Chapter I  Problems
Blinn College  Physics 2425  Terry Honan
Problem I.1
A 200 kg mass sits at
x
=
0 and a 500 kg mass sits at
x
=
0.4 m.
(a) What is the net gravitational force on a 50 kg mass at the midpoint of the two,
x
=
0.2 m.
(b) Where on the
x
axis would the net force on a third mass be zero.
Solution to I.1
m
1
=
200 kg
and
m
2
=
500 kg
(a) The force on
m
=
50 kg is the sum of the forces of
m
1
and
m
2
on
m
.
F
1
=
G
m
1
m
r
1
2
=
6.67
μ
10

11
200
μ
50
0.2
2
=
1.6675
μ
10

5
N
F
2
=
G
m
2
m
r
1
2
=
6.67
μ
10

11
500
μ
50
0.2
2
=
4.1688
μ
10

5
N
F
net
=
F
1
+
F
2
. Since the forces are in opposite directions we should subtract their magnitudes.
F
net
=
F
2

F
1
=
2.50
μ
10

5
N
(b) Take the distances from
m
1
and
m
2
to be
x
and
x

d
, where
d
=
0.4
m
.
F
2
=
F
1
ï
G
m
1
m
x
2
=
G
m
2
m
H
d

x
L
2
ï
d

x
x
=
m
2
ê
m
1
ï
d
=
x
+
x
m
2
ê
m
1
ï
x
=
d
1
+
m
2
ë
m
1
=
0.4
1
+
5
ê
2
=
0.155 m
Problem I.2
Consider a 80000 kg uniform solid sphere with a 1.2 m. What is the gravitational field a distance of
r
from the center for the values:
(a)
r
=
0, (b)
r
=
0.6 m, (c)
r
=
1.2 m, (d)
r
=
2.4 m
Solution to I.2
The gravitational field
g
is defined as the force per test mass,
g
=
F
ë
m
0
. Here we are just looking for the magnitude of the field. The
shell theorem implies the force and field at
r
go as
F
=
G
M
inside
m
0
r
2
ï
g
=
F
m
0
=
G
M
inside
r
2
where
M
inside
is the total mass inside a sphere of radius
r
.
Here take
M
=
80000 kg and
R
=
1.2 m. When outside the sphere
M
inside
is just
M
.
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r
¥
R
ï
M
inside
=
M
When inside the sphere
M
inside
depends on the fraction of the total volume inside
r
: call this
V
inside
.
r
<
R
ï
M
inside
=
M
V
inside
V
total
=
M
H
4
ê
3
L
p
r
3
H
4
ê
3
L
p
R
3
=
M
J
r
R
N
3
(a)
r
=
0
ï
M
inside
=
0
ï
g
=
0
(b)
r
=
0.6 m
ï
M
inside
=
80000
K
0.6
1.2
O
3
=
10000
ï
g
=
G
M
inside
r
2
=
1.85
μ
10

6
m
s
2
(c)
r
=
1.2 m
ï
M
inside
=
80000
ï
g
=
G
M
inside
r
2
=
3.70
μ
10

6
m
s
2
(d)
r
=
2.4 m
ï
M
inside
=
80000
ï
g
=
G
M
inside
r
2
=
0.926
μ
10

6
m
s
2
For the above calculations the value of
G
=
6.67
μ
10

11
N
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 Spring '09
 Force, Mass

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