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Pearson Physics

James S. Walker

Chapter 9

Gravity and Circular Motion - all with Video Answers

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Chapter Questions

01:23

Problem 1

A $6.1-\mathrm{kg}$ bowling ball and a $7.2-\mathrm{kg}$ bowling ball rest on a rack. If the force of gravity pulling each bowling ball toward the other is $3.1 \times 10^{-9} \mathrm{~N}$, what is the separation between the balls?

Melissa Walsh
Melissa Walsh
Numerade Educator
01:28

Problem 2

Two identical cars are parked $4.7 \mathrm{~m}$ apart on a car dealer's showroom floor. The force of gravity between the cars is $4.5 \times 10^{-6} \mathrm{~N}$. What is the mass of each car?

Supratim Pal
Supratim Pal
Numerade Educator
02:02

Problem 3

Find the magnitude of the gravitational forces $F_{1}$ and $F_{2}$ acting on the spaceship when it is on the $x$ axis, a distance of $2.00 \mathrm{~km}$ from point B.

James Kiss
James Kiss
Numerade Educator
01:27

Problem 4

Ceres, the largest asteroid known, has a mass of roughly $8.7 \times 10^{20} \mathrm{~kg}$. If Ceres passes within 14,000 $\mathrm{km}$ of a spaceship in which you are traveling, what force does it exert on a 95-kg astronaut in your ship?

Melissa Walsh
Melissa Walsh
Numerade Educator
01:18

Problem 5

Apply If the separation between two masses is doubled, does the gravitational force between them increase or decrease? By what factor?

Melissa Walsh
Melissa Walsh
Numerade Educator
02:47

Problem 6

Two gravitational forces act on a given object. How do you determine the total gravitational force acting on the object?

Supratim Pal
Supratim Pal
Numerade Educator
01:21

Problem 7

In what direction does the force of gravity act on a pair of masses?

Melissa Walsh
Melissa Walsh
Numerade Educator
01:38

Problem 8

Describe how factors such as mass and distance affect the force of gravity throughout the universe.

Supratim Pal
Supratim Pal
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Problem 9

Suppose someone makes the following comment: "Astronauts are weightless in orbit because they are beyond Earth's gravitational pull." How would you respond to this assertion?

Gregory Devenport
Gregory Devenport
Numerade Educator
01:52

Problem 10

The three equally spaced objects in Figure $9.5$ have the indicated masses. Is the total gravitational force acting on object B toward the left, toward the right, or zero? Explain.

Supratim Pal
Supratim Pal
Numerade Educator
02:45

Problem 11

Referring to Figure $9.5$, rank the objects in order of increasing magnitude of the total gravitational force. Indicate ties where appropriate.

Supratim Pal
Supratim Pal
Numerade Educator
01:30

Problem 12

You place a 0.18-kg can of soup and a $0.34-\mathrm{kg}$ jar of pickles on the kitchen counter, separated by a distance of $0.42 \mathrm{~m}$. What is the magnitude of the force of gravity that (a) the can of soup exerts on the jar of pickles and (b) the jar exerts on the can?

Narayan Hari
Narayan Hari
Numerade Educator
01:52

Problem 13

What is the magnitude of the force of gravity between two $1.6$-kg flower pots if their separation is (a) $1.0 \mathrm{~m}$ or (b) $3.0 \mathrm{~m}$ ?

Hubert Agamasu
Hubert Agamasu
Numerade Educator
01:37

Problem 14

The gravitational force between two volleyball players is $3.3 \times 10^{-7} \mathrm{~N}$. If the masses of the players are $66 \mathrm{~kg}$ and $72 \mathrm{~kg}$, what is their separation?

Hubert Agamasu
Hubert Agamasu
Numerade Educator
01:44

Problem 15

A batter checks her swing as a $0.15-\mathrm{kg}$ baseball crosses home plate outside the strike zone. If the separation between the batter and the ball is $0.77 \mathrm{~m}$ and the gravitational force exerted on the batter by the ball is $1.1 \times 10^{-9} \mathrm{~N}$, what is the mass of the batter?

Melissa Walsh
Melissa Walsh
Numerade Educator
02:41

Problem 16

Find the acceleration due to gravity at the altitude of the International Space Station's orbit, $370 \mathrm{~km}$ above Earth's surface.

