HW#3: Solutions to Problems Chapter 8
1.
(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
2
(0.341 kg)(9.80 m/s
)(0.452 m)
1.51 J
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
2
(0.341 kg)(9.80 m/s
)(0.452 m)
1.51 J.
W
mgL
= −
= −
= −
(c) The final position of the ball is at the same height as its initial position. The
displacement is 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:
2
(0.341 kg)(9.80 m/s
)(0.452 m)
1.51 J
U
mgL
∆
= −
= −
= −
as the ball goes to the lowest point.
(e) Continuing this line of reasoning, we find
2
(0.341 kg)(9.80 m/s
)(0.452 m)
1.51 J
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.
2.
We use Eq. 8-17, representing the conservation of mechanical energy (which neglects
friction and other dissipative effects).

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