Download rEVIEW CHAPTER 6

CHAPTER
6
Review
K/U
Knowledge/Understanding Knowledge
For each question, select the best answer from the four
alternatives.
1. Which of the following best describes the strength of the
gravitational force on Earth due to your mass? (6.1) K/U
(a) It is zero as long as you are standing on Earth’s
surface.
(b) It is much greater than Earth’s gravitational force
on you because Earth’s mass is so great.
(c) It is equal to the magnitude of the force that
Earth exerts on you.
(d) It is negligible compared to the force of gravity
on you because your mass is so small when
compared to Earth’s mass.
2. The gravitational force on a small rock sitting on
a 20 m–high cliff on Earth is Fg. How does the
gravitational force on the rock change if a hiker picks up the rock and carries it to a 200 m–high cliff? (6.1) K/U
(a) It will decrease by an insignificant amount.
(b) It will decrease by about one-tenth.
(c) It will decrease by about one-fourth.
(d) It will decrease by about one-half.
3. What major obstacle did Henry Cavendish face when
measuring the gravitational force between two objects
on Earth? (6.1) K/U
(a) The masses required had to be very small.
(b) The gravitational force between the two masses
was very small.
(c) The distance between the two masses had to be
extremely large.
(d) The gravitational force between the two masses
was extremely large.
4. Ball A, with mass m, is a distance d from ball B,
which has a mass of 3m. At which of the following
distances is the gravitational attraction of the balls on
each other equal? (6.1) K/U
d
(a)
9
d
(b)
3
2d
(c)
3
(d) any separation distance
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T/I
Thinking/Investigation C
Communication A
Application
5. Spherical planet A has mass m and radius r. Spherical
m
planet B has mass and radius 2r. How does the
2
gravitational field strength at the surface of planet B
compare to the gravitational field strength at the surface
of planet A? (6.1) K/U
(a) It is the same as planet A.
(b) It is twice that of planet A.
(c) It is half that of planet A.
(d) It is one-eighth that of planet A.
6. Two satellites are orbiting a planet at the same height
above its surface. The mass of satellite A is m, and the
mass of satellite B is 2m. What can you conclude about
the planet’s gravitational force on the satellites? (6.2) K/U
(a) The planet’s gravitational force on both satellites
is the same.
(b) The planet’s gravitational force on satellite B is
half the gravitational force on satellite A.
(c) The planet’s gravitational force on satellite B is
twice the gravitational force on satellite A.
(d) The planet’s gravitational force on satellite B is
four times the gravitational force on satellite A.
7. How does a planet’s gravity help keep a satellite in a
circular orbit? (6.2) K/U
(a) It pulls the satellite in the same direction as its
motion.
(b) It pulls the satellite at an angle of 30° to its
direction of motion.
(c) It pulls the satellite at an angle of 60° to its
direction of motion.
(d) It pulls the satellite at an angle of 90° to its
direction of motion.
8. To pinpoint the location of your vehicle within 15 m
using a Global Positioning System (GPS), how many
satellites’ signals must interact? (6.2) K/U
(a) 1
(b) 2
(c) 3
(d) 4
9. Which of the following conditions are necessary to
place a satellite in geosynchronous orbit? (6.2) K/U
(a) a varying orbital velocity so that it maintains a
constant position
(b) a varying orbital radius so that it maintains a
constant height above Earth
(c) a constant period that is equal to the orbital
speed of Earth about the Sun
(d) a constant period that matches the revolution rate
of Earth about its axis
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10. The period of a satellite is independent of
(a) its own mass
(b) the mass of the planet it orbits
(c) the value of the gravitational constant
(d) the orbital radius (6.2) K/U
Indicate whether each statement is true or false. If you think
the statement is false, rewrite it to make it true.
11. The gravitational constant, G, near the Moon is
different than G near Earth. (6.1) K/U
12. The gravitational field around Earth at a fixed
distance from its centre would be the same if Earth
had half the radius but the same mass. (6.1) K/U
13. A book is surrounded by its own gravitational field.
(6.1) K/U
14. Unlike most satellites, a geosynchronous satellite has
a fixed position and does not orbit Earth. (6.2) K/U
15. In order for a satellite to stay in a uniform circular
orbit, its speed must be constant. (6.2) K/U
16. The velocity of a satellite in uniform circular motion
depends on the satellite’s mass. (6.2) K/U
17. Satellites are useful for communication, astronomical
observations, and atmospheric studies. (6.3) K/U
18. According to the theory of general relativity, gravity has
no effect on light because light has no mass. (6.4) K/U
19. Gravitational lensing occurs when the gravitational
field changes the direction of motion of a massive
object. (6.4) T/I
Match each term on the left with the most appropriate
description on the right.
