College Physics 10th Edition Young

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College Physics, 10e (Young)
Chapter 6 Circular Motion and Gravitation

6.1 Multiple Choice Questions

1) A person ties a rock to a string and whirls it around in a vertical circle such that sometimes the
rock is going straight upward and sometimes the rock is going straight down. She whirls the rock
at the minimum speed (constant in time) such that the string is always taut (no sag). If she were
to use a longer string, she would have to whirl the rock at a
A) higher velocity.
B) lower velocity.
C) the same velocity.
Answer: A
Var: 1

2) A person ties a rock to a string and whirls it around in a vertical circle such that sometimes the
rock is going straight upward and sometimes the rock is going straight down. She whirls the rock
at the minimum speed (constant in time) such that the string is always taut (no sag). When is the
tension the highest?
A) It is highest when the rock is at the lowest elevation.
B) It is highest when the rock is at the highest elevation.
C) The tension is constant as the rock moves around in a circle.
Answer: A
Var: 1

3) A 76 kg mass is connected to a nail on a frictionless table by a (massless) string of length

If the tension in the string is while the mass moves in a uniform circle on the table,
how long does it take for the mass to make one complete revolution?
A) 8.7 s
B) 7.0 s
C) 8.1 s
D) 9.5 s
Answer: A
Var: 50+

4) A new roller coaster contains a loop-the-loop in which the car and rider are completely upside
down. If the radius of the loop is with what minimum speed must the car traverse the
loop so that the rider does not fall out while upside down at the top? Assume the rider is not
strapped to the car.
A) 13.2 m/s
B) 14.5 m/s
C) 10.1 m/s
D) 14.9 m/s
Answer: A
Var: 50+
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5) A tetherball is on a string which makes an angle of 56° with the vertical as it moves
around the pole in a horizontal plane. If the mass of the ball is what is the ball's speed?
A) 5.0 m/s
B) 4.0 m/s
C) 4.6 m/s
D) 5.7 m/s
Answer: A
Var: 50+

6) A merry-go-round is spinning at a fixed rate. As a person is walking toward the edge,

A) the force of static friction must increase in order for the person not to slide off.
B) the force of static friction must decrease in order for the person not to slide off.
C) the force of static friction such that the person does not slide off remains the same.
Answer: A
Var: 1

7) You need to make a sharp turn on a flat road, making a radius of curvature of 15 meters. How
does the required force of static friction between your tires compare if you make the turn at 30
mph vs. 60 mph?
A) The force of friction needs to be four times as large.
B) The force of friction needs to be twice as large.
C) the force of friction is the same for both speeds since the radius of curvature is the same.
D) None of the above
Answer: A
Var: 1

8) A roadway is designed for traffic moving at a speed of 66 m/s. A curved section of the
roadway is a circular arc of 290 m radius. The roadway is banked—so that a vehicle can go
around the curve—with the lateral friction forces equal to zero. The angle at which the roadway
is banked is closest to:
A) 57°
B) 59°
C) 55°
D) 53°
E) 51°
Answer: A
Var: 50+

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9) A roadway is designed for traffic moving at a speed of 94 m/s. A curved section of the
roadway is a circular arc of 740 m radius. The curved section is temporarily replaced with an
unbanked roadway of the same radius. The coefficient of friction of this roadway is 0.40. The
maximum safe driving speed for this unbanked, curved section is closest to:
A) 54 m/s
B) 52 m/s
C) 50 m/s
D) 48 m/s
E) 46 m/s
Answer: A
Var: 50+

Figure 6.1

10) A ball of mass 8.0 kg is suspended by two wires from a horizontal arm, which is attached to
a vertical shaft, as shown in Figure 6.1. The shaft is in uniform rotation about its axis such that
the linear speed of the ball equals 2.3 m/s. The tension in wire 1 is closest to:
A) 39 N
B) 49 N
C) 29 N
D) 20 N
E) 9.8 N
Answer: A
Var: 50+

