Muraj, Hamza – Homework 30 – Due: Apr 14 2006, 4:00 am – Inst: Florin
1
This
printout
should
have
11
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
The due time is Central
time.
001
(part 1 of 2) 10 points
Given:
G
= 6
.
67259
×
10

11
N m
2
/
kg
2
.
A 1550 kg geosynchronous satellite orbits a
planet similar to Earth at a radius 193000 km
from the planet’s center. Its angular speed at
this radius is the same as the rotational speed
of the Earth, and so they appear stationary
in the sky. That is, the period of the satellite
is 24 h
.
What is the force acting on this satellite?
Correct answer: 1582
.
05 N.
Explanation:
Let :
G
= 6
.
67259
×
10

11
N m
2
/
kg
2
,
M
satellite
= 1550 kg
,
and
T
= 86400 s
.
Solution:
v
=
2
π r
T
F
=
M
satellite
v
2
r
=
M
satellite
4
π
2
r
T
2
(1)
= (1550 kg)
4
π
2
(1
.
93
×
10
8
m)
(86400 s)
2
= 1582
.
05 N
.
002
(part 2 of 2) 10 points
What is the mass of this planet?
Correct answer: 5
.
69783
×
10
26
kg.
Explanation:
Using the general gravitation law and Eq.
1, we have
F
=
G
M
satellite
M
planet
r
2
=
M
satellite
4
π
2
r
T
2
G
M
satellite
M
planet
r
2
=
M
satellite
4
π
2
r
T
2
,
so
M
planet
=
4
π
2
G T
2
r
3
=
4
π
2
(6
.
67259
×
10

11
N m
2
/
kg
2
) (86400 s)
2
×
(1
.
93
×
10
8
m)
3
= 5
.
69783
×
10
26
kg
.
003
(part 1 of 3) 10 points
The density of a sphere is given by
ρ
(
r
) =
C
r
.
The sphere has a radius of 4
.
21 m and a mass
of 1011 kg.
Find the constant
C
.
Correct answer: 9
.
07835 kg
/
m
2
.
Explanation:
r
= 4
.
21 m
and
M
= 1011 kg
.
The mass of a differential element of the
sphere is
dm
=
ρ dV
=
C
r
(4
π r
2
dr
)
.
M
=
Z
dm
= 4
π C
Z
r
0
R dR ,
= 4
π C
1
2
R
2
¶ fl
fl
fl
fl
r
0
= 2
π C r
2
= (35
.
4482 m
2
)
π C
C
=
M
(35
.
4482 m
2
)
π
=
1011 kg
(35
.
4482 m
2
)
π
=
9
.
07835 kg
/
m
2
.
004
(part 2 of 3) 10 points
Find the gravitational field 5
.
25 m from the
center of the sphere.
Correct answer: 2
.
44753
×
10

9
N
/
kg.
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 Spring '09
 Turner
 Potential Energy, Correct Answer

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