20. (a) satellite
(b) artificial
satellite
(c) space station
(i) a spacecraft in which people
live and work
(ii) an object or body that revolves
around another body
(iii) an object that has been
intentionally placed by humans
into orbit around Earth or
another body (6.2) K/U
Understanding
21. The gravitational force is inversely proportional to
1
the square of the separation of two masses: Fg ~ 2 .
r
Earth’s gravitational pull on an object is defined as the
object’s weight. Explain why the weight of any object
on Earth is not infinite, even though the distance
between the object and Earth is zero. (6.1) T/I A
22. An Internet site states that the value of g on Earth is
9.806 65 N/kg. Is this figure accurate for all places on
Earth? Why or why not? (6.1) K/U T/I C
23. Relate the universal law of gravitation to Newton’s
third law of motion. (6.1) K/U C
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24. Henry Cavendish conducted experiments to measure
the force of gravity between two objects on Earth. In a
short paragraph, summarize Cavendish’s experimental
setup and results. (6.1) K/U C
25. Explain why you do not feel the gravitational force
between you and a car 5 m away, even though a car’s
mass is so great that you cannot lift it. (6.1) T/I
26. Every object is surrounded by a gravitational field.
(6.1) K/U C
(a) The unit of the gravitational field strength g is
newtons per kilogram (N/kg). Explain how the
unit of gravitational field strength relates to the
unit of force.
(b) How does g vary with distance? How does it vary
with the object’s mass?
(c) Describe the direction of the gravitational field
around a spherical object.
27. The universal law of gravitation describes the force of
gravity between two bodies. What does it say about
the strength of the gravitational field? How does the
size of the object affect the use of the gravitational
force equation? (6.1) K/U
28. Rank the following from least to greatest gravitational
attraction on you. (6.1) T/I
(a) a mass of 4m a distance of 2d away
(b) a mass of 6m a distance of 5d away
(c) a mass of 2m a distance of 3d away
(d) a mass of m a distance of 2d away
29. A 68 kg spherical boulder is sitting 1.5 m from a 27 kg spherical rock. What is the gravitational force
between the boulder and the rock? (6.1) K/U
30. A traffic officer is standing 4.5 m from a 1200 kg
pickup truck. The gravitational force between the
officer and the truck is 1.7 3 10–7 N. What is the
officer’s mass? (6.1) T/I A
31. In 2005, the space probe Deep Impact launched a
370 kg projectile into Comet Tempel 1. Observing
the collision helped scientists learn about the comet’s
characteristics. The comet is estimated to have a mass
of about 9.0 3 1013 kg. (6.1) K/U T/I
(a) Assuming the estimated mass of the comet at
that time was correct, at what distance from the
comet’s centre was the gravitational force between
the comet and the projectile 32 N?
(b) What was the magnitude of the gravitational
force between the comet and the projectile at a
distance of 350 m?
(c) Deep Impact also released a probe to fly by
the comet and record images of the collision.
Determine the strength of the comet’s
gravitational field at the probe’s distance of 5.0 3 103 km from the comet.
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32. Which is a more important factor in order for a
satellite to remain in orbit at a certain distance above
Earth’s surface: the speed or the mass of the satellite?
Explain your answer. (6.2) T/I A
33. Two identical satellites are orbiting different planets at
the same orbital radius, but one planet has twice the
mass of the other planet. How do the satellite’s orbital
speeds compare with each other? (6.2) K/U T/I
34. Two identical satellites are orbiting different planets
at the same orbital radius, but one satellite’s orbital
speed is twice as fast as the other’s. What can you
conclude about the masses of the planets the satellites
are orbiting? (6.2) K/U T/I A
35. The RADARSAT-1 and RADARSAT-2 satellites were
placed in orbit at an altitude of approximately 800 km
and have a mass of about 2750 kg each. RADARSAT
Constellation satellites orbit at approximately 600 km
and have masses of about 1300 kg. (6.3) K/U A
(a) Which set of satellites has greater speeds?
(b) What effect does the mass have on the speeds?