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11) A ball of mass 6.0 kg is suspended by two wires from a horizontal arm, which is attached to
a vertical shaft, as shown in Figure 6.1. The shaft is in uniform rotation about its axis such that
the linear speed of the ball equals 1.5 m/s. The tension in wire 2 is closest to:
A) 21 N
B) 17 N
C) 25 N
D) 28 N
E) 32 N
Answer: A
Var: 50+

12) A ball of mass 7.0 kg is suspended by two wires from a horizontal arm, which is attached to
a vertical shaft, as shown in Figure 6.1. The shaft is in uniform rotation about its axis such that
the linear speed of the ball equals 2.2 m/s. The rate of rotation is adjusted so that the tensions in
the two wires are equal. The radial acceleration of the ball is closest to:
A) 5 m/
B) 6 m/
C) 7 m/
D) 8 m/
E) 10 m/
Answer: A
Var: 50+

13) In an amusement park ride passengers stand inside an 8 m radius cylinder. Initially the
cylinder rotates with its axis oriented along the vertical. After the cylinder has acquired sufficient
speed, it tilts into a vertical plane, that is, the axis tilts into the horizontal, as shown in Figure
6.2. Suppose that, once the axis has tilted into the horizontal, the ring rotates once every . If
a rider's mass is 40 kg, with how much force does the ring push on her at the top of the ride?

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 Figure 6.2

A) 230 N
B) 620 N
C) 1,000 N
D) 390 N
Answer: A
Var: 50+

14) Future space stations will create an artificial gravity by rotating. Consider a cylindrical space
station of 380 m diameter rotating about its axis. Astronauts walk on the inside surface of the
space station. What rotation period will provide "normal" gravity?
A) 28 s
B) 39 s
C) 6.2 s
D) 4.4 s
Answer: A
Var: 50+

15) A 90 g bead on a 60 cm long string is swung in a vertical circle about a point 200 cm above
the floor. The tension in the string when the bead is at the very bottom of the circle is 2.2 N. A
very sharp knife is suddenly inserted, as shown in Figure 6.3, to cut the string directly below the
point of support. How far to the right of the center of the circle does the ball hit the floor?

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 Figure 6.3

A) 160 cm
B) 200 cm
C) 240 cm
D) 190 cm
Answer: A
Var: 40

16) Figure 6.4 shows a 3.0 kg ball tied to the end of a 50 cm long string being swung in a circle
in a vertical plane at constant speed. The center of the circle is above the floor. The
ball is swung at the minimum speed necessary to make it over the top without the string going
slack. If the string is released at the instant the ball is at the top of the loop, how far to the right
of the center of the circle does the ball hit the ground?

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 Figure 6.4

A) 240 cm
B) 230 cm
C) 210 cm
D) 0.0 cm
Answer: A
Var: 50+

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17) Figure 6.5 shows two wires that are tied to a 150 g mass which revolves in a horizontal circle
at a constant speed of 7.5 m/s. What is the tension in the upper wire?

A) 7.1 N
B) 4.2 N
C) 5.7 N
D) 8.6 N
Answer: A
Var: 50+

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18) Figure 6.6 shows two wires tied to a 8.8 kg sphere which revolves in a horizontal circle at
constant speed. At this particular speed the tension is the same in both wires. What is the
tension?

A) 63 N
B) 86 N
C) 120 N
D) 59 N
Answer: A
Var: 50+

19) The gravitational acceleration at the surface of planet X is 11.6 m/ , and the radius of the
planet is 66,500 km. The altitude above the surface of planet X at which the weight of a body is
equal to that on the surface of the earth, in km, is closest to:
A) 5,800
B) 7,000
C) 8,200
D) 9,400
E) 11,000
Answer: A
Var: 50+

20) At a given point above the surface of the earth, the gravitational acceleration is equal to
The altitude of this point, above the surface of the earth, in km, is closest to:
A) 770
B) 970
C) 1,500
D) 2,000
E) 2,400
Answer: A
Var: 39
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21) What is the gravitational force acting on a person due to another person standing 2 meters
away? Assume each individual has 59 kg mass.
A) 5.8 × 10-8 N
B) 8.5 × 103 N
C) 1.2 × 10-7 N
D) 9.8 × 10-10 N
E) 2.0 × 10-9 N
Answer: A
Var: 50+

