Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1)
Sarah drives at a constant speed of 15 m/s around a circular horizontal curve of
diameter 60 m. What are the magnitude and direction of her acceleration?
1)
2)
A child sits on a merry-go-round, 1.5 meters from the center. The
merry-go-round is turning at a constant rate, and the child is observed to have a
radial acceleration of 2.3 m/s2. How long does it take for the merry-go-round to
make one revolution?
2)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
3)
An object moves with a constant speed of 30 m/s on a circular track of radius 150 m.
What is the acceleration of the object?
A) 0.17 m/s2
B) 5.0 m/s2
C) 6.0 m/s2
D) 0 m/s2
3)
4)
You are driving at 30.0 m/s on a freeway curve of radius 25.0 m. What is the
magnitude of your acceleration?
A) 20.8 m/s2
B) 1.20 m/s2
C) 36.0 m/s2
D) 0.833 m/s2
4)
5)
A car moving at a steady 10 m/s on a level highway encounters a depression that has a
circular cross-section with a radius of 30 m. The car maintains its speed as it drives
through the depression. What is the force exerted by the seat of the car on a 60.0-kg
passenger when the car is at the bottom of the depression?
5)
A) 590
6)
B) 200
N
C)
490 N
D) 790
N
E) 390
N
Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle. At
the bottom of the dive, the speed of the airplane is 320 m/s. What is the smallest radius
allowable for the vertical circle if the pilot's apparent weight (the force that the pilot
exerts on the seat) is not to exceed 7.0 times his true weight?
A) 230
7)
N
m
B) 42
m
C)
2200 m
D) 1500
m
E) 1700
m
A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve
with the tires on the verge of slipping. What is the maximum speed with which this car
can round a second unbanked curve of radius 320 m if the coefficient of static friction
between the car's tires and the road surface is the same in both cases?
A) 80
m/s
B) 160
m/s
C)
30 m/s
1
D) 40
m/s
E) 70
6)
m/s
7)
8)
A satellite of mass M takes time T to orbit a planet. If the satellite had twice as much
mass, the time for it to orbit the planet at the same altitude would be
A) 4T.
B) 2T.
C)
T/4.
D) T/2.
8)
E) T.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
9)
The International Space Station is orbiting at an altitude of about 370 km above
the earth's surface. The mass of the earth is 5.97 × 1024 kg, the radius of the
earth is 6.38 × 106 m, and G = 6.67 × 10-11 N ∙ m2/kg2. Assume a circular
orbit.
(a) What is the period of the International Space Station's orbit?
(b) What is the speed of the International Space Station in its orbit?
9)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
10) An
astronaut goes out for a "space-walk" at a distance above the earth equal to the
radius of the earth. What is her free-fall acceleration at that point?
A) g/4
B) zero
C)
g
D) g/2
E) g/
10)
2
11) Suppose
NASA wants a satellite to revolve around Earth 5 times a day. What should be
the radius of its orbit if we neglect the presence of the Moon? (G = 6.67 × 10-11 N ∙
m2/kg2, Mearth = 5.97 × 1024 kg)
A) 0.69
× 107
B) 1.44
m
× 107
C)
m
7.22 × 107
m
D) 2.11
× 107
m
12) A
spherically symmetric planet has four times the earth's mass and twice its radius. If a
jar of peanut butter weighs 12 N on the surface of the Earth, how much would it weigh
on the surface of this planet?
A) 36
N
B) 3.0
N
C)
12 N
D) 6.0
N
E) 24
how many newtons does the weight of a 100-kg person decrease when he goes
from sea level to mountain top at an altitude of 5000 m? The mean radius of the earth is
6.38 × 106 m.
N
B) 0.60
N
C)
3.6 N
14) At
D) 1.5
N
E) 2.6
13)
N
a distance of 14,000 km from the center of Planet Z-99, the free-fall acceleration is
32 m/s2. What is the free-fall acceleration at a point 28,000 km from the center of this
planet?
A) 4.0
B) 16 m/s2
C) 8.0
D) 128
E) 2.0
2
2
2
m/s
m/s
m/s
m/s2
2
12)
N
13) By
A) 9.8
11)
14)
another solar system, a planet has an airless moon Zygo that is 4.0 × 10 5 m in
diameter. Experiments reveal that a freely falling object at the surface of Zygo
accelerates at 0.20 m/s2. What is the mass of Zygo? (G = 6.67 × 10-11 N ∙ m2/kg2)
15) In
15)
× 1020 kg
B) 4.8 × 1019 kg
A) 4.8
1.2 × 1020 kg
D) 2.4 × 1020 kg
C)
E) 2.4
× 1019 kg
16) What
would be the gravitational force that a planet with the same density as Earth and
having twice Earth's radius exerts on a 59.1-kg astronaut?
