Download Ch 6.2 and 7 study guide-Circular Motion and Gravitation

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6
c. If the plane is traveling with a horizontal speed of 483 km/h when the capsule is released, what
is the horizontal distance between the point at which the capsule is released and the point at
which the capsule strikes the ground? Draw a diagram to help you answer the question.
Section 6.2
Uniform Circular Motion
In your textbook, read about uniform circular motion on page 153.
Answer the following questions. Use complete sentences.
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1. What are the two conditions necessary for an object to be in uniform circular motion?
2. Why is a particle in uniform circular motion not moving at a constant velocity?
3. Use Newton’s laws to explain how you know that an object in uniform circular motion must be
experiencing a force.
4. Use Newton’s laws to explain how you know that an object in uniform circular motion is being
accelerated.
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5. An object in uniform circular motion is at position r 1 at the beginning of a time interval and position r 2 at the end of the time interval. Write an algebraic expression that describes the object’s
average velocity during this time interval. You may want to draw a diagram to help you answer the
question.
6. The object described in the Question 5 has a velocity vector v1 at the beginning of the time interval
and v2 at the end of the time interval. Write an algebraic expression that describes the object’s
average acceleration during this time interval.
In your textbook, read about uniform circular motion on page 153.
Answer the following questions. Use complete sentences.
7. For each situation below, what provides the force that causes centripetal acceleration? You may
want to draw a diagram to help you answer some of the questions.
a. a ball on a string swinging in a circle in uniform circular motion
c. a car driving in a circle in uniform circular motion
d. a person on a carnival ride that has hanging baskets that are whirled around horizontally in
uniform circular motion
8. What is the relationship between the centripetal acceleration of an object in uniform circular
motion and the object’s velocity?
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b. a satellite moving around Earth in uniform circular motion
Date
Period
Name
CHAPTER
7
Study Guide
Gravitation
Vocabulary Review
Write the term that correctly completes the statement. Use each term once.
Kepler’s second law
gravitational mass
Newton’s law of universal gravitation
inertial mass
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
gravitational field
1.
describes the amount of resistance an object has to any application
of force.
2.
states that an imaginary line line drawn between a planet and the
Sun sweeps out equal areas in equal time periods.
3.
If the
of an object is increased, the gravitational force it
experiences will increase as a result.
4.
The region around Earth in which objects experience a force due to
Earth’s gravity is called the
.
5.
suggests that objects attract other objects with a force that is
proportional to the product of their masses and inversely proportional to the square of the distance between them.
Section 7.1
Planetary Motion and Gravitation
In your textbook, read about planetary motion, Kepler’s laws and Newton’s law of universal gravitation
on pages 171–176.
Match the name of the scientist with the correct contribution. Each name may be used more than once.
Nicholas Copernicus
Johannes Kepler
Tycho Brahe
Isaac Newton
1.
was the first astronomer to propose that the Sun is the center of
the solar system.
2.
believed that all planets except Earth orbit the Sun.
3.
used huge instruments he built himself to record the exact
positions of the planets and stars.
4.
used 30 years worth of observations made by other scientists and
concluded that the planets orbit the Sun.
5.
proposed that the force exerted on a planet by the Sun is inversely
proportional to the distance between centers of the planet and the
Sun.
Physics: Principles and Problems
Chapters 6–10 Resources
45
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Study Guide
continued
6.
discovered that the shape of a planet’s orbit is an ellipse.
7.
was the first to theorize that the force that makes objects fall to
Earth is the same force that the Sun exerts on the planets.
8.
used geometry and mathematics to discover his three laws of
planetary motion.
Write first, second, or third in the blanks to indicate which of Kepler’s laws the statement is describing.
9. relates the motion of more than one object about a single body
10. describes the shape of the planets’ orbits
11. states that the Sun is located at one focus of a planet’s orbit
12.