Supratim Pal
Supratim Pal
Numerade Educator
05:53

Problem 17

At what altitude above Earth's surface is the acceleration due to gravity equal to $g / 2 ?$

H M
H M
Numerade Educator
01:07

Problem 18

The lunar rover on the Apollo missions had a mass of $225 \mathrm{~kg}$. What was its weight on Earth and on the Moon?

Melissa Walsh
Melissa Walsh
Numerade Educator
02:11

Problem 19

At a certain distance from the center of Earth, a 4.6-kg object has a weight of $2.2 \mathrm{~N}$.
(a) Find this distance.
(b) If the object is released at this location and allowed to fall toward Earth, what is its initial acceleration?

Melissa Walsh
Melissa Walsh
Numerade Educator
03:21

Problem 20

The acceleration due to gravity at the Moon's surface is known to be about one-sixth of that on Earth. Given that the radius of the Moon is roughly one-quarter of Earth's radius, find the mass of the Moon in terms of the mass of Earth.

Andy Chen
Andy Chen
Numerade Educator
01:28

Problem 21

What assumption can be used to model a large spherical mass like the Sun?

James Kiss
James Kiss
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01:15

Problem 22

Explain Why is a black hole called "black"?

James Kiss
James Kiss
Numerade Educator
01:25

Problem 23

If both the mass and the radius of a planet were doubled, would the acceleration due to gravity at its surface increase, decrease, or stay the same? Explain.

Melissa Walsh
Melissa Walsh
Numerade Educator
01:23

Problem 24

A spaceship orbits a distant star. The star suddenly collapses to half its original size, with no change in its mass. What effect does this have on the spaceship? Explain.

James Kiss
James Kiss
Numerade Educator
01:35

Problem 25

The radius of Mercury is $2400 \mathrm{~km}$, and the acceleration due to gravity at its surface is $3.7 \mathrm{~m} / \mathrm{s}^{2}$. What is the mass of Mercury?

Melissa Walsh
Melissa Walsh
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Problem 26

What is the acceleration due to gravity at a distance of two Earth radii from Earth's center?

Gregory Devenport
Gregory Devenport
Numerade Educator
01:46

Problem 27

What is the acceleration due to gravity at the surface of Mars? The mass of Mars is $6.4 \times 10^{23} \mathrm{~kg}$, and its radius is $3400 \mathrm{~km}$.

Hubert Agamasu
Hubert Agamasu
Numerade Educator
02:29

Problem 28

At what distance from the center of the Moon is the acceleration due to the Moon's gravity equal to $0.50 \mathrm{~m} / \mathrm{s}^{2}$ ?

Supratim Pal
Supratim Pal
Numerade Educator
02:12

Problem 29

What is the minimum coefficient of static friction needed to hold the car on the road?

James Kiss
James Kiss
Numerade Educator
01:13

Problem 30

When riding in a $1300-\mathrm{kg}$ car, you go around a curve of radius $59 \mathrm{~m}$ with a speed of $16 \mathrm{~m} / \mathrm{s}$. The coefficient of static friction between the car and the road is $0.88$. Assuming that the car doesn't skid, what is the force exerted on it by static friction?

Melissa Walsh
Melissa Walsh
Numerade Educator
01:59

Problem 31

What must be true of a force that produces circular motion?

Supratim Pal
Supratim Pal
Numerade Educator
01:44

Problem 32

What is the magnitude of a centripetal force? What is its direction?

Supratim Pal
Supratim Pal
Numerade Educator
02:51

Problem 33

How does centripetal acceleration differ from other accelerations? How is it similar to other accelerations?

Supratim Pal
Supratim Pal
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Problem 34

The gas pedal and the brake pedal are capable of causing a car to accelerate. Can the steering wheel also produce an acceleration? Explain.

Gregory Devenport
Gregory Devenport
Numerade Educator
01:18

Problem 35

An object moves with a speed $v$ on a circular path of radius $r$. If both the speed and the radius are doubled, does the centripetal acceleration of the object increase, decrease, or stay the same? Explain.

