p08_019.pdf

19. The reference point for the gravitational potential energy U g (and height h ) is at the block when the

spring is maximally compressed. When the block is moving to its highest point, it is ﬁrst accelerated

by the spring;later, it separates from the spring and ﬁnally reaches a point where its speed v f is

(momentarily) zero. The x axis is along the incline, pointing uphill (so x 0 for the initial compression is

negative-valued);its origin is at the relaxed position of the spring. We use SI units, so k = 1960 N/m

and x 0 =

2 kx 0 =39 . 2J.

(b) Since initially U g = 0, the change in U g is the same as its ﬁnal value mgh where m =2 . 00 kg.

That this must equal the result in part (a) is made clear in the steps shown in the next part. Thus,

∆ U g = U g =39 . 2J.

K 0 + U 0 = K f + U f

0+ 1

which yields h =2 . 00 m. The problem asks for the distance along the incline ,sowehave d =

h/ sin 30 ◦ =4 . 00 m.

0 . 200 m.

−

(a) The elastic potential energy is

2 kx 0 =0+ mgh