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Physics: Principles with Applications

Douglas C. Giancoli

Chapter 5

CIRCULAR MOTION; GRAVITATION - all with Video Answers

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Chapter Questions

01:49

Problem 1

(I) A child sitting 1.20 m from the center of a merry-go-round moves with a speed of 1.10 m/s. Calculate ($a$) the centripetal acceleration of the child and ($b$) the net horizontal force exerted on the child (mass $=$ 22.5 kg).

Keshav Singh
Keshav Singh
Numerade Educator
03:10

Problem 2

(I) A jet plane traveling 1890 km/h (525 m/s)pulls out of a dive by moving in an arc of radius 5.20 km. What is the plane's acceleration in $g$'s?

Netra Sharma
Netra Sharma
University of Wisconsin - Milwaukee
01:59

Problem 3

(I) A horizontal force of 310 N is exerted on a 2.0-kg ball as it rotates (at arm's length) uniformly in a horizontal circle of radius 0.90 m. Calculate the speed of the ball.

Rachel Wellington
Rachel Wellington
University of Georgia
07:32

Problem 4

II) What is the magnitude of the acceleration of a speck of clay on the edge of a potter's wheel turning at 45 rpm (revolutions per minute) if the wheel's diameter is 35 cm?

Netra Sharma
Netra Sharma
University of Wisconsin - Milwaukee
01:52

Problem 5

(II) A 0.55-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N, what is the maximum speed the ball can have?

Rachel Wellington
Rachel Wellington
University of Georgia
06:22

Problem 6

(II) How fast (in rpm) must a centrifuge rotate if a particle 7.00 cm from the axis of rotation is to experience an acceleration of 125,000 $g$'s?

Netra Sharma
Netra Sharma
University of Wisconsin - Milwaukee
01:40

Problem 7

(II) A car drives straight down toward the bottom of a valley and up the other side on a road whose bottom has a radius of curvature of 115 m.At the very bottom, the normal force on the driver is twice his weight. At what speed was the car traveling?

Suzanne W.
Suzanne W.
Numerade Educator
02:13

Problem 8

(II) How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 125 m at a speed of 95 km/h?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:31

Problem 9

(II) What is the maximum speed with which a 1200-kg car can round a turn of radius 90.0 m on a flat road if the coefficient of friction between tires and road is 0.65? Is this result independent of the mass of the car?

Rachel Wellington
Rachel Wellington
University of Georgia
08:16

Problem 10

(II) A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.20 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N. ($a$) Find the speed of the bucket. ($b$) How fast must the bucket move at the top of the circle so that the rope does not go slack?

Donald Albin
Donald Albin
Numerade Educator
02:41

Problem 11

(II) How many revolutions per minute would a 25-m-diameter Ferris wheel need to make for the passengers to feel "weightless" at the topmost point?

Nishant Kumar
Nishant Kumar
Numerade Educator
07:47

Problem 12

(II) A jet pilot takes his aircraft in a vertical loop (Fig. 5-38). ($a$) If the jet is moving at a speed of 840 km/h at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 $g$'s. ($b$) Calculate the 78-kg pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle, and ($c$) at the top of the circle (assume the same speed). FIGURE 5-38(Figure Cant copy)

Dading Chen
Dading Chen
Numerade Educator
06:52

Problem 13

(II) A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire), Fig. 5-39. The circle formed by the tube has a diameter of 1.1 km.What must be the rotation speed (revolutions per day) if an effect nearly equal to gravity at the surface of the Earth (say, 0.90 $g$) is to be felt? FIGURE 5-39(Figure Cant copy)

Donald Albin
Donald Albin
Numerade Educator
01:20

Problem 14

(II) On an ice rink two skaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 55.0 kg, how hard are they pulling on one another?

Sachin Rao
Sachin Rao
Numerade Educator
03:57

Problem 15

(II) A coin is placed 13.0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 38.0 rpm (revolutions per minute) is reached, at which point the coin slides off. What is the coefficient of static friction between the coin and the turntable?