Supratim Pal
Supratim Pal
Numerade Educator
02:16

Problem 36

The masses of four objects and their speeds on circular paths of the indicated radii are shown below. Rank these objects in order of increasing centripetal force. Indicate ties where appropriate.
$$
\begin{array}{|c|c|c|c|c|}
\hline & \text { Object A } & \text { Object B } & \text { Object C } & \text { Object D } \\
\hline \text { Mass }(\mathbf{k g}) & 60 & 5 & 24 & 2 \\
\hline \text { Speed }(\mathbf{m} / \mathbf{s}) & 1 & 2 & 2 & 4 \\
\hline \text { Radius }(\mathbf{m}) & 5 & 2 & 8 & 1 \\
\hline
\end{array}
$$

Melissa Walsh
Melissa Walsh
Numerade Educator
02:05

Problem 37

Use the information in Problem 36 to rank the objects in order of increasing centripetal acceleration. Indicate ties where appropriate.

Supratim Pal
Supratim Pal
Numerade Educator
View

Problem 38

You swing a bucket of water in a vertical circle of radius $1.3 \mathrm{~m}$. What speed must the bucket have if it is to complete the circle without any water spilling?

Gregory Devenport
Gregory Devenport
Numerade Educator
01:04

Problem 39

A car experiences a centripetal acceleration of $4.4 \mathrm{~m} / \mathrm{s}^{2}$ as it rounds a corner with a speed of $15 \mathrm{~m} / \mathrm{s}$. What is the radius of the corner?

Melissa Walsh
Melissa Walsh
Numerade Educator
01:42

Problem 40

What is the shape of a planet's orbit?

Hubert Agamasu
Hubert Agamasu
Numerade Educator
01:30

Problem 41

How does the area a planet sweeps out in a given amount of time change throughout its orbit?

Hubert Agamasu
Hubert Agamasu
Numerade Educator
02:17

Problem 42

How does the orbital period of a planet change if the radius of its orbit is increased?

Supratim Pal
Supratim Pal
Numerade Educator
02:23

Problem 43

Does the orbital period of a planet depend on the mass of the planet or on the mass of the star that it orbits?

Supratim Pal
Supratim Pal
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View

Problem 44

How long does it take for a geosynchronous satellite to complete one orbit?

Gregory Devenport
Gregory Devenport
Numerade Educator
01:34

Problem 45

When a communications satellite is placed in a geosynchronous orbit above the equator, it remains fixed over a given point on the ground. Is it possible to put a satellite into an orbit such that it will remain fixed above the North Pole? Explain.

James Kiss
James Kiss
Numerade Educator
02:37

Problem 46

Suppose the orbital radius of a satellite is quadrupled.
(a) Does the period of the satellite increase, decrease, or stay the same?
(b) By what factor does the period of the satellite change?
(c) By what factor does the orbital speed change?

Supratim Pal
Supratim Pal
Numerade Educator
02:39

Problem 47

Calculate Venus orbits the Sun with a period of $1.94 \times 10^{7} \mathrm{~s}$. What is its average distance from the Sun?

Supratim Pal
Supratim Pal
Numerade Educator
02:06

Problem 48

On the Apollo missions to the Moon, the command module orbited constantly at an altitude of $110 \mathrm{~km}$ above the lunar surface. How much time did it take for the command module to complete one orbit?

James Kiss
James Kiss
Numerade Educator
02:25

Problem 49

How much time does it take for Jupiter to complete one orbit around the Sun? Does your result depend on the mass of Jupiter?

Supratim Pal
Supratim Pal
Numerade Educator
02:23

Problem 50

A GPS satellite orbits at an altitude of $20,200 \mathrm{~km}$ above the surface of Earth. What is the speed of the satellite? (Recall that $R_{\mathrm{E}}=6.37 \times 10^{6} \mathrm{~m}$.)

Supratim Pal
Supratim Pal
Numerade Educator
View

Problem 51

When a person passes you on the street, you do not feel a gravitational tug. Explain.

Gregory Devenport
Gregory Devenport
Numerade Educator
02:27

Problem 52

What happens to the gravitational force between two masses if their separation is halved?