36. Why is the concept of dark matter sometimes referred
to as the missing mass problem? (6.4) K/U C
40. Henry Cavendish used freely moving balls to
measure the gravitational force between two masses
on Earth’s surface. Suppose a scientist repeated the measurement using masses m1 5 0.032 kg
and m2 5 5500 kg. What is the gravitational force
between the masses when the distance between their
centres is r 5 0.75 m? (6.1) T/I
41. Calculate the strength of the gravitational field of a
6520 kg elephant at a distance of 5.75 m. (6.1) T/I
42. The world’s largest ball of twine was made by one
man in Minnesota in the United States. A basketball
sitting 55.0 m (measured from centre to centre) from
the ball of twine would experience a gravitational
field of 1.74 3 10–10 N/kg from the ball of twine.
Calculate the ball of twine’s mass. (6.1) T/I
43. The highest peak in Canada is Mount Logan
(Figure 2), which has an altitude of 5959 m above
sea level. Assume that sea level defines the height of
Earth’s surface. (6.1) T/I
Analysis and Application
37. Three balls are sitting on the ground, as shown in
Figure 1. The centre of each ball is an equal distance
from you. Ball A has mass m and radius r. Ball B has
mass 2m and radius r. Ball C has mass m and radius
2r. Compare the gravitational force of each ball on
you. Explain your answer. (6.1) T/I A
2m
Figure 2
B
m
A
C
m
Figure 1
38. Two people are standing 1.0 m apart (centre to
centre). Assume that each person has a mass of 45 kg. Calculate the gravitational force between the
two people. (6.1) T/I
39. Two small balls of mass 22 kg and 25 kg are a
distance of 1.2 m apart. (6.1) T/I
(a) Calculate the gravitational force between the
balls.
(b) How far apart would two balls of mass 16 kg and
21 kg have to be to have this same gravitational
force between them?
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(a) Calculate the strength of Earth’s gravitational field
at the altitude of Mount Logan.
(b) What is the ratio of the strength of Earth’s
gravitational field at the top of Mount Logan to
the strength at Earth’s surface?
44. Neptune, the most distant planet in our solar system,
is at an average distance of 4.5 3 109 km from the
Sun. Its mass is 1.03 3 1026 kg. (6.1) T/I A
(a) Calculate the strength of the Sun’s gravitational
field at Neptune’s location.
(b) Calculate the strength of Neptune’s gravitational
field at the Sun’s location.
(c) Calculate the gravitational force between the Sun
and Neptune.
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45. The gravitational force due to the Sun on the planets
in our solar system decreases as the planetary
distance from the Sun increases. In your notebook,
draw a larger version of Figure 3, and complete it
for the force of gravity on an imaginary Earth–mass
planet if its distance were between the Sun’s radius, rS, and 100rS. (6.1) K/U T/I C
Fg
on planet
(N)
Sun
rS
rS
50rS 100rS
Distance from the
centre of the Sun
Figure 3
46. How does the weight of a Mars lander change as it
travels from Earth to Mars? Does the weight ever
equal zero? Does the mass of the lander change?
Explain your answers. (6.1) K/U T/I C
47. Ceres is a dwarf planet located in the asteroid belt
between the orbits of Mars and Jupiter. The radius of
Ceres is 4.76 3 105 m. Suppose an astronaut stands
on the surface of Ceres and drops a 0.85 kg hammer
from a height of 1.25 m. The hammer takes 3.0 s to
reach the ground. (6.1) T/I A
(a) Determine the gravitational field strength of
Ceres at this height.
(b) Calculate the mass of Ceres.
(c) Determine the gravitational field strength of
Ceres at an altitude of 150 km above its surface.
48. Three balls of mass m1 5 13 kg, m2 5 17 kg, and
m3 5 12 kg are arranged in a straight line. Mass m1
is in the middle, 6 m from both mass m2 and mass
m3. Calculate the total gravitational force exerted by
balls 2 and 3 on ball 1. State both the magnitude and
the direction of the force in your answer. (6.1) T/I
49. Titan, one of the moons of Saturn, has a radius of 2.57 3 106 m and a mass of 1.35 3 1023 kg.
(6.1) T/I A
(a) Determine the gravitational field strength on the
surface of Titan.
(b) What is the ratio of Titan’s gravitational field
strength at its surface to the gravitational field
strength on the surface of Earth?
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50. The International Space Station (ISS) orbits Earth at a
height of approximately 375 km. (6.1) T/I A
(a) Calculate the gravitational field strength on the ISS.
(b) Are astronauts truly weightless?
(c) Why do astronauts and other objects on the ISS appear to float?
