A block of mass 12.0 kg slides from rest down a frictionless 35.0° incline and is stopped by a strong spring with k = 4.00 104 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?

Question

A block of mass 12.0 kg slides from rest down a frictionless 35.0° incline and is stopped by a strong spring with k = 4.00  104 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?

drwls · Answer

Let the compression of the spring be x. When the block comes to rest, the potential energy loss equals (1/2) k x^2 The P.E. loss is M*g*3.00 sin35 = 202.4 J Solve 202.4 = (1/2)kx^2 for x.