Hubert Agamasu
Hubert Agamasu
Numerade Educator
01:57

Problem 53

Two objects experience a gravitational attraction. Give a reason why the gravitational force between them depends on the product of their masses and not on the sum of their masses. (Hint: What happens if one of the masses goes to zero? What happens if one of the masses is doubled?)

Hubert Agamasu
Hubert Agamasu
Numerade Educator
02:30

Problem 54

Four two-mass systems are described below. Rank the systems in order of increasing gravitational force. Indicate ties where appropriate.
$$
\begin{array}{|l|c|c|c|c|}
\hline \text { System } & \text { A } & \text { B } & \text { C } & \text { D } \\
\hline \text { Mass 1 } & m & m & 2 m & 4 m \\
\hline \text { Mass 2 } & m & 2 m & 3 m & 5 m \\
\hline \text { Separation } & r & 2 r & 2 r & 3 r \\
\hline
\end{array}
$$

Supratim Pal
Supratim Pal
Numerade Educator
01:41

Problem 55

In each hand you hold a $0.16-\mathrm{kg}$ peach. What is the gravitational force exerted by one peach on the other when their separation is (a) $0.25 \mathrm{~m}$ and (b) $0.50 \mathrm{~m}$ ?

James Kiss
James Kiss
Numerade Educator
01:25

Problem 56

A $6.8-\mathrm{kg}$ bowling ball and a $7.1-\mathrm{kg}$ bowling ball rest on a rack $0.75 \mathrm{~m}$ apart. What is the force of gravity pulling each ball toward the other?

Melissa Walsh
Melissa Walsh
Numerade Educator
01:12

Problem 57

In one hand you hold a $0.11-\mathrm{kg}$ apple, in the other hand a $0.24-\mathrm{kg}$ orange. The apple and orange are separated by $0.85 \mathrm{~m}$. What is the magnitude of the force of gravity that (a) the orange exerts on the apple and (b) the apple exerts on the orange?

Hubert Agamasu
Hubert Agamasu
Numerade Educator
04:11

Problem 58

A spaceship of mass $m$ travels from Earth to the Moon along a line that passes through the center of Earth and the center of the Moon. (a) At what distance from the center of Earth does the gravitational force due to Earth have twice the magnitude of that due to the Moon? (b) How does your answer to part (a) depend on the mass of the spaceship? Explain.

Supratim Pal
Supratim Pal
Numerade Educator
03:36

Problem 59

At new moon, Earth, Moon, and Sun are in a line, as shown in Figure 9.25. Find the direction and magnitude of the net gravitational force exerted on the Moon.

Supratim Pal
Supratim Pal
Numerade Educator
05:21

Problem 60

Three 6.75-kg masses are at the corners of an equilateral triangle and located in space far from any other masses. If the sides of the triangle are $1.25 \mathrm{~m}$ long, find the magnitude of the total force exerted on each mass.

Prabhakar Kumar
Prabhakar Kumar
Numerade Educator
07:46

Problem 61

Four masses are positioned at the corners of a rectangle, as indicated in Figure 9.26. Find the magnitude and the direction of the net force acting on the $2.0-\mathrm{kg}$ mass.

Supratim Pal
Supratim Pal
Numerade Educator
03:11

Problem 62

Examine objects A, B, and C shown in Figure 9.27. Rank the objects in order of increasing net gravitational force experienced. Indicate ties where appropriate.

Supratim Pal
Supratim Pal
Numerade Educator
View

Problem 63

How does the acceleration due to gravity at the surface of a planet change if the planet's mass is doubled?

Gregory Devenport
Gregory Devenport
Numerade Educator
View

Problem 64

How does the acceleration due to gravity at the surface of a planet change if the planet's radius is doubled?

Gregory Devenport
Gregory Devenport
Numerade Educator
01:11

Problem 65

Examine the objects in Figure 9.27. Rank them in order of increasing initial acceleration if each object alone was allowed to move. Indicate ties where appropriate.

James Kiss
James Kiss
Numerade Educator
01:20

Problem 66

Titan is the largest moon of Saturn and the only moon in the solar system known to have a substantial atmosphere. Find the acceleration due to gravity at Titan's surface, given that its mass is $1.35 \times 10^{23} \mathrm{~kg}$ and its radius is $2570 \mathrm{~km}$.

