HELP; Physics question just an explanation needed?

You know the spring constant k, and you know how much the spring compresses before the block stops moving, x0 = 0.2 m . So you know the energy stored in the spring: U = 1/2kx0^2 Now energy is conserved here since the plane is frictionless. So the potential energy the block had before it slide U0 must be equal to the energy in the spring.

Use the gravitational potential energy of the block at the top of the plane: U0 = mgh where h = height above the spring's compressed position, x0. H and the distance along the plane, x, are related by the and q = 30 deg: x = h/sin(q) so U0 = mgh = mgx*sin(q) Now equate U0 and U --> mgx*sin(q) = 1/2kx0^2 --> x = kx0^2/(2mg*sin(q)) = kx0^2/(mg) since sin(30) = 1/2 Plug in and you are done.

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