought momentarily to rest?

M g H sin37 = (1/2)*kX^2
X = 0.20 m
k = 200 N/m
M = 1.0 kg
g = 9.8 m/s^2
Solve for H. This neglects additional work done during spring compression, but should be close enough.
The exact equation is
M g (H+X) sin37 = (1/2)*kX^2 
Use simple harmonic motion

W(g)=U(s)
mgdsin(37)=1/2kx^2
d=kx^2/2mgsin(37)
d=0.68m