Melissa Walsh
Melissa Walsh
Numerade Educator
03:14

Problem 67

Find the acceleration due to gravity at the surface of (a) Mercury, and (b) Venus.

Andy Chen
Andy Chen
Numerade Educator
02:25

Problem 68

At what altitude above Earth's surface is the acceleration due to gravity equal to $\mathrm{g} / 4$ ?

Andy Chen
Andy Chen
Numerade Educator
02:03

Problem 69

What is the acceleration due to Earth's gravity at a distance from the center of Earth equal to the orbital radius of the Moon?

Andy Chen
Andy Chen
Numerade Educator
01:50

Problem 70

A communications satellite with a mass of $480 \mathrm{~kg}$ is in a circular orbit about Earth. The radius of the orbit is $35,000 \mathrm{~km}$, measured from the center of Earth. Calculate the gravitational force exerted on the satellite by Earth.

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
01:55

Problem 71

At a certain distance from the center of Earth, a $12-\mathrm{kg}$ object has a weight of $15 \mathrm{~N}$. Find this distance.

James Kiss
James Kiss
Numerade Educator
02:40

Problem 72

In one of his novels author Jules Verne imagined that astronauts inside a spaceship walked on the floor of the cabin when the force exerted on the ship by Earth was greater than the force exerted by the Moon. When the force exerted by the Moon was greater, he thought the astronauts walked on the ceiling of the cabin. (a) At what distance from the center of Earth would the forces exerted on the spaceship by Earth and the Moon be equal? (b) Explain why Verne's description of gravitational effects is incorrect.

James Kiss
James Kiss
Numerade Educator
02:41

Problem 73

The acceleration due to gravity at the surface of Mars is $38 \%$ of the acceleration due to gravity on Earth. Given that the radius of Mars is $0.53$ of that of Earth, find the mass of Mars in terms of the mass of Earth.

Nishant Kumar
Nishant Kumar
Numerade Educator
01:02

Problem 74

Discuss the physics involved in the spin cycle of a washing machine. In particular, how is circular motion related to the removal of water from the clothes?

James Kiss
James Kiss
Numerade Educator
02:49

Problem 75

In many science fiction stories a rotating space station, like that shown in Figure $9.28$, provides "artificial gravity" for its inhabitants. How does this work?

James Kiss
James Kiss
Numerade Educator
01:48

Problem 76

A car drives with constant speed on an elliptical track, as shown in Figure 9.29. Rank the points A, B, and $C$ in order of increasing likelihood that the car might skid. Indicate ties where appropriate.

Supratim Pal
Supratim Pal
Numerade Educator
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Problem 77

A car is driven with constant speed around a circular track. Answer the following questions with "Yes" or "No". (a) Is the car's velocity constant? (b) Is its speed constant? (c) Is the magnitude of its acceleration constant? (d) Is the direction of its acceleration constant?

Gregory Devenport
Gregory Devenport
Numerade Educator
01:43

Problem 78

To test the effects of high acceleration on the human body, the National Aeronautics and Space Administration (NASA) constructed a large centrifuge at the Manned Spacecraft Center in Houston. Astronauts are placed in a capsule that moves in a circular path with a radius of $15 \mathrm{~m}$. If the astronauts in this centrifuge experience a centripetal acceleration $9.0$ times that due to gravity, what is the linear speed of the capsule?

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
01:04

Problem 79

The rotating drum in a clothes-dryer has a radius of $0.31 \mathrm{~m}$. If the acceleration at the rim of the drum is $27 \mathrm{~m} / \mathrm{s}^{2}$, what is the tangential speed of the rim?

Melissa Walsh
Melissa Walsh
Numerade Educator
01:35

Problem 80

Find the linear speed of the bottom of a test tube in a centrifuge if the centripetal acceleration there is 52,000 times the acceleration due to gravity. The distance from the axis of rotation to the bottom of the test tube is $7.5 \mathrm{~cm}$.