Rachel Wellington
Rachel Wellington
University of Georgia
06:41

Problem 16

(II) The design of a new road includes a straight stretch that is horizontal and flat but that suddenly dips down a steep hill at 18$^\circ$. The transition should be rounded with what minimum radius so that cars traveling 95 km/h will not leave the road (Fig. 5-40)?
FIGURE 5-40(Figure Cant copy)

João Gabriel Alencar Caribé
João Gabriel Alencar Caribé
Numerade Educator
04:51

Problem 17

(II) Two blocks, with masses $m_A$ and $m_B$ are connected to each other and to a central post by thin rods as shown in Fig. 5-41. The blocks revolve about the post at the same frequency $f$ (revolutions per second) on a frictionless horizontal surface at distances $r_A$ and $r_B$ from the post. Derive an algebraic expression for the tension in each rod. FIGURE 5-41(Figure Cant copy)

Keshav Singh
Keshav Singh
Numerade Educator
01:35

Problem 18

(II) Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 5-42). If his arms are capable of exerting a force of 1150 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 78 kg and the vine is 4.7 m long. FIGURE 5-42(Figure Cant copy)

Dading Chen
Dading Chen
Numerade Educator
04:31

Problem 19

(II) A 975-kg sports car (including driver) crosses the rounded top of a hill (radius $=$ 88.0 m) at 18.0 m/s. Determine ($a$) the normal force exerted by the road on the car, ($b$) the normal force exerted by the car on the 62.0-kg driver, and ($c$) the car speed at which the normal force on the driver equals zero.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:35

Problem 20

(II) Highway curves are marked with a suggested speed. If this speed is based on what would be safe in wet weather, estimate the radius of curvature for an unbanked curve marked 50 km/h. Use Table 4-2 (coefficients of friction).

Dading Chen
Dading Chen
Numerade Educator
01:42

Problem 21

(III) A pilot performs an evasive maneuver by diving vertically at 270 m/s. If he can withstand an acceleration of 8.0 $g$'s without blacking out, at what altitude must he begin to pull his plane out of the dive to avoid crashing into the sea?

Rachel Wellington
Rachel Wellington
University of Georgia
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Problem 22

(III) If a curve with a radius of 95 m is properly banked for a car traveling 65 km/h, what must be the coefficient of static friction for a car not to skid when traveling at 95 km/h?

DS
Doug Shields
Numerade Educator
11:59

Problem 23

(III) A curve of radius 78 m is banked for a design speed of 85 km/h. If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely make the curve? [$Hint$: Consider the direction of the friction force when the car goes too slow or too fast.]

Keshav Singh
Keshav Singh
Numerade Educator
02:12

Problem 24

(I) Determine the tangential and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 15 m/s. The car's mass is 950 kg.

Keshav Singh
Keshav Singh
Numerade Educator
09:46

Problem 25

(II) A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 270 km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the arc, assuming constant tangential acceleration. If the curve were flat, what coefficient of static friction would be necessary between the tires and the road to provide this
acceleration with no slipping or skidding?

Rachel Wellington
Rachel Wellington
University of Georgia
02:26

Problem 26

(II) For each of the cases described below, sketch and label the total acceleration vector, the radial acceleration vector, and the tangential acceleration vector. ($a$) A car is accelerating from 55 km/h to 70 km/h as it rounds a curve of constant radius. ($b$) A car is going a constant as it rounds a curve of constant radius. ($c$) A car slows down while rounding a curve of constant radius.

Bethany Campbell
Bethany Campbell
Numerade Educator
04:23

Problem 27

(III) A particle revolves in a horizontal circle of radius 1.95 m. At a particular instant, its acceleration is 1.05 m/s$^2$, in a direction that makes an angle of 25.0$^\circ$ to its direction of motion. Determine its speed ($a$) at this moment, and ($b$) 2.00 s later, assuming constant tangential acceleration.

Rachel Wellington
Rachel Wellington
University of Georgia
01:14

Problem 28

(I) Calculate the force of Earth's gravity on a spacecraft 2.00 Earth radii above the Earth's surface if its mass is 1850 kg.

Keshav Singh
Keshav Singh
Numerade Educator
02:06

Problem 29

(I) At the surface of a certain planet, the gravitational acceleration $g$ has a magnitude of 12.0 m/s$^2$. A 24.0-kg brass ball is transported to this planet.What is ($a$) the mass of the brass ball on the Earth and on the planet, and ($b$) the weight of the brass ball on the Earth and on the planet?