Table 6.1

gravitational
acceleration orbital orbital
radius at the surface radius period
Moon I 5× m
Moon II 9× m 3× s
Moon III 2× m 0.20 m/ 2× s

An Earth station receives data transmitted back in time from a future intergalactic expedition.
Table 6.1 summarizes the data for the moons of a planet that will be discovered in a distant
galaxy.

22) In Table 6.1, the mass of the planet is closest to:

A) 1.2 × kg
B) 1.7 × kg
C) 2.4 × kg
D) 3.4 × kg
E) 4.8 × kg
Answer: E
Var: 1

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23) In Table 6.1, the mass of Moon III is closest to:
A) 2.4 × kg
B) 4.8 × kg
C) 1.2 × kg
D) 2.4 × kg
E) 4.8 × kg
Answer: C
Var: 1

24) In Table 6.1, the centripetal acceleration of Moon II due to orbital motion is closest to:
A) 0.02 m/
B) 0.04 m/
C) 0.06 m/
D) 0.08 m/
E) 0.10 m/
Answer: B
Var: 1

Table 6.2

Ekapluto is an unknown planet that has two moons in circular orbits. Table 6.2 summarizes the
hypothetical data about the moons.

25) In Table 6.2, the mass of Ekapluto is closest to:

A) 1 × kg
B) 3 × kg
C) 1 × kg
D) 3 × kg
E) 1 × kg
Answer: D
Var: 1

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26) In Table 6.2, the maximum gravitational force between the two moons is closest to:
A) 1.6 × N
B) 4.4 × N
C) 1.0 × N
D) 2.0 × N
E) 4.0 × N
Answer: E
Var: 1

27) In Table 6.2, a meteoroidal fragment is in circular orbit around Moon B, at a small altitude
above the surface. The speed of this body is closest to:
A) 220 m/s
B) 320 m/s
C) 440 m/s
D) 640 m/s
E) 880 m/s
Answer: A
Var: 1

28) In Table 6.2, the gravitational acceleration at the surface of Moon B is closest to:
A) 0.10 m/
B) 0.15 m/
C) 0.20 m/
D) 0.25 m/
E) 0.30 m/
Answer: D
Var: 1

29) The reason an astronaut in an earth satellite feels weightless is that

A) the astronaut is beyond the range of the earth's gravity.
B) the astronaut is falling.
C) the astronaut is at a point in space where the effects of the moon's gravity and the earth's
gravity cancel.
D) this is a psychological effect associated with rapid motion.
E) the astronaut's acceleration is zero.
Answer: B
Var: 1

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30) From what height off the surface of the Earth should an object be dropped to initially
experience an acceleration of
A) 2,298 km
B) 1,689 km
C) 5,426 km
D) 2,930 km
Answer: A
Var: 46

31) An astronaut is in equilibrium when he is positioned from planet X and from

planet Y, along the straight line joining the planets' centers. What is the ratio of the masses X/Y?
A) 0.382
B) 2.62
C) 0.618
D) 1.62
Answer: A
Var: 50+

32) If we assume that an electron is orbiting a proton just like the moon orbits the Earth, find the
electron's orbital speed due to the gravitational attraction between itself and the proton. Take the
orbital radius as (This is a very wrong assumption to make.)
A) 3.33 × 10-14 m/s
B) 1.11 × 10-13 m/s
C) 1.11 × 10-27 m/s
D) 1.06 × 10-27 m/s
Answer: A
Var: 1

33) Suppose we want a satellite to revolve around the Earth 5 times a day. What should the
radius of its orbit be? (Neglect the presence of the moon.)
A) 1.44 × 107 m
B) 0.69 × 107 m
C) 7.22 × 107 m
D) 2.11 × 107 m
Answer: A
Var: 9

