HOMEWORK:
Week 11 – Chapter 12  SOLUTIONS
1.
(12.15)
Two 6.3kg bowling balls, each with a radius of 0.11 m, are in contact with one
another. What is the gravitational attraction between the bowling balls?
SOLUTION
A sphere acts like a point mass at the sphere’s center.
2
2
2
11
8
2
2
2
N m
(6.3 kg)
6.67 10
5.5 10
N
kg
(0.22 m)
m
F G
r


⋅
=
=
×
=
×
2. (12.22)
Consider a spherical asteroid with a radius of 12 km and a mass of 345
10
15
.
.
×
kg
(a)
What is the acceleration of gravity on the surface of this asteroid?
(b)
Suppose the
asteroid spins about an axis through its center, like the Earth, with an angular speed
ϖ
What is the greatest value
can have before loose rocks on the asteroid’s equator
begin to fly off the surface?
SOLUTION
(a)
2
15
11
3
2
A
A
2
2
3
2
A
N m
(3.45 10 kg)
6.67 10
1.6 10
m/s
kg
(12 10 m)
M
g
G
R


⋅
×
=
=
×
=
×
×
(b)
A
A
2
3
2
4
esc
A
3
A
A
A
2
2(1.6 10
m/s )
5.2 10
rad/s
12 10 m
GM
R
v
g
R
R
R


×
=
=
=
=
=
×
×
3.
(12.37)
Calculate the gravitational potential energy of a 5.0kg mass
(a)
on the
surface
of the Earth and
(b)
at an altitude of 1.0 km.
(c)
Take the difference between the
results for parts (b) and (a), and compare with
mgh
, where
h
=
10
.
.
km
SOLUTION
E
M m
U
G
r
= 
(a)
2
24
11
8
1
2
6
N m
(5.97 10
kg)(5.0 kg)
6.67 10
3.12558 10 J
kg
6.37 10 m
U

⋅
×
= 
×
= 
×
×
(b)
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 Fall '09
 WOODAHL
 Physics, Mass, Potential Energy, Work, kg, mgh

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