Rachel Wellington
Rachel Wellington
University of Georgia
02:22

Problem 30

(II) At what distance from the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull in opposite directions with equal force?

Suzanne W.
Suzanne W.
Numerade Educator
04:47

Problem 31

(II) Two objects attract each other gravitationally with a force of 2.5 $\times$ 10$^{-10}$ N when they are 0.25 m apart. Their total mass is 4.00 kg. Find their individual masses.

Rachel Wellington
Rachel Wellington
University of Georgia
03:44

Problem 32

(II) A hypothetical planet has a radius 2.0 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

Dading Chen
Dading Chen
Numerade Educator
02:49

Problem 33

(II) Calculate the acceleration due to gravity on the Moon, which has radius 1.74 $\times$ 10$^6$ m and mass 7.35 $\times$ 10$^{22}$ kg.

Rachel Wellington
Rachel Wellington
University of Georgia
07:15

Problem 34

(II) Estimate the acceleration due to gravity at the surface of Europa (one of the moons of Jupiter) given that its mass is 4.9 $\times$ 10$^{22}$ kg and making the assumption that its mass per unit volume is the same as Earth's.

Dading Chen
Dading Chen
Numerade Educator
03:15

Problem 35

(II) Given that the acceleration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars' radius is 3400 km, determine the mass of Mars.

Rachel Wellington
Rachel Wellington
University of Georgia
07:13

Problem 36

(II) Find the net force on the Moon ($m_M = 7.35 \times 10^{22}$ kg) due to the gravitational attraction of both the Earth ($m_E = 5.98 \times 10^{24}$ kg) and the Sun ($m_S = 1.99 \times 10^{30}$ kg), assuming they are at right angles to each other, Fig. 5-43. FIGURE 5-43(Figure Cant copy)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:46

Problem 37

(II) A hypothetical planet has a mass 2.80 times that of Earth, but has the same radius. What is $g$ near its surface?

Rachel Wellington
Rachel Wellington
University of Georgia
01:26

Problem 38

(II) If you doubled the mass and tripled the radius of a planet, by what factor would g at its surface change?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
04:54

Problem 39

(II) Calculate the effective value of $g$, the acceleration of gravity, at ($a$) 6400 m, and ($b$) 6400 km, above the Earth's surface.

Rachel Wellington
Rachel Wellington
University of Georgia
05:16

Problem 40

(II) You are explaining to friends why an astronaut feels weightless orbiting in the space shuttle, and they respond that they thought gravity was just a lot weaker up there. Convince them that it isn't so by calculating how much weaker (in %) gravity is 380 km above the Earth's surface.

Kunal Patel
Kunal Patel
Numerade Educator
11:04

Problem 41

(II) Every few hundred years most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line, Fig. 5-44. The masses are $m_V = 0.815 m_E , m_J = 318 m_E , m_{Sat} = 95.1 m_E$ and the mean distances of the four planets from the Sun are 108, 150, 778, and 1430 million km. What fraction of the Sun's force on the Earth is this? FIGURE 5-44(Figure Cant copy)

Rachel Wellington
Rachel Wellington
University of Georgia
05:09

Problem 42

(II) Four 7.5-kg spheres are located at the corners of a square of side 0.80 m. Calculate the magnitude and direction of the gravitational force exerted on one sphere by the other three.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:06

Problem 43

(II) Determine the distance from the Earth's center to a point outside the Earth where the gravitational acceleration due to the Earth is ${1\over10}$ of its value at the Earth's surface.

Rachel Wellington
Rachel Wellington
University of Georgia
05:17

Problem 44

(II) A certain neutron star has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster.

Artemisa Mazón
Artemisa Mazón
Numerade Educator
02:43

Problem 45

(I) A space shuttle releases a satellite into a circular orbit 780 km above the Earth. How fast must the shuttle be moving (relative to Earth's center) when the release occurs?

Rachel Wellington
Rachel Wellington
University of Georgia
11:12

Problem 46

(I) Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 4800 km.

Rahul Sharma
Rahul Sharma
Numerade Educator
02:20

Problem 47

(II) You know your mass is 62 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 77 kg. What is the acceleration of the elevator, and in which direction?

Rachel Wellington
Rachel Wellington
University of Georgia
01:01

Problem 48

(II) A 12.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 185 N and breaks as the elevator accelerates. What was the elevator's minimum acceleration (magnitude and direction)?

