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 knowledge can be acquired and transmitted, however,
there
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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 lower surfaces of each
sole are offset. The shear modu
S E C TI O N 1 3 . 7 Energy Considerations in Planetary and Satellite Motion
405
Example 13.6 The Change in Potential Energy
A particle of mass m is displaced through a small vertical distance y near the Earths surface. Show that in this situation
the gen
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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 is necessarily less
than zero because we have chosen the
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 associated with the conguration of a system of objects i
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) If the satellite is to be geosynchronous (that is, appe
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(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 vectors point in the
direction of the acceleration a par
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398
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 radius vector, directed
toward the Sun (Fig. 13.7a). T
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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 statements
is true about the possibility of a collision betw
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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 early history, scientists regarded the Earth as the center
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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 gravitational potential energy function:
Uf Ui GM E m
Uf Ui
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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 inuence is
impossible because the gravitational force
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 orbit 280 km above the surface of the Earth.
A rocket
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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 achieved a maximum speed
of 125 000 km/h on its way to ph
Problems
415
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 1 000-kg meteor comes in from outer space and impacts
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 object, assuming the spheres are isolated from
the rest of
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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 AU 1.50 1011 m is the mean EarthSun distance.)
How far f
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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 weigh less?
3. Use Keplers second law to convince yours
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 in equal
time intervals.
3. The square of the orbital
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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 material moving away from the
center of the galaxy toward t
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 massive star. The material that remains in the central core
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
5.98 1024
6.42 1023
1.90 1027
5.68 1026
8.68 1025
1.03 1
S E C TI O N 1 3 . 3 Free-Fall Acceleration and the Gravitational Force
395
Quick Quiz 13.3
Superman stands on top of a very tall mountain and
throws a baseball horizontally with a speed such that the baseball goes into a circular
orbit around the Earth.
S E C TI O N 1 3 . 4 Keplers Laws and the Motion of Planets
L
397
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 at the center of
the ellipse.
Center
Orbit
of Pluto
(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 horizontal and vertical forces the
ground exerts on the bas
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 coefcient of static friction between the
pole and 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
= coached solution with hints available at http:/www.pse6.com
=
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 constructed of light rods, light strings, and
beach souv
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 in order to just start the
wheel over the brick? (b) Wha
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 axis:
F 0
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