TA 2
r 3
A
TB
rB
13. states that an imaginary line drawn from a planet to the Sun will sweep out equal
areas in equal time intervals
In your textbook, read about Kepler’s laws and Newton’s law of universal gravitation on pages 172–176.
Refer to the diagram to answer questions 14–18.
Planet A
t1
Sun
1
3
t2
t3 t
4
Planet B
14. The shaded portions of Planet A’s orbit represent the area swept out by an imaginary line between
the Sun and the planet between times t1 and t2 and between times t3 and t4. If the area of these
shaded regions is equal, what must be true about the time intervals t2 t1 and t4 t3?
15. If you know the period of both Planets A and B, what other information would you need to
determine Planet A’s average distance from the Sun?
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2
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7
16. The gravitational field of the Sun exerts a force on Planet B. At which point on the orbit of Planet
B is this force at its least? At which point is it greatest?
17. At point 3, Planet B is six times further from the Sun than it is at point 1. If the magnitude of
the force exerted on Planet B by the gravitational field of the Sun at point 1 is F, what is the
magnitude of the force at point 3?
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18. If the period of Planet A is TA and the period of Planet B is TB and Planet A’s average distance from
the Sun is rA, write a formula that represents rB, Planet B’s average distance from the Sun.
In your textbook, read about universal gravitation on pages 176–178.
Fill in the chart with the correct values of F for each change in the system described in questions 19–23.
The magnitude of the gravitational force between two masses, P and Q, is F.
Change in System
New Magnitude of Force
19. The mass of P is doubled.
20. The distance between the masses is doubled.
21. The mass of P is doubled and the mass of Q
is tripled.
22. The entire mass of the system is increased by
a factor of four.
23. The distance between the masses is halved.
Physics: Principles and Problems
Chapters 6–10 Resources
47
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Study Guide
7
continued
Answer the following questions. Use complete sentences or show your calculations.
24. Given the value of pi and the universal gravitational constant, what other information would you
need to calculate the period of a planet orbiting the Sun?
25. Describe the balance Cavendish used to find an experimental value for the universal gravitational
constant.
26. What is the gravitational force between two 1.00-kg masses that are placed 1.00 m apart? What is
another name for this number?
Using the Law of Universal Gravitation
In your textbook, read about the orbits of planets and satellites on pages 179–180.
Write the term that correctly completes the statement.
1. The motion of a projectile has both
and
components.
2. A projectile fired horizontally will accelerate toward Earth at a rate of
.
3. If the magnitude of the
component of a projectile’s motion is great
enough, the projectile will fall to Earth at the same rate that Earth curves away from the projectile.
4. A projectile fired horizontally from less than 150 km above the surface of Earth will fall back to
Earth no matter how fast it is traveling because of
.
5. An object that falls to Earth at the same rate that Earth curves away from the object is said to be in
.
48 Chapters 6–10 Resources
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Section 7.2
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Study Guide
continued
7
In your textbook, read about the motion of satellites and acceleration due to gravity on pages 180–182.
For each statement below, write true or rewrite the italicized part to make the statement true.
6. The speed of a satellite orbiting Earth depends only on the mass of Earth and the
mass of the satellite.
7. The equations of motion are different for objects in orbit around Earth and for
planets orbiting the Sun.
8. Orbital speed and period are independent of the mass of the satellite.
9. If the radius of Earth were changed but the mass remained the same, acceleration
due to gravity would not change.
10. As you move farther away from Earth’s center, acceleration due to gravity changes
according to a direct relationship.
11. Even though astronauts on the space shuttle appear to be weightless, Earth’s
gravitational force on the space shuttle is not zero.
In your textbook, read about the gravitational field, inertial mass, and gravitational mass on
pages 182–184.
Answer the following questions. Use complete sentences.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12. What units are used to measure the strength of gravitational fields?