Matt Braby
Matt Braby
Numerade Educator
04:32

Problem 49

(II) Calculate the period of a satellite orbiting the Moon, 95 km above the Moon's surface. Ignore effects of the Earth. The radius of the Moon is 1740 km.

Rachel Wellington
Rachel Wellington
University of Georgia
07:40

Problem 50

(II) Two satellites orbit Earth at altitudes of 7500 km and 15,000 km above the Earth's surface.Which satellite is faster, and by what factor?

Robert Curtis
Robert Curtis
Numerade Educator
03:55

Problem 51

(II) What will a spring scale read for the weight of a 58.0-kg woman in an elevator that moves ($a$) upward with constant speed 5.0 m/s, ($b$) downward with constant speed 5.0 m/s, ($c$) with an upward acceleration 0.23 $g$, ($d$) with a downward acceleration 0.23 $g$, and ($e$) in free fall?

Keshav Singh
Keshav Singh
Numerade Educator
04:09

Problem 52

(II) Determine the time it takes for a satellite to orbit the Earth in a circular $\textbf{near-Earth orbit}$. A "near-Earth" orbit is at a height above the surface of the Earth that is very small compared to the radius of the Earth. [$Hint$: You may take the acceleration due to gravity as essentially the same as that on the surface.] Does your result depend on the mass of the satellite?

Kon Aoki
Kon Aoki
Numerade Educator
02:44

Problem 53

(II) What is the apparent weight of a 75-kg astronaut 2500 km from the center of the Moon in a space vehicle ($a$) moving at constant velocity and ($b$) accelerating toward the Moon at 1.8 m/s$^2$? State "direction" in each case.

Narayan Hari
Narayan Hari
Numerade Educator
03:25

Problem 54

(II) A Ferris wheel 22.0 m in diameter rotates once every 12.5 s (see Fig. 5-9).What is the ratio of a person's apparent weight to her real weight at ($a$) the top, and ($b$) the bottom?

EK
Edison King
Numerade Educator
02:29

Problem 55

(II) At what rate must a cylindrical spaceship rotate if occupants are to experience simulated gravity of 0.70 $g$? Assume the spaceship's diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 9, Fig 5-33.)

Rachel Wellington
Rachel Wellington
University of Georgia
06:15

Problem 56

(III) ($a$) Show that if a satellite orbits very near the surface of a planet with period $T$, the density ( $=$ mass per unit volume) of the planet is $\rho = m/V = 3\pi /GT^2$. ($b$) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of 85 min. Approximate the Earth as a uniform sphere.

Matthew Miranda
Matthew Miranda
Numerade Educator
02:00

Problem 57

(I) Neptune is an average distance of 4.5 $\times$ 10$^9$ km from the Sun. Estimate the length of the Neptunian year using the fact that the Earth is 1.50 $\times$ 10$^8$ km from the Sun on average.

Krystal K
Krystal K
Numerade Educator
01:22

Problem 58

(I) The $asteroid$ Icarus, though only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:15

Problem 59

(I) Use Kepler's laws and the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth's surface.

Rachel Wellington
Rachel Wellington
University of Georgia
02:57

Problem 60

(II) Determine the mass of the Earth from the known period and distance of the Moon.

Keshav Singh
Keshav Singh
Numerade Educator
03:27

Problem 61

(II) Our Sun revolves about the center of our Galaxy ($m_G \approx 4 \times 10^{41} kg$) at a distance of about 3 $\times$ 10$^4$ light years [$1 ly = (3.00 \times 10^8 m/s) \cdot (3.16 \times 10^7 s/yr) \cdot (1.00 yr)$ D.What is the period of the Sun's orbital motion about the center of the Galaxy?

Rachel Wellington
Rachel Wellington
University of Georgia
03:55

Problem 62

(II) Table 5-3 gives the mean distance, period, and mass for the four largest moons of Jupiter (those discovered by Galileo in 1609). Determine the mass of Jupiter: ($a$) using the data for Io; ($b$) using data for each of the other three moons. Are the results consistent?

BG
Bernd Geels
Numerade Educator
04:31

Problem 63

(II) Determine the mean distance from Jupiter for each of Jupiter's principal moons, using Kepler's third law. Use the distance of Io and the periods given in Table 5-3. Compare your results to the values in Table 5-3.

