93. (a) The potential energy is
U
q
d
=
=
×
⋅
×
=
−
2
9
6
4
8 99
10
50
10
100
0 225
π
0
ε
.
.
.
.
N
m
C
C
m
J
2
2
2
c
hc
h
relative to the potential energy at infinite separation.
(b) Each sphere repels the other with a force that has magnitude
F
q
d
=
=
×
⋅
×
=
−
2
2
9
6
4
8 99
10
50
10
0 225
π
0
ε
.
.
.
N
m
C
C
1.00 m
N.
2
2
2
2
c
hc
h
b
g
According to Newton’s second law the acceleration of each sphere is the force divided by
the mass of the sphere. Let
m
A
and
m
B
be the masses of the spheres. The acceleration of
sphere
A
is
a
F
m
A
A
=
=
×
=
−
0 225
450
3
.
.
N
5.0
10
kg
m s
2
and the acceleration of sphere
B
is
a
F
m
B
B
=
=
×
=
−
0 225
22 5
3
.
.
.
N
10
10
kg
m s
2
(c) Energy is conserved. The initial potential energy is
U
= 0.225 J, as calculated in part
(a). The initial kinetic energy is zero since the spheres start from rest. The final potential
energy is zero since the spheres are then far apart. The final kinetic energy is
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 Spring '10
 Rebello,NobelS
 Energy, Force, Kinetic Energy, Mass, Potential Energy

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