13. In which direction does the force of Earth’s gravitational field always act?
14. Describe the difference between gravitational and inertial mass.
15. Does the inertial mass depend on the distance between objects? Explain.
Physics: Principles and Problems
Chapters 6–10 Resources
49
Name
7
Study Guide
continued
Read about Einstein and his general theory of relativity on pages 184–185.
For each description on the left, write the letter of the matching term on the right.
16. the effect of mass on space
a. gravitational field
17. effect of gravity on light
b. general theory of
relativity
c. curvature
18. Einstein thought gravity was a(n)
d. effect of space
e. deflection
19. an object so dense that light leaving the object is bent
back on itself
f.
black hole
20. predicts the effects of gravity
21. allows us to picture gravity acting at a distance
Complete each statement by writing the correct term in the blank provided.
22. Newton’s law of universal gravitation allows us to calculate the
force that exists between two bodies because of their mass.
, but rather an effect of
itself.
24. According to Einstein, the mass of a body changes the
25.
around it.
causes space to be curved, and other bodies are accelerated because
of the way they follow this curved space.
26. According to Einstein’s theory of
enough, any light it emits is actually bent back to the object.
50 Chapters 6–10 Resources
, if an object is massive and dense
Physics: Principles and Problems
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23. Einstein proposed that gravity is not a
Date
Period
Name
CHAPTER
7
Section 7-1 Quiz
Planetary Motion and Gravitation
1. Write Kepler’s laws next to their respective numbers below.
1st
2nd
3rd
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. Mercury is 57.9106 km from the Sun. Venus is 108.2106 km from the Sun. If Venus has a
period of 224.7 Earth days, how many Earth days does it take Mercury to make one trip around
the Sun?
3. The Sun has a mass of 1.991030 kg. The planet Neptune has a mass of 1.031026 kg and is
4.501012 m from the Sun. Calculate the gravitational force between the Sun and Neptune.
4. Describe the process and equipment Cavendish used to establish an experimental value for the
universal gravitational constant.
Physics: Principles and Problems
Chapters 6–10 Resources
51
Date
Period
Name
CHAPTER
7
Section 7-2 Quiz
Using the Law of Universal Gravitation
1. Explain the conditions necessary for an object to attain and then stay in orbit around Earth.
2. What are the orbital speed (in m/s) and period (in seconds) of a satellite orbiting 350 km above
the surface of Earth? Earth has a mass of 5.981024 kg and a radius of 6.38106 m.
4. Briefly explain how Einstein’s general theory of relativity accounts for gravity, both its causes and
effects. In your answer, include an explanation of how the general theory of relativity differs from
Newton’s law of universal gravitation.
52 Chapters 6–10 Resources
Physics: Principles and Problems
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3. A satellite orbits Earth 270 km above Earth’s surface. Calculate the acceleration due to gravity at
this altitude.
Answer Key
Chapter 6 continued
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Section 6-2
Uniform Circular Motion
1. The object must be moving in a circle with a
fixed radius and the object must be moving
at a constant speed.
2. While speed is a directionless quantity,
velocity is a vector and therefore any change
in direction indicates a change in velocity.
3. Newton’s first law states that a body moving
at a constant velocity will continue moving
at a constant velocity unless a force acts on
that body. Since an object in uniform circular motion has a changing velocity, it must
be experiencing a force.
4. Newton’s second law states that when a
force acts on a mass, that force causes acceleration along the same axis that the force is
applied. As shown in Question 3, an object
in uniform circular motion must be experiencing a force since is has a changing velocity.
Therefore, that force must be causing the
object to accelerate along the same axis as
the force.
r2 r1
r
5. v or v t
t2 t1
v2 v1
v
6. a or a t
t2 t1
7. a. the string
b. the force of gravity
c. the force of friction between the tires
and the pavement
d. the chain on which the basket hangs
8. The centripetal acceleration is directly proportional to the square of the velocity.
9. The centripetal acceleration is inversely proportional to the radius of rotation.
1
10. 2
11. 4
12. 2
Physics: Principles and Problems
Section 6-3
Relative Velocity
1. a. 3 m/s
b. 2 m/s
c. 5 m/s
2. a. 3 m/s
b. 2 m/s
c. 1 m/s
3. north
4. a. southwest
b.
vboat/water
N
vJohn/boat
vJohn/water
Section 6-1 Quiz
1. Newton’s second law states that when a
force is applied to an object, the object will
accelerate along the same axis that the force
is applied. Assuming that air resistance is
negligible, no forces act on a projectile along
the horizontal axis and therefore the object
has no horizontal component to its acceleration other than the initial force.