51. Consider what you have learned about the inversesquare law. Would it be possible for the force of
gravity between two very heavy supertankers to cause
them to float toward each other and collide? Explain
your reasoning. (6.1) T/I C A
52. A satellite in orbit above Earth’s equator is travelling
at an orbital speed of 7.45 km/s. (6.2) T/I
(a) Determine the altitude of the satellite.
(b) Determine the satellite’s period.
53. Saturn rotates once in 645 min (just under 11 h) and
has a mass of 5.69 3 1026 kg. Suppose that scientists
have placed a satellite in orbit around Saturn that has
the same period as Saturn. (6.2) T/I C
(a) Calculate the radius at which the satellite must
orbit.
(b) In a few sentences, compare this radius to Saturn’s
equatorial radius of 6.03 3 107 m, and compare
the ratio of these two numbers to the same ratio
for a satellite in geostationary orbit (around Earth).
54. Neptune has an orbital radius from the Sun of 4.5 3 109 km. (6.2) T/I A
(a) Assume the orbit is circular. Calculate the orbital
speed of Neptune. Express your answer in metres
per second and in kilometres per hour.
(b) Calculate Neptune’s orbital period in Earth years.
55. Two satellites are placed in their desired orbit by
releasing them from the International Space Station
using the Canadarm2. Satellite A is released to an
orbital radius of r. Satellite B is released to an orbital
9
radius of
r. How does the velocity of satellite B
10
compare to the velocity of satellite A? (6.2) K/U T/I
56. The microsatellite MOST (Microvariability and
Oscillations of STars) has a mass of just 52 kg. It travels in an almost circular orbit at an average
altitude of 820 km above Earth’s surface. (6.2) T/I A
(a) Calculate the gravitational force between Earth
and the MOST satellite at this altitude.
(b) What speed does the MOST satellite need to
maintain its altitude? Express the speed in metres
per second and in kilometres per hour.
(c) Determine the orbital period of MOST.
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57. Determine the ratio of the speed of a satellite in orbit
around Earth to the speed of a similar satellite in orbit
around the Moon, assuming the satellites have equal
orbital radii. The Moon’s mass is 1.23 % of Earth’s mass
and its radius is 27.2 % of Earth’s radius. (6.2) T/I A
58. A space vehicle is in circular orbit at a height of 390 km above Earth’s surface. Explain how the
orbital speed of the vehicle would have to change in order for its altitude above Earth to decrease by 75 km. (6.2) T/I
59. The Canadian Telesat communications satellite Anik
F2 has a mass of 5900 kg and orbits 35 000 km above
the equator. (6.2, 6.3) T/I A
(a) Determine the gravitational field of Earth at this
altitude.
(b) Determine the gravitational force between the
satellite and Earth.
(c) Calculate the speed needed by Anik F2 to
maintain its orbit. Express the speed in metres
per second and in kilometres per hour.
(d) Calculate the orbital period of Anik F2.
60. The black hole at the centre of the Milky Way galaxy
is called Sagittarius A* (Figure 4). Determining its
mass is difficult, but a typical value calculated for the
mass is 4.3 3 106 times the mass of the Sun. The mass
of the Sun is 1.99 3 1030 kg. (6.4) T/I
Figure 4
(a) If this value for the mass of Sagittarius A* is correct,
how would the black hole’s gravitational force on a
1 kg object compare with the gravitational force on
a 1 kg object the same distance from the Sun?
(b) Suppose an 8.5 kg space probe is a distance of
4.5 3 1012 m from the black hole’s centre. (This
is about the distance from Neptune to the Sun.)
What gravitational force does the black hole exert
on the probe?
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Evaluation
61. A magazine article claims that people are influenced
by the movement of the planets. Use the following
steps to evaluate this claim. (6.1) T/I A
(a) The planet closest to Earth is Venus. It has a mass
of 4.85 3 1024 kg, and its distance to Earth is
1.5 3 1010 m. Calculate the gravitational force
of Venus on an 85 kg person.
(b) Calculate the gravitational pull on an 85 kg
person by a 10 000 kg school bus a distance of 0.5 m away.
(c) What is the ratio of the gravitational pull of the
bus to the gravitational pull of Venus?
(d) Interpret your findings.
62. Isaac Newton developed the equation for universal
gravitation several decades before Henry Cavendish
did his experiment. It was not until he did his
experiment that calculations using Newton’s equation
could produce data from observations. Cavendish’s experiment yielded a value for G that is slightly higher
than today’s accepted value of 6.67 3 10211N # m2/kg 2.
