p08_005.pdf

5. (a) The only force that does work on the ball is the force of gravity; the force of the rod is perpendicular

to the path of the ball and so does no work. In going from its initial position to the lowest point

on its path, the ball moves vertically through a distance equal to the length L of the rod, so the

work done by the force of gravity is W = mgL .

(b) In going from its initial position to the highest point on its path, the ball moves vertically through

a distance equal to L , but this time the displacement is upward, opposite the direction of the force

of gravity. The work done by the force of gravity is W =

mgL as the ball goes to the

lowest point

(e) Continuing this line of reasoning, we ﬁnd ∆ U = mgL as it goes to the highest point.

(f) Continuing this line of reasoning, we have ∆ U =0 as it goes to the point at the same height.

(g) The change in the gravitational potential energy depends only on the initial and ﬁnal positions of

the ball, not on its speed anywhere. The change in the potential energy is the same since the initial

and ﬁnal positions are the same.

mgL .

horizontal, perpendicular to the force of gravity. The force of gravity does no work during this

displacement.

(d) The force of gravity is conservative. The change in the gravitational potential energy of the ball-

Earth system is the negative of the work done by gravity: ∆ U =

−