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34) Spaceman Speff orbits planet X with his spaceship. To remain in orbit at from the
planet's center, he should maintain a speed of What is the mass of planet X?
A) 2.8 × 1019 kg
B) 4.2 × 1017 kg
C) 2.8 × 1016 kg
D) 4.2 × 1014 kg
Answer: A
Var: 50+

35) A proton moving at 0.999 of the speed of light orbits a black hole from the center
of the attractor. What is the mass of the black hole?
A) 6.71 × 1033 kg
B) 6.71 × 1030 kg
C) 6.71 × 1036 kg
D) 6.71 × 1025 kg
Answer: A
Var: 50+

36) Find the orbital speed of an ice cube in the rings of Saturn, if the mass of Saturn is
and the rings have an average radius of
A) 19.5 km/s
B) 27.5 km/s
C) 13.8 km/s
D) 1.95 km/s
Answer: A
Var: 1

37) You are the science officer on a visit to a distant solar system. Prior to landing on a planet
you measure its diameter to be 1.8 × 107 m. You have previously determined that the planet
orbits 2.9 × 1011 m from its star with a period of 402 earth days. Once on the surface you find
that the acceleration due to gravity is 19.5 m/s2. What are the masses of (a) the planet and (b) the
star?
A) (a) 2.4 kg × kg, (b) 1.2 kg × kg
B) (a) 4.3 kg × kg, (b) 1.2 kg × kg
C) (a) 2.4 kg × kg, (b) 7.1 kg × kg
D) (a) 4.3 kg × kg, (b) 7.1 kg × kg
Answer: A
Var: 50+

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38) If you stood on a planet having a mass four times higher than Earth's mass, and a radius two
times longer than Earth's radius, you would weigh
A) the same as you do on Earth.
B) two times more than you do on Earth.
C) two times less than you do on Earth.
D) four times more than you do on Earth.
Answer: A
Var: 1

39) A satellite having orbital speed V orbits a planet of mass M. If the planet had half as much
mass, the orbital speed of the satellite would be
A) V
B) 2V
C) V
D) V/
E) V/2
Answer: D
Var: 1

40) 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 would be
A) 4T
B) 2T
C) T
D) T/2
E) T/4
Answer: C
Var: 1

6.2 Short Answer Questions

1) A tobogganer coasts down a hill and then goes over a slight rise with speed 2.7 m/s. The top
of this rise can be taken to be a circle of radius 4.1 m. The toboggan and occupant have a
combined mass of 110 kg. If the coefficient of kinetic friction between the snow and the
toboggan is 0.10, what frictional force is exerted on the toboggan by the snow as the toboggan
goes over the top of the rise? Start with a free-body diagram of the toboggan with the person
inside, at the top of the rise.
Answer: 88 N
Var: 1

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2) A Ferris wheel has radius 5.0 m and makes one revolution in 8.0 seconds. A person weighing
670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent
weight (the the normal force exerted on her by the bench) of the person as she passes through the
highest point of her motion?
Answer: 460 N
Var: 1

3) What is the difference in the weight of a 117 kg person as measured at sea level and at the top
of the Vinson Massif, the highest peak in Antarctica? The product
the radius of the Earth is and the height
above sea level of the Vinson Massif is Neglect the flattening of the Earth at the
poles.
Answer: 1.85 N
Var: 50+

4) A man-made satellite of mass 8,410 kg is in orbit around the earth, making one revolution in
927 minutes. What is the magnitude of the gravitational force exerted on the satellite by the
earth? (The mass of the earth is
Answer: 3.4 × 103 N
Var: 50+

5) A 1500 kg point mass (A) and a 1200 kg point mass (B) are held in place 1.00 m apart on a
frictionless table. A third point mass is placed between the masses 20.0 cm from B along the line
connecting A and B and then released. Find the magnitude and direction (toward A or toward B)
of the acceleration of the third mass just after it is released.
Answer: 1.84 × 10-6 m/s2, toward B
Var: 1

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