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Physics: Principles and Problems
7
10.
Name
Date
Period
Chapter Assessment
A coin rolls along the top of a 1.33 m-high desk with a constant velocity. It reaches the edge of
the desk and hits the ground 10.25 m from the edge of the desk. What was the velocity of the
coin as it rolled across the desk?
R
1
y 5 y0 1 vy0t 2 }2 gt 2
R 5 vx0t; vx0 5 }
t
22y
0.25 m
2
t 5}
5}
g
0.52 s
22y
t5 }
5 0.48 m/s
g
(22)(21.33 m)
5 }}
9.8 m/s2
!§
!§§
8
Use with Chapter 8.
Understanding Concepts Part A
Write the letter of the choice that best completes each statement.
a
1. During its orbital period, as a planet moves closer to the sun, the orbital velocity of
.
the planet
a. increases
b
b. decreases
c. remains the same
2. According to Newton’s law of universal gravitation, the force of attraction between any two
.
masses is directly related to the
a. distance between the masses
c. velocity of the two masses
b. product of the two masses
d. sum of the two masses
b
3. As the distance between two bodies increases, the force of attraction between
.
the bodies
a
4. Astronauts in an orbiting space shuttle experience a sensation of weightlessness
because
.
a. increases
a. If the disk makes three complete revolutions per second, what is the force exerted by the wire
on the object?
4p2mr
Fc 5 mac 5 }
T2
(4) (3.14)2 (0.050 kg) (0.150 m)
5 }}}}
((1.00 s)/3)2
5 2.7 N
Chapter Assessment
Universal Gravitation
5 0.52 s
11. A 0.050-kg disk attached to the end of a 0.150-m wire revolves uniformly on a flat, frictionless
surface.
Name
b. decreases
c. remains the same
a. the space shuttle is falling freely toward Earth
b. the space shuttle is not affected by Earth’s gravity
c. the mass of the space shuttle decreases as the distance from Earth increases
d. the space shuttle is moving away from Earth
c
5. Anything that has mass is surrounded by a
a.
Teacher Guide and Answers 17T
b. What is the speed of the disk?
d
2pr
v5}5}
t
T
(2)(3.14)(0.15 m)
5 }}}
((1.00 s)/3)
5 2.8 m/s
.
satellite in orbit
c. gravitational field
b. magnetic field
b
b
6. The force of gravity exerts a
d. black hole
on an orbiting satellite.
a. balanced force
c. tangential force
b. centripetal force
d. All these are true.
7. The pair of spheres that experiences the
greatest force of attraction is
.
A
B
1 kg
a. A and B
3 kg
b. B and C
c. A and C
C
2 kg
34 Chapter Assessment
Physics: Principles and Problems
Physics: Principles and Problems
Chapter Assessment 35
18T
Teacher Guide and Answers
8
Name
8
Chapter Assessment
Name
Chapter Assessment
Understanding Concepts Part B
Applying Concepts
Answer the following questions, showing your calculations.
Answer the following questions, using complete sentences.
1. Which of the pairs of masses below will have the greatest force of attraction between the spheres?
90 kg
80 kg
32 kg
25 kg
20 kg
10 kg
20 cm
40 cm
15 cm
A
B
C
m 1m 2
Fgrav ~ }
d2
(32 kg)(25 kg)
A Fgrav ~ }}
(20 cm)2
800 kg2
~ }}
400 cm2
~ 2.0
~ 1.0
kg2/cm2
(90 kg)(10 kg)
C Fgrav ~ }}
(15 cm)2
900 kg2
~ }}
225 cm2
~ 4.0
kg2/cm2
kg2/cm2
2. Two spheres, each having a mass of 20.0 kg, are positioned so that their centers are 8.00 m apart.
What is the gravitational force between the spheres?
m1m2
F5G}
d2
(6.67 3 10211 N?m2 /kg2)(2.00 3 101 kg)(2.00 3 101 kg)
5 }}}}}}}
(8.0 m)2
5 4.17 3 10210 N
Physics: Principles and Problems
3. What will the force be if the spheres described in problem 2 are positioned with their centers
4.00 m apart?
m1m2
F5G}
d2
(6.67 3 10211 N?m2 /kg2)(2.00 3 101 kg)(2.00 3 101 kg)
5 }}}}}}}
(4.0 m)2
5 1.67 3 1029 N
4. If the mass of one of the spheres described in problem 2 were doubled, how far apart would the
spheres have to be to maintain the same gravitational force between them?
Gm m
(6.67 3 10
N?m /kg )(4.00 3 10 kg)(2.00 3 10 kg)
}} 5 !§§§§
}}}}}}}
!§
F
(4.17 3 10
N)
1
211
2
2
2
1
2. Earth is closer to the sun in December than it is in July. What happens to the orbital speed of the
planet between July and December? Explain your answer.
The orbital speed of Earth increases between July and December. During this period, Earth is
its orbit.
3. What would happen to the magnitude of the gravitational force between two bodies if:
a. the mass of one of the bodies were doubled?
The gravitational force between them would be doubled.
b. the distance between the two bodies were doubled?
The gravitational force between them would be one-fourth as great.
4. What information do you need to find the period of a planet using Kepler’s third law?
You need to know the period of another planet and the orbital radii of both planets.
5. The mass of Jupiter is approximately 318 times that of Earth. Yet the surface gravity of Jupiter is less
than three times the surface gravity of Earth. How do you account for this apparent discrepancy?
