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24.
REASONING
Each particle experiences two gravitational forces, one due to
each of the remaining particles.
To get the net gravitational force, we must add the two
contributions, taking into account the directions.
The magnitude of the gravitational
force that any one particle exerts on another is given by Newton’s law of gravitation as
2
12
/
FG
m
mr
=
.
Thus, for particle A, we need to apply this law to its interaction with
particle B and with particle C.
For particle B, we need to apply the law to its interaction
with particle A and with particle C.
Lastly, for particle C, we must apply the law to its
interaction with particle A and with particle B.
In considering the directions, we
remember that the gravitational force between two particles is always a force of
attraction.
SOLUTION
We begin by calculating the magnitude of the gravitational force for
each pair of particles:
()
–11
2
2
–5
22
–11
2
2
–5
–11
2
2
–6
6.67 10
N m / kg
363 kg
517 kg
5.007 10
N
0.500 m
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 Spring '08
 SOFFER

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