A) 1160
N
B) 290
N
C)
580 N
D) 1200
N
E) 2320
N
17) Planet
Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third
that of Earth. With g representing, as usual, the free-fall acceleration at the surface of
Earth, the free-fall acceleration at the surface of Z-34 is
A) 9g.
B) g/3.
C)
g/9.
D) 6g.
16)
17)
E) 3g.
18) What
is the distance from the center of the Moon to the point between Earth and the
Moon where the gravitational pulls of Earth and Moon are equal in magnitude? The
mass of Earth is 5.97 × 1024 kg, the mass of the Moon is 7.35 × 1022 kg, the
center-to-center distance between Earth and the Moon is 3.84 × 10 8 m, and G = 6.67 ×
10-11 N ∙ m2/kg2.
A) 3.84 × 107 m
18)
× 108 m
C) 4.69 × 106 m
B) 3.45
× 106 m
E) 4.69 × 107 m
D) 3.83
spaceship with a mass of 2.8 × 106 kg is traveling toward two spherical asteroids,
each with a mass of 5.0 × 1016 kg, that are 40 km apart center-to-center. Its path is
perpendicular to the line joining the asteroids and is aimed at the midpoint of that line.
What is the sum of the gravitational forces exerted by the asteroids on the spaceship
when the spaceship is 30 km away from that midpoint? (G = 6.67 × 10-11 N ∙ m2/kg2)
19) A
A) 18,000
N
B) 12,000
N
C)
16,000
N
3
D) 6,200
N
E) 8,000
N
19)
20)
20)
Mass
Radius
4.0 × 1020 kg unknown
1.5 × 1020 kg 2.0 × 105 m
Moon A
Moon B
Orbital radius Orbital period
2.0 × 108 m 4.0 × 106 s
3.0 × 108 m unknown
Mithra is an unknown planet that has two moons, A and B, in circular orbits around it.
The table summarizes the hypothetical data about these moons. What is the magnitude of
the maximum gravitational force that Moon A exerts on Moon B? (G = 6.67 × 10-11 N
∙ m2/kg2)
A) 1.0 × 1014 N
× 1014 N
C) 4.0 × 1014 N
B) 2.0
× 1013 N
E) 4.4 × 1013 N
D) 1.6
21) When
a spacecraft is launched from the earth toward the sun, at what distance from
center of the earth will the gravitational forces exerted on it by the sun and earth
cancel?
Earth's mass is 5.97 × 1024 kg, the sun's mass is 1.99 × 1030 kg, and the Earth-sun
distance is 1.5 × 1011 m.
A) 2.6 × 1010
B) 2.6 × 108 m
C) 1.3 × 108 m
D) 1.3 × 1010
m
m
21)
22) As
22)
a 70-kg person stands at the seashore gazing at the tides (which are caused by the
Moon), how large is the gravitational force exerted on that person by the Moon? The
mass of the Moon is 7.35 × 1022 kg, the distance to the Moon is 3.82 × 108 m, and G =
6.67 × 10-11 N ∙ m2/kg2.
A) 0.24
N
B) 0.0024
N
C)
0.024 N
D) 0.00024
N
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
23) Two
identical tiny balls of highly compressed matter are 1.50 m apart. When
released in an orbiting space station, they accelerate toward each other at 2.00
cm/s2. What is the mass of each of them? (G = 6.67 × 10-11 N ∙ m2/kg2)
4
23)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
24) What
is the gravitational force acting on a 59-kg person due to another 59-kg person
standing 2.0 m away? We can model each person as a small sphere. (G = 6.67 × 10-11
N ∙ m2/kg2)
A) 5.8 × 10-8 N
B) 1.2
C)
24)
× 10-7 N
8.5 × 103 N
D) 2.0
× 10-9 N
E) 9.8
× 10-10 N
25) A
20-g bead is attached to a light 120 cm-long string as shown in the figure. If the
angle α is measured to be 18°, what is the speed of the bead?
A) 2.0
m/s
B) 0.55
C)
3.8 m/s
m/s
5
D) 1.3
m/s
E) 1.1
25)
m/s
Answer Key
Testname: GRAVEPRACTICE
7.5 m/s2 toward the center of the circle
2) 5.1 s
1)
3)
4)
5)
6)
7)
8)
C
C
D
E
D
E
9) (a)
10) A
11) B
12) C
13) D
14) C
15) C
16) A
17) E
18) A
19) B
20) C
21) B
22) B
5.5 × 103 s
23) 6.75
24) A
25) E
(b) 7.7 × 103 m/s
× 108 kg
6