James Kiss
James Kiss
Numerade Educator
01:15

Problem 81

A driver takes a $1400-\mathrm{kg}$ car out for a spin, going around a corner with a radius of $63 \mathrm{~m}$ at a speed of $18 \mathrm{~m} / \mathrm{s}$. The coefficient of static friction between the car and the road

Melissa Walsh
Melissa Walsh
Numerade Educator
01:22

Problem 82

Driving in a car with a constant speed of $12 \mathrm{~m} / \mathrm{s}$, you encounter a bump in the road that has a circular crosssection, as shown in Figure 9.30. If the radius of curvature of the bump is $35 \mathrm{~m}$, find the apparent weight of a 67-kg person in your car as you pass over the top of the bump.

James Kiss
James Kiss
Numerade Educator
01:52

Problem 83

Referring to the Problem 82 , at what speed must you go over the bump in order to feel "weightless"?

Supratim Pal
Supratim Pal
Numerade Educator
01:23

Problem 84

Jill of the Jungle swings on a vine $6.9 \mathrm{~m}$ long. What is the tension in the vine if Jill, whose mass is $63 \mathrm{~kg}$, is moving at $2.4 \mathrm{~m} / \mathrm{s}$ when the vine is vertical?

Sachin Rao
Sachin Rao
Numerade Educator
04:25

Problem 85

(a) As you ride on a Ferris wheel like the one in Figure $9.31$, your apparent weight is different at the top than at the bottom. Explain.
(b) Calculate your apparent weight at the top and bottom of a Ferris wheel, given that the radius of the wheel is $7.2 \mathrm{~m}$, it completes one revolution every $28 \mathrm{~s}$, and your mass is $55 \mathrm{~kg}$.

Hubert Agamasu
Hubert Agamasu
Numerade Educator
01:12

Problem 86

Does the radius of Mars's orbit sweep out the same amount of area per time as that of Earth? Explain.

James Kiss
James Kiss
Numerade Educator
00:59

Problem 87

In 2 months a planet sweeps out the area A. How much area does it sweep out in 1 month? In 3 months?

James Kiss
James Kiss
Numerade Educator
00:53

Problem 88

Friend 1 says that an orbiting satellite is in free fall. Friend 2 disagrees, reasoning that a satellite in free fall would crash to the ground. Who is right? How would you explain this phenomenon to your friends?

James Kiss
James Kiss
Numerade Educator
01:18

Problem 89

On June 22, 1978, James Christy made the first observation of a moon orbiting Pluto. Until that time the mass of Pluto was not known, but the discovery of its moon, Charon, allowed its mass to be calculated with some accuracy. Explain.

James Kiss
James Kiss
Numerade Educator
02:02

Problem 90

One day in the future you may take a pleasure cruise to the Moon. While there you might climb a lunar mountain and throw a rock horizontally from its summit. If, in principle, you could throw the rock fast enough, it might end up hitting you in the back. Explain.

James Kiss
James Kiss
Numerade Educator
02:14

Problem 91

The force exerted by the Sun on the Moon is more than twice the force exerted by Earth on the Moon. Should the Moon be thought of as orbiting Earth or the Sun? Explain.

Supratim Pal
Supratim Pal
Numerade Educator
05:28

Problem 92

Laser reflectors left on the surface of the Moon by the Apollo astronauts show that the average distance from Earth to the Moon is increasing at the rate of $3.8 \mathrm{~cm}$ per year. (a) As a result, will the length of the month increase, decrease, or remain the same? (b) Choose the best explanation from among the following:
A. The greater the radius of an orbit, the greater the period, which implies a longer month.
B. The length of the month will remain the same because of conservation of angular momentum.
C. The speed of the Moon increases with increasing orbital radius; therefore, the length of the month will be less.

Mark J
Mark J
Numerade Educator
01:36

Problem 93

Satellites that make up the Global Positioning System, or GPS, orbit at an altitude of $2.02 \times 10^{7} \mathrm{~m}$. Find the orbital period of a GPS satellite.

James Kiss
James Kiss
Numerade Educator
02:45

Problem 94

In July of 1999 a planet was reported to be orbiting the Sun-like star Iota Horologii with a period of 320 days. Find the radius of the planet's orbit, assuming that Iota Horologii has the same mass as the Sun.

James Kiss
James Kiss
Numerade Educator
01:58

Problem 95

Phobos, one of the moons of Mars, orbits at a distance of $9378 \mathrm{~km}$ from the center of the red planet. What is the orbital period of Phobos?

