Robert James Gillin
PHYS 301- Physicists View of Nature
Paper # 1
July 13, 2012
For scientific and philosophical thought to progress, standard measurements and
language must be developed such that kno
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C H A P T E R 1 2 Static Equilibrium and Elasticity
The footprint area of each shoe sole is 14.0 cm2, and
the thickness of each sole is 5.00 mm. Find the horizontal
distance by which the upper and
S E C TI O N 1 3 . 7 Energy Considerations in Planetary and Satellite Motion
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Example 13.6 The Change in Potential Energy
A particle of mass m is displaced through a small vertical distance y near
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C HAPTE R 1 3 Universal Gravitation
v
m
r
This equation shows that E may be positive, negative, or zero, depending on the value
of v. However, for a bound system,8 such as the EarthSun system, E i
S E C TI O N 1 3 . 6 Gravitational Potential Energy
13.6 Gravitational Potential Energy
Radial segment
F
In Chapter 8 we introduced the concept of gravitational potential energy, which is the
energy a
S E C TI O N 1 3 . 5 The Gravitational Field
401
Solving for v and remembering that the distance r from the
center of the Earth to the satellite is r RE h, we obtain
(1)
v
GM E
r
r
GM E
RE h
h
RE
(B)
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C HAPTE R 1 3 Universal Gravitation
(a)
(b)
Figure 13.10 (a) The gravitational eld vectors in the vicinity of a uniform spherical
mass such as the Earth vary in both direction and magnitude. The v
C HAPTE R 1 3 Universal Gravitation
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MP
Sun
Fg
r
v
so much more massive than the planet that the Sun does not move. The gravitational
force acting on the planet is a central force, always along the
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C HAPTE R 1 3 Universal Gravitation
Quick Quiz 13.5
An asteroid is in a highly eccentric elliptical orbit around
the Sun. The period of the asteroids orbit is 90 days. Which of the following state
C HAPTE R 1 3 Universal Gravitation
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13.4 Keplers Laws and the Motion of Planets
People have observed the movements of the planets, stars, and other celestial objects
for thousands of years. In ear
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404
where the negative sign indicates that the force is attractive. Substituting this expression for F(r) into Equation 13.11, we can compute the change in the grav
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L
C HAPTE R 1 3 Universal Gravitation
PITFALL PREVENTION
13.3 You Cant Really
Escape
Although Equation 13.22 provides the escape speed from the
Earth, complete escape from the
Earths gravitational
S E C TI O N 1 3 . 7 Energy Considerations in Planetary and Satellite Motion
407
Example 13.7 Changing the Orbit of a Satellite
The space shuttle releases a 470-kg communications satellite
while in an
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34. (a) What is the minimum speed, relative to the Sun, necessary for a spacecraft to escape the solar system if it starts at
the Earths orbit? (b) Voyager 1 ac
Problems
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white dwarf, (b) the free-fall acceleration, and (c) the gravitational potential energy of a 1.00-kg object at its surface.
M
30. How much work is done by the Moons gravitational eld
as a
Problems
5. Three uniform spheres of mass 2.00 kg, 4.00 kg, and
6.00 kg are placed at the corners of a right triangle as in
Figure P13.5. Calculate the resultant gravitational force on
the 4.00-kg obj
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17. Comet Halley (Figure P13.17) approaches the Sun
to within 0.570 AU, and its orbital period is 75.6 years.
(AU is the symbol for astronomical unit, where
1 A
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C HAPTE R 1 3 Universal Gravitation
would you expect to weigh more at night than during the
day? Note also that you are farther away from the Sun at
night than during the day. Would you expect to
Questions
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Keplers laws of planetary motion state that
1. All planets move in elliptical orbits with the Sun at one focus.
2. The radius vector drawn from the Sun to a planet sweeps out equal areas
C HAPTE R 1 3 Universal Gravitation
H. Ford et al. & NASA
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Figure 13.19 Hubble Space Telescope images of the galaxy M87. The inset shows the
center of the galaxy. The wider view shows a jet of mate
S E C TI O N 1 3 . 7 Energy Considerations in Planetary and Satellite Motion
409
Black Holes
In Example 11.7 we briey described a rare event called a supernovathe catastrophic
explosion of a very mass
S E C TI O N 1 3 . 4 Keplers Laws and the Motion of Planets
Table 13.2
Useful Planetary Data
Body
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Moon
Sun
Mass (kg)
1023
3.18
4.88 1024
5
S E C TI O N 1 3 . 3 Free-Fall Acceleration and the Gravitational Force
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Quick Quiz 13.3
Superman stands on top of a very tall mountain and
throws a baseball horizontally with a speed such that the
S E C TI O N 1 3 . 4 Keplers Laws and the Motion of Planets
L
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PITFALL PREVENTION
13.2 Where is the Sun?
Sun
The Sun is located at one focus
of the elliptical orbit of a planet.
It is not located a
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C H A P T E R 1 2 Static Equilibrium and Elasticity
14. A uniform ladder of length L and mass m1 rests against a
frictionless wall. The ladder makes an angle with the horizontal. (a) Find the hori
Problems
41. A uniform pole is propped between the oor and the ceiling of a room. The height of the room is 7.80 ft, and the
coefcient of static friction between the pole and the ceiling is 0.576. The
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C H A P T E R 1 2 Static Equilibrium and Elasticity
PROBLEMS
1, 2, 3 = straightforward, intermediate, challenging
= full solution available in the Student Solutions Manual and Study Guide
= coache
Problems
long, and is solid. The runway is cut such that it forms a
parabola with the equation y (x 3)2/9. Locate the horizontal coordinate of the center of gravity of this track.
7.
10. A mobile is c
Problems
The handles make an angle of 15.0 below the horizontal. A downward force of 400 N is exerted on the wheel,
which has a radius of 20.0 cm. (a) What force must
Stephen apply along the handles i
S E C T I O N 1 2 . 4 Questions
S U M MARY
A rigid object is in equilibrium if and only if the resultant external force acting on it is
zero and the resultant external torque on it is zero about any a