#### Answer

39.2 J

#### Work Step by Step

Since only conservative forces are acting on the block, we have that the mechanical energy of the system is conserved and thus
ΔEmec = ΔUs + ΔUg + ΔK = 0,
where ΔUs is the change in elastic potential energy, ΔUg is the change in gravitational potential energy and ΔK is the change in kinetic energy. Since the block is not moving before being released and also at the highest point on the incline, we have that ΔK = 0.
In Problem 31a, we found that Us before the block was released was 39.2 J. At its highest point on the incline, the block is off the spring, so Us = 0. Therefore, ΔUs = – 39.2 J.
Substituting these values we get:
ΔUs + ΔUg + ΔK = 0
–39.2 J + ΔUg + 0 = 0
ΔUg = 39.2 J
So the change in the gravitational potential energy of the system is 39.2 J.