2. The force of gravity acts along the vertical
axis of a projectile’s flight. This force is constant and thus the acceleration the projectile
experiences along the vertical axis is constant and is equal to the acceleration due to
gravity.
3. a. d vt
d
235 m
v 5.0 m/s
t
47 s
b. As the projectile travels up and then
down again, it reaches its maximum
height at the midway point of its path,
47 s
t 24 s
2
1
1
yf at2 (9.80 m/s2)(24 s)2
2
2
2800 m
Chapters 6–10 Resources
179
Answer Key
Chapter 7 continued
Analyze
1. See Data Table.
2. See Data Table.
3. See Data Table. Sample Calculation for
Pluto: e 4/16 0.25
4. See Data Table.
5. Both foci are at the center.
6. It is very close to being a circle.
7. The comet. It looks more flattened out then
the other orbits.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Conclude and Apply
1. Yes, the planets and comet travel in elliptical
orbits.
2. Since the eccentricity of Earth is so small,
Kepler might not have concluded that planets have elliptical orbits.
3. It travels fastest at perihelion. According to
Kepler’s second law, equal areas are swept
out in equal time. Since there is less area
available at perihelion, the planet must
move faster.
vP
A
10.0
1.7
4. vA
P
6 .0
1
5. vA minimum velocity
3.7 km/s
vP 1.7 vA
1.7 3.7 km/s
6.3 km/s
Going Further
1. Collect data using dates of location of a
planet. Use areas and dates to confirm the
second law.
2. In order to show the third law, a computer
model would have a planet actually moving
so that periods and distances could be
measured.
Real-World Physics
Students can research elliptical orbits of satellites.
Encourage the students to pick one or two satellites and, if possible, plot orbit data to determine
the path that each satellite takes.
Physics: Principles and Problems
Study Guide
Vocabulary Review
1.
2.
3.
4.
5.
inertial mass
Kepler’s second law
gravitational mass
gravitational field
Newton’s law of universal gravitation
Section 7-1
Planetary Motion and Gravitation
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
Copernicus
Brahe
Brahe
Kepler
Newton
Kepler
Newton
Kepler
third
first
first
third
second
t2 t1 t4 t3
planet B’s average distance from the Sun
It is least at point 3 and greatest at point 1.
1
The magnitude of the force at point 3 is F
36
TB2rA3
rB 3 TA2
2F
1
F
4
6F
4F
4F
the planet’s mean distance from the Sun as
well as the mass of the Sun
Chapters 6–10 Resources
185
Answer Key
25. It was a thin rod with small lead spheres at
each end. The rod was suspended by a thin
wire attached at its center so that the rod
could spin freely. He then placed two larger
lead spheres in fixed positions near the
smaller spheres. The gravitational attraction
between the lead spheres allowed Cavendish
to obtain a value for the universal gravitational constant.
m1m2
26. F G (6.671011 N·m2/kg2)
r2
(1.00 kg)(1.00 kg)
6.671011 N. This
(1.00 m)2
number is significant because it is equal to
the value of the universal gravitational constant. Thus, the constant is defined as the
value of the gravitational force between two
1.00 kg masses placed exactly one meter
apart.
horizontal, vertical
9.80 m/s2
horizontal
air resistance
orbit
the radius of the satellite’s orbit.
the same
true
would change
inverse-square relationship
true
N/kg
toward Earth’s center
Gravitational mass determines the force of
attraction between two masses and inertial
mass determines an object’s resistance to
any type of force
15. No; the inertial mass is a function of an
object’s resistance to an exterior force, not to
its position relative to other objects.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
186 Chapters 6–10 Resources
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
c
e
d
f
b
a
gravitational
force; space
space
mass
general relativity
Section 7-1 Quiz
Planetary Motion and Gravitation
1. 1st: The paths of the planets are ellipses with
the Sun at one focus.