Rachel Wellington
Rachel Wellington
University of Georgia
01:27

Problem 64

(II) Planet A and planet B are in circular orbits around a distant star. Planet A is 7.0 times farther from the star than is planet B. What is the ratio of their speeds $v_A/v_B$ ?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:42

Problem 65

(II) $Halley's$ $comet$ orbits the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5-45). Estimate the greatest distance of the comet from the Sun. Is it still "in" the solar system? What planet's orbit is nearest when it is out there? FIGURE 5-45(Figure Cant copy)

Rachel Wellington
Rachel Wellington
University of Georgia
02:39

Problem 66

The $comet$ $Hale-Bopp$ has an orbital period of 2400 years. ($a$) What is its mean distance from the Sun? ($b$) At its closest approach, the comet is about 1.0 AU from the Sun (1 AU $=$ distance from Earth to the Sun). What is the farthest distance? ($c$) What is the ratio of the speed at the closest point to the speed at the farthest point?

Dading Chen
Dading Chen
Numerade Educator
View

Problem 67

Calculate the centripetal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50 $\times$ 10$^{11}$ m.

Ankur S
Ankur S
Numerade Educator
01:05

Problem 68

A flat puck (mass $M$) is revolved in a circle on a frictionless air hockey table top, and is held in this orbit by a massless cord which is connected to a dangling mass (mass $m$) through a central hole as shown in Fig. 5-46. Show that the speed of the puck is given by $v = \sqrt{mgR/M}$. FIGURE 5-46(Figure Cant copy)

Dading Chen
Dading Chen
Numerade Educator
02:37

Problem 69

A device for training astronauts and jet fighter pilots is designed to move the trainee in a horizontal circle of radius 11.0 m. If the force felt by the trainee is 7.45 times her own weight, how fast is she revolving? Express your answer in both m/s and rev/s.

Rachel Wellington
Rachel Wellington
University of Georgia
04:43

Problem 70

A 1050-kg car rounds a curve of radius 72 m banked at an angle of 14$^\circ$. If the car is traveling at 85 km/h, will a friction force be required? If so, how much and in what direction?

Dading Chen
Dading Chen
Numerade Educator
03:38

Problem 71

In a "Rotor-ride" at a carnival, people rotate in a vertical cylindrically walled "room." (See Fig. 5-47.) If the room radius is 5.5 m, and the rotation frequency 0.50 revolutions per second when the floor drops out, what minimum coefficient of static friction keeps the people from slipping down? People on this ride said they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides nausea)? [$Hint$: Draw a free-body diagram for a person.]

Averell Hause
Averell Hause
Carnegie Mellon University
03:22

Problem 72

While fishing, you get bored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.75 s. What is the angle that the fishing line makes with the vertical? [$Hint$: See Fig. 5-10.]

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:47

Problem 73

At what minimum speed must a roller coaster be traveling so that passengers upside down at the top of the circle (Fig. 5-48) do not fall out? Assume a radius of curvature of 8.6 m. FIGURE 5-48(Figure Cant copy)

Rachel Wellington
Rachel Wellington
University of Georgia
05:13

Problem 74

Consider a train that rounds a curve with a radius of 570 m at a speed of 160 km/h (approximately 100 mi/h ). ($a$) Calculate the friction force needed on a train passenger of mass 55 kg if the track is not banked and the train does not tilt. ($b$) Calculate the friction force on the passenger if the train tilts at an angle of 8.0$^\circ$ toward the center of the curve.

Supratim Pal
Supratim Pal
Numerade Educator
04:34

Problem 75

Two equal-mass stars maintain a constant distance apart of 8.0 $\times$ 10$^{11}$ m and revolve about a point midway between them at a rate of one revolution every 12.6 yr. ($a$) Why don't the two stars crash into one another due to the gravitational force between them? ($b$) What must be the mass of each star?

Averell Hause
Averell Hause
Carnegie Mellon University
06:10

Problem 76

How far above the Earth's surface will the acceleration of gravity be half what it is at the surface?

Hong Joo Ryoo
Hong Joo Ryoo
Numerade Educator
02:15

Problem 77

Is it possible to whirl a bucket of water fast enough in a vertical circle so that the water won't fall out? If so, what is the minimum speed? Define all quantities needed.

