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Discussion Question 1B
P212, Week 1
P211 Review: Gravitational Forces and Superposition
page 1
2
1
ˆ
r
12
r
12
,
F
1
→
2
=−
G
m
1
m
2
r
12
2
ˆ
r
12
This problem develops skills you will need in P112 in finding the electric fields
created by
sets of point charges.
Four particles of equal mass
M
are fixed at the corners of a square with sides of length
a
.
A fifth
particle has mass
m
and moves under the gravitational forces of the other four.
(a)
Find the
x
 and
y
components
of the net gravitational force on
m
due to the other four
masses when
m
is located at the center of the square (lefthand figure).
Hint:
Draw a sketch!
Use superposition and draw a
vector diagram
consisting of four
vectors, each representing the force exerted by one of the corner particles on
m
.
For ease
of reference, label the four (equal) corner masses
M
1
,
M
2
,
M
3
, and
M
4
.
Label the
corresponding force vectors
F
1,
F
2
, etc.
With the vector diagram in hand, it is vastly easier
to calculate the requested components of the total force.
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 Spring '08
 Kim
 Charge, Electric Fields, Magnetism, Force

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