The surface gravity of each planet is inversely related to the square of the radius of the planet.
Jupiter’s radius is much greater (almost 11 times) than Earth’s radius.
6. How does an artificial satellite remain in orbit at a constant distance from Earth’s surface?
The satellite moves with uniform circular motion so that the curvature of Earth’s surface
exactly matches the curvature of the trajectory of the satellite. Earth’s surface “falls away”
from the satellite at the same rate that the satellite falls toward Earth.
7. How does Einstein’s general theory of relativity account for the blackness of black holes in the
universe?
According to Einstein’s theory, light is deflected by the mass of a body. If an object is massive
1
210
5
Kepler applied Brahe’s data to the motions of planets in a sun-centered system.
moving closer to the sun, and the closer a planet is to the sun, the faster the planet moves in
(80 kg)(20 kg)
B Fgrav ~ }}
(40 cm)2
1600 kg2
~ }}
1600 cm2
The force of attraction will be the greatest between the spheres in set C.
d5
1. Explain why Kepler was able to use Tycho Brahe’s data about the positions of stars and planets to
develop his laws of planetary motion, while Brahe was unable to use the same data successfully.
Brahe believed in an Earth-centered universe. In formulating his laws of planetary motion,
Ï1w.2
w8ww
3w
10
w2wm
w2w
enough, light leaving the object will be bent back toward it. If no light ever escapes the object,
the object appears to be a black hole.
5 11.3 m
36 Chapter Assessment
Physics: Principles and Problems
Physics: Principles and Problems
Chapter Assessment 37
Physics: Principles and Problems
Name
8
Date
Period
Chapter Assessment
9
Answer the following questions, showing your calculations.
8. The distance between Earth and the sun is often expressed as 1 astronomical unit (AU). Using this
unit, find the distance between the sun and Mars, which has a period of approximately 686 Earth
days.
2
TM
rM 5 rE }
2
TE
TM 2
rM 3
}
5 }
TE
rE
1 2 1 2
(686 d)2
rM 5 1 AU }}
(365 d)2
1
1 2
2
1
}
3
51
1
}
3
1
}
AU(3.53) 3
Ts
rs
3
5 1.52 AU
5 1}2
1}
T 2
r
m
rs 5
m
T 2s }13
rm }
2
Tm
d)2
(9.1
rs 5 3.84 3 108 m }}
(27.3 d)2
1 2
1
5 3.84 3
Understanding Concepts Part A
108
m
2
a
1
}
(0.11) 3
3. Impulse can be represented by
.
a. Dv/Dt
c. mv
b. FDt
d. m/v
a
4. When a golf club hits a golf ball, the change in momentum of the ball is
momentum of the club.
c
5. A system is closed if
b. greater than
the change in
c. less than
.
a. no net external force acts on it
b. the momentum of each object in the system remains constant
11. A body orbits the sun at a distance ten times the mean distance of Earth’s orbit from the sun. The
sun’s mass is 1.99 3 1030 kg, and its distance from Earth is 1.50 3 1011 m.
c. the system does not gain or lose mass
d. objects can enter, but not leave, the system
a. Find the period of the body in years.
c
Teacher Guide and Answers 19T
!§ !§
!§
r 3x
}
5
r E3
TE (10rE )3
}}
3
rE
5 (1 year)
6. An internal force
a. increases
b
103
}
13
5 32 years
b. Determine the speed of the body.
a
!§ !§§§
Gms 5
}
r
.
c. large force acting over a short time
b
5 50 kg
v5
d. time
2. The greatest change in momentum will be produced by a
a. equal to
(2.50 3 1028 N)(1.05 m)2
5 }}}}
(6.67 3 10211 N?m2/kg2)(8.2 kg)
1 2 1 2
c. impulse
b. small force acting over a short time
Fd 2
m2 5 }
Gm 1
Tx 5 TE
a. acceleration
b. velocity
a. large force acting over a long time
1
}
3
10. The gravitational force between two spheres is 2.50 3 10–8 N. Their centers are 105 cm apart. The
smaller sphere has a mass of 8.2 kg. Find the mass of the larger sphere.
Tx 2
rx 3
}
5 }
TE
rE
Use with Chapter 9.
Momentum and Its Conservation
5 1.84 3 108 m
G m 1m 2
F 5 }}
d2
Chapter Assessment
Write the letter of the choice that best completes the statement or answers the question.
b
1. The linear momentum of an object can be calculated by multiplying the mass of the object by
.
its
9. The mean distance between the center of Earth and the center of the moon is 3.84 3 108 m, and
the moon has an orbital period of 27.3 days. Find the distance from Earth of an artificial satellite
that has an orbital period of 9.1 days.
2
Name
(6.67 3 10211 N?m 2 /kg)(1.99 3 1030 kg)
}}}}}
(1.50 3 1012 m)
the total momentum of a closed system.
b. decreases
c. does not change
7. A person is standing on roller blades and is holding a heavy medicine ball. If he throws the
medicine ball horizontally to the right, what will be his resulting motion?
a. to the right
c. backward
b. to the left
d. no motion
8. Two moving objects collide and move on paths that are 1208 apart. The total momentum of
the objects after the collision is
the total momentum before the collision.
a. equal to
b. greater than
c. less than
5 9.41 3 103 m/s
38 Chapter Assessment
Physics: Principles and Problems
Physics: Principles and Problems
Chapter Assessment 39