Andy Chen
Andy Chen
Numerade Educator
01:23

Problem 96

The largest moon in the solar system is Ganymede, a moon of Jupiter. Ganymede orbits at a distance of $1.07 \times 10^{9} \mathrm{~m}$ from the center of Jupiter with an orbital period of about $6.18 \times 10^{5} \mathrm{~s}$. Using this information, find the mass of Jupiter.

James Kiss
James Kiss
Numerade Educator
03:23

Problem 97

(a) Calculate the orbital period of a satellite that orbits two Earth radii above the surface of Earth. (b) How does your answer to part (a) depend on the mass of the satellite? Explain.

James Kiss
James Kiss
Numerade Educator
01:33

Problem 98

The Martian moon Deimos has an orbital period that is greater than the other Martian moon, Phobos. Both moons have approximately circular orbits. (a) Is Deimos closer to or farther from Mars than

James Kiss
James Kiss
Numerade Educator
02:52

Problem 99

Find the orbital speed of a satellite in a geosynchronous circular orbit $3.58 \times 10^{7} \mathrm{~m}$ above the surface of Earth.

Andy Chen
Andy Chen
Numerade Educator
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Problem 100

What is the orbital speed of Earth around the Sun?

Gregory Devenport
Gregory Devenport
Numerade Educator
01:48

Problem 101

The asteroid 243 Ida has its own small moon, Dactyl. Ida and Dactyl are shown in Figure 9.32. (a) Outline a strategy to find the mass of 243 Ida, given that the orbital radius of Dactyl is $89 \mathrm{~km}$ and its period is $19 \mathrm{hr}$. (b) Use your strategy to calculate the mass of 243 Ida.

James Kiss
James Kiss
Numerade Educator
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Problem 102

Given that the orbital speed of a satellite depends only on $G, M_{E}$, and $r$, use dimensional analysis to find a formula for the orbital speed. (The simplest dimensionally consistent formula is the correct result.)

Gregory Devenport
Gregory Devenport
Numerade Educator
01:43

Problem 103

Two satellites orbit Earth, with satellite 1 at a greater altitude than satellite 2. (a) Which satellite has the greater orbital speed? Explain.
(b) Calculate the orbital speed of a satellite that orbits at an altitude of one Earth radius above the surface of Earth.

Anand Jangid
Anand Jangid
Numerade Educator
02:02

Problem 104

You weigh yourself on a scale inside an airplane that is flying due east above the equator. If the airplane turns around and heads due west with the same speed, will the reading on the scale increase, decrease, or stay the same?

Andy Chen
Andy Chen
Numerade Educator
02:40

Problem 105

Triple Choice A small satellite orbits at the same altitude as the International Space Station. Is the orbital speed of the satellite greater than, less than, or equal to the orbital speed of the space station? Explain.

James Kiss
James Kiss
Numerade Educator
01:57

Problem 106

The period of a planet or satellite increases with distance to the $3 / 2$ power. How does the orbital speed depend on distance? Does increasing the distance increase or decrease the orbital speed?

James Kiss
James Kiss
Numerade Educator
02:25

Problem 107

Large ships often have circular structures in their windshields, as shown in Figure $9.33$. What is their purpose? Called clearview screens, they consist of a glass disk that is rotated at high speed by a motor (in the center of the circle) to disperse rain and spray. If the screen has a diameter of $0.39 \mathrm{~m}$ and rotates at $1700 \mathrm{rpm}$, the speed at the rim of the screen is $35 \mathrm{~m} / \mathrm{s}$.
What is the centripetal acceleration at the rim of the screen? (A large centripetal acceleration will keep liquid from remaining on the screen. For comparison, recall that the acceleration due to gravity is $9.81 \mathrm{~m} / \mathrm{s}^{2}$.)

James Kiss
James Kiss
Numerade Educator
01:33

Problem 108

Some dragonflies splash down on the surface of a lake and then fly upward, spinning rapidly to spray the water off their bodies. When the dragonflies spin, they tuck themselves into a "ball."
They spin with a linear speed of $2.3 \mathrm{~m} / \mathrm{s}$ and produce a centripetal acceleration of $250 \mathrm{~m} / \mathrm{s}^{2}$. What is the radius of the ball they form?