Some more recent measurements have shown the
value to be 6.69 3 10211N # m2/kg2. What would
be the effect of changing the value of the constant?
(6.1) T/I A
63. In 1970, a NASA spacecraft called Apollo 13
experienced an explosion which crippled the
spacecraft. Engineers and scientists evaluated whether they should turn the spacecraft around
immediately and use rockets to get the astronauts
aboard the spacecraft home or use the Moon’s
gravitational field to get back. They opted for the
use of the Moon’s gravitational field. Suggest some
reasons for this decision. (6.2) T/I A
64. A satellite is in orbit with velocity v at a distance d
above Earth’s surface. A student says that the satellite’s
velocity would not change if it were in orbit at the
same distance d around a planet with twice the mass
and twice the radius. (6.2) T/I C A
Gm
to determine
Å r
whether or not the student is correct.
(b) Would the satellite’s velocity around the more
massive planet be higher or lower? Defend your
answer.
(a) Use the equation v 5
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65. Earth’s orbit around the Sun is almost but not quite
circular. We can approximate, however, a small piece
of the orbit as though it is part of a perfectly circular
orbit of the same radius. Earth’s orbital speed is
slightly greater during the winter in the northern
hemisphere than during the summer in the northern
hemisphere. (6.2) K/U T/I C A
(a) In which season, winter or summer, is Earth
closest to the Sun?
(b) Does your answer to (a) explain why summer in
the northern hemisphere is so much warmer than
in the winter? Why or why not?
66. Consider a specific type of artificial satellite and
assess the impact of that satellite technology on
society or the environment. (6.3) T/I C A
67. Canada first used satellites in the early 1960s for
atmospheric observations. In the 1970s, however, the
use shifted to communications satellites. Satellites are
also used in Canada for weather and environmental
observations. Make a poster explaining the ways
that satellites affect your everyday life. Evaluate how
your life would be different without this type of
technology. (6.3) T/I C A
68. Communication satellites have made talking
anywhere in the world on a cellphone possible. These
communication satellites are difficult to service if
anything goes wrong. If a satellite has stopped working
completely, it is often left up in space to orbit. As more
and more satellites end up in orbit, they will create
clutter and possibly space junk. How will this clutter
affect future space travel? (6.3) T/I A
Reflect on Your Learning
69. When studying this chapter, you first read about
universal gravitation and then about gravitational
fields. Write a short paragraph explaining why it
was helpful to learn about these topics in this order
instead of the reverse order. T/I C
70. Look back at the diagrams and images in this chapter.
Create a slide show presentation that shows how they
helped you understand universal gravitation and
orbits. Be sure to include specific examples in your
presentation. T/I C
71. Consider the different topics you have studied in this
chapter. Choose one that you feel has an important
impact on your life. Formulate your thoughts on paper
and then express your thoughts to a parent or sibling,
explaining about the topic and why it is important
to you. What else would you like to know about this
topic? How could you go about learning this? T/I C
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Research
WEB LINK
72. View some actual radar images of Earth. Choose a
current meteorological or environmental event, explore
the information available on the Internet, and then report
your findings in the form of a brief news release. T/I C
73. Application of gravitational concepts has enabled
great advancements in astronomical research and
understanding. Gravity explains how stars are bound
together in galaxies, how galaxies are bound together
in groups, and how groups of stars and galaxies are
bound together in clusters. Knowledge of gravity
helps scientists develop theories about black holes and
dark matter. Research and prepare a report, two pages
or longer, about how the application of gravitational
concepts has helped astronomers. T/I C
74. The Lagrange points, labelled numerically as shown
in Figure 5, are positions in space where satellites can
be placed in stationary orbits relative to two larger
objects, such as Earth and the Sun. Research Lagrange
points. T/I C A
4
2
1
3
5
Figure 5
(a) In an email to a peer, explain why there are five
Lagrange points in the Earth–Sun system.
(b) What do the designations 1, 2, and so on, mean?
(c) How do scientists use these points when choosing
the placement of satellites in orbits?
(d) What satellites are currently in orbit at different
Lagrange points and why?
75. A geostationary satellite is a geosynchronous satellite in orbit directly above the equator. In a
few sentences, describe why a satellite must orbit
above the equator to be geostationary and not just
geosynchronous. K/U T/I
76. Technology now allows researchers to map Earth’s
gravitational field and to use the map to study the
material making up Earth’s interior. Research gravity
surveys and how gravitational fields are used to
search for mineral deposits. C A
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