2nd: An imaginary line from the Sun to a
planet sweeps out equal areas in equal time
intervals.
3rd: The square of the periods of two planets
is equal to the cube of their respective mean
TA 2
rA 3
distances from the Sun, or TB
rB
(224.7 d)
r 2. TM TV
rM 3
V
57910 km
87.8 days
108210 km 6
6
3
mSmN
3. F G (6.671011 N·m2/kg2)
r2
(1.991030 kg)(1.031026 kg)
(4.501012 m)2
6.771020 N
4. Cavendish used a small rod suspended at its
midpoint by a thin wire. The rod had small
lead spheres at either end. He then placed
larger lead spheres in fixed positions near the
rod. He then used the angle through which
the rod turned to calculate the attractive
force between the spheres and then to calculate the universal gravitational constant.
Physics: Principles and Problems
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Section 7-2
Using the Law of Universal
Gravitation
Chapter 7 continued
Answer Key
Chapter 7 continued
Section 7-2 Quiz
Using the Law of Universal Gravitation
1. The horizontal component of the object’s
velocity must be great enough that the
object falls toward Earth at the same rate
that Earth curves away from the moving
object. For the object to remain moving fast
enough to stay in orbit, the object must be
more than 150 km above the surface of
Earth so that air resistance does not decrease
the horizontal component of the object’s
velocity.
GmE
r
2. v (6.671011 N·m2/kg2)(5.981024 kg)
(350103 m 6.38106 m)
7700 m/s
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
T 2
2
r3
GmE
(350103 m 6.38106 m)3
(6.671011 N·m2/kg2)(5.981024 kg)
5500 s
rE 2
3. a g (9.80 m/s2)
r
6.3810 m
27010
m 6.3810 m
6
3
2
6
9.0 m/s2
4. According to the general theory of relativity,
mass curves the space around it. Other bodies are then accelerated by the curvature of
the space through which they might pass.
Thus, gravity is not a force but an effect of
space itself. Newton’s law of universal gravitation simply allows us to calculate the magnitude of the gravitational attraction
between two bodies.
2. The apparent position of the star on the day
of the eclipse is meaningless by itself. For
Einstein’s theory to be true, light from the
star must be bent by the Sun’s gravity. This
means that the astronomers would observe a
change in the star’s apparent position. Since,
it is the change that is important and not
the star’s position on any one date, the
results of this experiment would have
proved nothing if the star’s position had not
previously been noted.
3. The experiment provided support for Einstein’s theory because the apparent position
of the star changed when its light passed
close to the Sun. This change in apparent
position indicates that the path and direction of the light was bent, presumably by
the Sun’s gravitational field.
Chapter 7 Enrichment
Variations in the Acceleration Due to
Gravity on Earth
1. Acceleration due to gravity is less near the
equator and less at higher elevations. Thus,
you would find the lowest value of acceleration due to gravity at a high elevation near
the equator and you would find the highest
value near the North or South Pole at sea
level.
2. There appears to be a stronger correlation
between acceleration due to gravity and latitude. While acceleration due to gravity
increases consistently with increases in latitude, the values for acceleration due to gravity in Table 1 don’t increase consistently with
increases in elevation. In some cases, an
increase in elevation corresponds to a
decrease in acceleration due to gravity.
Chapter 7 Reinforcement
Gravitation
1. According to the general theory of relativity,
only the Sun has enough mass to curve
space and deflect the light from distant stars
to any measurable degree.
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187