James Kiss
James Kiss
Numerade Educator
04:03

Problem 109

Skylab, the largest spacecraft ever to fall back to Earth, met its fiery end on July 11, 1979, after flying directly over Everett, Washington, on its last orbit. On the news that night before the crash, broadcaster Walter Cronkite, in his rich baritone voice, said, "NASA says there is $a$ little chance it will land in a populated area." (Italics added.) After a commercial he immediately corrected himself, saying, "I meant to say 'there is little chance' Skylab will hit a populated area." In fact, it landed primarily in the Indian Ocean off the west coast of Australia, though several pieces were recovered near the town of Esperance, Australia, which sent the U.S. State Department a $\$ 400$ bill for littering. The cause of Skylab's crash was the friction it experienced in the upper reaches of Earth's atmosphere. As the radius of Skylab's orbit decreased, did its speed increase, decrease, or stay the same?

Mark J
Mark J
Numerade Educator
02:09

Problem 110

An astronaut exploring a distant solar system lands on an unnamed planet with a radius of $3860 \mathrm{~km}$. When the astronaut jumps upward with an initial speed of $3.10 \mathrm{~m} / \mathrm{s}$, she rises to a height of $0.580 \mathrm{~m}$. What is the mass of the planet?

James Kiss
James Kiss
Numerade Educator
02:00

Problem 111

A child sits on a rotating merry-go-round, $2.3 \mathrm{~m}$ from its center. If the speed of the child is $2.2 \mathrm{~m} / \mathrm{s}$, what is the minimum coefficient of static friction between the child and the merry-go-round that will prevent the child from slipping?

Sachin Rao
Sachin Rao
Numerade Educator
03:33

Problem 112

In the future astronauts may travel to Mars to carry out scientific explorations. As part of their mission, it is likely that a "geosynchronous" satellite will be placed above a given point on the Martian equator to facilitate communications. At what altitude above the surface of Mars should such a satellite orbit? (Note: The Martian "day" is $24.6229 \mathrm{hr}$, and the mass of Mars is $\left.6.4 \times 10^{23} \mathrm{~kg} .\right)$

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
01:26

Problem 113

A hockey puck of mass $m$ is attached to a string that passes through a hole in the center of a table, as shown in Figure 9.34. The hockey puck moves in a circle of radius $r$. Tied to the other end of the string, and hanging vertically beneath the table, is a mass $M$. Assuming that the tabletop is perfectly smooth, what speed must the hockey puck have if the mass $M$ is to remain at rest?

James Kiss
James Kiss
Numerade Educator
01:46

Problem 114

Write a report describing the operation of the global positioning system (GPS). Your report should address the following questions: How many satellites are used? What are their orbital altitudes? What are their periods? How fast do the GPS satellites move? How accurate are they?

Dominador Tan
Dominador Tan
Numerade Educator
01:13

Problem 115

If gravity has an infinite range, how is it that astronauts feel weightless in space? Is the weightlessness of an astronaut any different from the "weightlessness" you feel as you go over the top of a hill on a high-speed roller coaster? Explain.

James Kiss
James Kiss
Numerade Educator
02:37

Problem 116

Which curve in Figure $9.36$ corresponds to Comet Wild 2?
A. Curve I
B. Curve II

Mark J
Mark J
Numerade Educator
01:42

Problem 117

What is the mass of Comet Wild 2?
A. $1.1 \times 10^{8} \mathrm{~kg}$
C. $1.1 \times 10^{14} \mathrm{~kg}$
B. $1.1 \times 10^{12} \mathrm{~kg}$
D. $1.1 \times 10^{18} \mathrm{~kg}$

Supratim Pal
Supratim Pal
Numerade Educator
03:23

Problem 118

Suppose Comet Wild 2 had a small satellite, like the asteroid Ida in Figure 9.32. If this satellite were to orbit at twice the radius of the comet, what would be its period of revolution?
A. $0.93 \mathrm{~h}$
C. $5.8 \mathrm{~h}$
B. $2.9 \mathrm{~h}$
D. $8.2 \mathrm{~h}$

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator