Phys 2101
Homework 10 Solution Spring `11
These solutions use the parameter values from the problems printed in the book, not those that
appear in your personal homework assignment. The logic used to get to the answer is the same,
however.
1. Using
F
=
GmM/r
2
, we find that the topmost mass pulls upward on the one at the origin with 1.9
10
8
N, and the rightmost mass pulls rightward on the one at the origin with 1.0
10
8
N. Thus,
the (
x, y
) components of the net force, which can be converted to polar components (here we use
magnitudeangle notation), are
8
8
8
net
1.04 10 ,1.85 10
2.13 10
60.6 .
F
(a) The magnitude of the force is 2.13
10
8
N.
(b) The direction of the force relative to the +
x
axis is
60.6
.
2 Both the Sun and the Earth exert a gravitational pull on the space probe. The net force can be
calculated by using superposition principle. At the point where the two forces balance, we have
22
12
//
es
GM m r
GM m r
, where
M
e
is the mass of Earth,
M
s
is the mass of the Sun,
m
is the mass of
the space probe,
r
1
is the distance from the center of Earth to the probe, and
r
2
is the distance from
the center of the Sun to the probe. We substitute
r
2
=
d
r
1
, where
d
is the distance from the center
of Earth to the center of the Sun, to find
1
1
=.
MM
r
dr
Using the values for
M
e
,
M
s
, and
d
given in Appendix C, we take the positive square root of both
sides to solve for
r
1
. A little algebra yields
11
8
1
30
24
1.50 10 m
2.60 10 m.
1/
1
(1.99 10 kg)/(5.98 10 kg)
se
d
r
Note: The fact that
1
rd
=
indicates that the probe is much closer to the Earth than the Sun.
3. We use
m
1
for the 20 kg of the sphere at (
x
1
,
y
1
) = (0.5, 1.0) (SI units understood),
m
2
for the 40
kg of the sphere at (
x
2
,
y
2
) = (
1.0,
1.0), and
m
3
for the 60 kg of the sphere at (
x
3
,
y
3
) = (0,
0.5).
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View Full DocumentThe mass of the 20 kg object at the origin is simply denoted
m
. We note that
12
1.25,
2
rr
,
and
r
3
= 0.5 (again, with SI units understood). The force
n
F
that the
n
th
sphere exerts on
m
has
magnitude
2
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 Spring '07
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