Averell Hause
Averell Hause
Carnegie Mellon University
02:24

Problem 78

How long would a day be if the Earth were rotating so fast that objects at the equator were apparently weightless?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:12

Problem 79

The $rings$ $of$ $Saturn$ are composed of chunks of ice that orbit the planet. The inner radius of the rings is 73,000 km, and the outer radius is 170,000 km. Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's own rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times$ 10$^{26}$ kg.

Averell Hause
Averell Hause
Carnegie Mellon University
05:00

Problem 80

During an $Apollo$ lunar landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once?

Youssef Eweis
Youssef Eweis
Numerade Educator
02:17

Problem 81

The $\textbf{Navstar Global Positioning System}$ (GPS) utilizes a group of 24 satellites orbiting the Earth. Using "triangulation" and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed around the Earth, allowing continuous navigational "fixes." The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical mile $=$ 1.852 km $=$ 6076 ft].($a$) Determine the speed of each satellite. ($b$) Determine the period of each satellite.

Averell Hause
Averell Hause
Carnegie Mellon University
05:55

Problem 82

The $Near$ $Earth$ $Asteroid$ $Rendezvous$ (NEAR) spacecraft, after traveling 2.1 billion km, is meant to orbit the asteroid Eros with an orbital radius of about 20 km. Eros is roughly 40 km $\times$ 6 km $\times$ 6 km. Assume Eros has a density (mass/volume) of about 2.3 $\times$ 10$^3$ kg/m$^3$.($a$) If Eros were a sphere with the same mass and density, what would its radius be? ($b$) What would g be at the surface of a spherical Eros? ($c$) Estimate the orbital period of $NEAR$ as it orbits Eros, as if Eros were a sphere.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:15

Problem 83

A train traveling at a constant speed rounds a curve of radius 215 m. A lamp suspended from the ceiling swings out to an angle of 16.5$^\circ$ throughout the curve. What is the speed of the train?

Averell Hause
Averell Hause
Carnegie Mellon University
03:59

Problem 84

The Sun revolves around the center of the $Milky$ $Way$ $Galaxy$ (Fig. 5-49) at a distance of about 30,000 light-years from the center (1 ly $=$ 9.5 $\times$ 10$^{15}$ m). If it takes about 200 million years to make one revolution, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun (2 $\times$ 10$^{30}$ kg), how many stars would there be in our Galaxy? FIGURE 5-49(Figure Cant copy)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:48

Problem 85

A satellite of mass 5500 kg orbits the Earth and has a period of 6600 s. Determine ($a$) the radius of its circular orbit, ($b$) the magnitude of the Earth's gravitational force on the satellite, and ($c$) the altitude of the satellite.

Supratim Pal
Supratim Pal
Numerade Educator
04:18

Problem 86

Astronomers using the Hubble Space Telescope deduced the presence of an extremely massive core in the distant $galaxy$ M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 km/s at a distance of 60 light-years ($=$5.7 $\times$ 10$^{17}$ m) from the core. Deduce the mass of the core, and compare it to the mass of our Sun.

Melissa Munoz
Melissa Munoz
Numerade Educator
02:48

Problem 87

Suppose all the mass of the Earth were compacted into a small spherical ball. What radius must the sphere have so that the acceleration due to gravity at the Earth's new surface would equal the acceleration due to gravity at the surface of the Sun?

Rachel Wellington
Rachel Wellington
University of Georgia
02:49

Problem 88

A science-fiction tale describes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-50). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate livable), and that the ring rotates quickly enough to produce an apparent gravity of $g$ as on Earth. What will be the period of revolution, this planet's year, in Earth days? FIGURE 5-50(Figure Cant copy)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:56

Problem 89

An asteroid of mass $m$ is in a circular orbit of radius $r$ around the Sun with a speed $v$. It has an impact with another asteroid of mass $M$ and is kicked into a new circular orbit with a speed of 1.5 $v$.What is the radius of the new orbit in terms of $r$?

Rachel Wellington
Rachel Wellington
University of Georgia
02:35

Problem 90

Use $\textbf{dimensional analysis}$ (Section 1-8) to obtain the form for the centripetal acceleration,$a_R = v^2/r$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator