Ablock of mass 12.0kg slides from rest
downa frictionless 35.0 degree incline and is stopped by a
strongspring with k=3.00x10 the 4th n/m. the block slides 3.00m
from thepoint where it comes to rest against the spring. when the
blockcomes to rest, how far has the spring been compressed.

The spring is compressed 0.11 m.

Explanation:

We will use the conservation of energy between the initial position (A) and the position when the block comes to rest (B).

Since the block is released from rest, and comes to rest finally, first and final kinetic energies are zero.

since there is no friction, the initial gravitational potential energy of the block is equal to the final elastic potential energy stored in the spring.

be subject to a force andchange its motion