Chapter 12 Even Problem Solution
54. We are asked to nd the speed at which a solid baseball is moving after
it has rolled down 8.4m along a 30 degree incline. We do this with conservation
of energy. We rst note that the height that the baseball has rolled down is:
h = l sin(θ) = 8.4 sin(30◦ ) = 4.2m
(1)
Thus, by conservation of energy:
mgh =
1
1
mv 2 + Iω 2
2
2
(2)
We know from table 12-2 that the moment of inertia for the solid sphere is
I = 25 mr2 so that:
mgh =
1
1
mv 2 + mr2 ω 2
2
5
(3)
We also know that rω = v , therefore:
gh =
7 2
1 2 1 2
v + v =
v
2
5
10
(4)
Solving for v we obtain:
r
v=
10
gh =
7
r
m
10
∗ 9.8 ∗ 4.2 = 7.7
7
s
1
(5)