Deck 6: Gravitation and Newtons6 Synthesis

Question 1

A thin uniform spherical shell exerts a force on a particle located outside of it as if all the shell's mass were located at the center.

Answer 1

True

Question 2

State Einstein's principle of equivalence.

Answer 2

There is no experiment observers can perform to distinguish if an acceleration arises because of a gravitational force or because their reference frame is accelerated.

Question 3

State Kepler's first law of planetary motion.

Answer 3

The path of each planet about the Sun is an ellipse with the Sun at one focus.

Question 4

Kepler's third law can be used to compare the Moon's orbit around the Earth to the orbit of the Earth around the Sun.

Question 5

An astronaut is piloting a spacecraft, which is in a circular orbit around Earth. A space station is ahead, on the same circular orbit. If he fires his rockets briefly to increase the forward speed of the rocket, what will happen?

Question 6

State Newton's Law of Universal Gravitation.

Question 7

State Kepler's third law of planetary motion.

Question 8

The acceleration of gravity can vary locally on the Earth's surface because of the presence of rocks of different densities.

Question 9

An astronaut is piloting a spacecraft, which is in a circular orbit around Earth. A space station is ahead, on the same circular orbit. If he fires his rockets briefly to decrease the forward speed of the rocket, what will happen?

Question 10

Two massive objects are fixed in position. A third object is placed directly between the first two at the position at which the total gravitational force on the third object due to the two massive objects is zero. The object is displaced slightly toward one of the two massive objects, the total gravitational force on the third object is now

A)zero.
B)in a direction which depends on which of the massive objects has a greater mass.
C)in the same direction the object is displaced.
D)in the opposite direction to the displacement of the object.
E)perpendicular to the displacement of the object.

Question 11

A thin uniform spherical shell exerts zero force on a particle located inside of the thin shell.

Question 12

The gravitational force that the Sun exerts on Earth is much larger than the gravitational force that Earth exerts on the Sun.

Question 13

Apparent weightlessness can be experienced in freely falling elevator.

Question 14

State Kepler's second law of planetary motion.

Question 15

The gravitational force exerted on a particle outside a sphere with a spherically symmetric mass distribution is the same as if the entire mass of the sphere was concentrated at its center.

Question 16

A geosynchronous satellite is one that stays above the same point on the Earth, which is possible only if it is above one of the Earth's poles.

Question 17

The reason that when an object falls towards Earth, Earth does not move toward the object, is that the force exerted by Earth on the object is so much bigger.

Question 18

List the fundamental forces in nature.

Question 19

An object is located inside a thin, uniform density spherical shell. At what locations would the object not be subject to a net gravitational force?

A)only against the inside boundary of the shell
B)only at locations on a sphere that is one-half the inside radius of the shell
C)anywhere within the shell
D)only at locations on a sphere that is one-half the mean radius of the shell
E)only at the center of the shell

Question 20

Describe how a satellite is placed into orbit and remains in orbit around the earth.

Question 21

An elevator accelerates upward with an acceleration equal to the acceleration of gravity. A ray of light emitted from one wall inside the elevation at a height h relative to the floor of the elevator will hit the opposite wall at a height (relative to the floor)

A)greater than h.
B)less than h.
C)equal to h.

Question 22

A planet of mass M has a moon of mass m in a circular orbit of radius R. An object is placed between the planet and the moon on the line joining the center of the planet to the center of the moon so that the net gravitational force on the object is zero. How far is the object placed from the center of the planet?

A)
R
B) R
C) R
D)
R
E) R

Question 23

Kepler's second law tells us that a planet sweepa out equal areas in equal times. If you compare the amount of area per time swept by Earth with the one of Jupiter, you would conclude:

A)They sweep the same area per time.
B)Jupiter sweeps a larger area per time because it has much more mass than Earth.
C)Jupiter sweeps a larger area per time because it has a much larger orbital path than Earth.
D)Earth sweeps a larger area per time because it has much less mass than Jupiter.
E)Earth sweeps a larger area per time because it has a much smaller orbital path than Jupiter.

Question 24

At their closest approach, Venus and Earth are 4.20 × 10¹⁰ m apart. The mass of Venus is 4.87 × 10²⁴ kg, the mass of Earth is 5.97 × 10²⁴ kg, and G = 6.67 x 10^-11 N•m²/kg². What is the force exerted by Venus on Earth at that point?

A)1.10 × 10¹⁸ N
B)4.62 × 10²⁸ N
C)5.43 × 10²⁶ N
D)6.30 × 10²⁰ N
E)1.72 × 10¹⁹ N

Question 25

List the four fundamental forces in nature.

A)gravitational, normal, tension, friction
B)gravitational, normal, kinetic friction, static friction
C)gravitational, electromagnetic, strong nuclear, weak nuclear
D)gravitational, electromagnetic, contact, nuclear
E)gravitational, contact, strong nuclear, weak nuclear

Question 26

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 acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the surface of Z-34 is

A)g/3.
B)3 g.
C)6 g.
D)g/9.
E)9 g.

Question 27

What is the distance from the moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal? The mass of Earth is 5.97 × 10²⁴ kg, the mass of the Moon is 7.35 × 10²² kg, the distance between Earth and the Moon is 3.84 × 10⁸ m, and G = 6.67 x 10^-11 N•m²/kg².

A)3.45 × 10⁸ m
B)3.83 × 10⁷ m
C)4.69 × 10⁶ m
D)3.83 × 10⁶ m
E)4.69 × 10⁷ m

Question 28

You ride on an elevator that is moving with constant upward acceleration while standing on a bathroom scale. The reading on the scale is

A)equal to your true weight, mg.
B)more than your true weight, mg.
C)less than your true weight, mg.
D)zero.
E)could be more or less than your true weight, mg, depending on the magnitude of the acceleration.

Question 29

According to Einstein's equivalence principle, which of the following cannot be distinguished from a system accelerating with uniform acceleration in the presence of no gravity by any measurement within the system?

A)a system moving with constant velocity in the presence of no gravitational force
B)a system that only contains massless objects
C)a system that is not accelerating, but is subject to a uniform gravitational acceleration
D)a system that is moving at the speed of light
E)a system in free fall

Question 30

A satellite of mass 500 kg orbits the Earth with a period of 6000 s. The Earth has a mass of 5.98 x 10²⁴ kg. (a) Calculate the magnitude of the Earth's gravitational force on the satellite. (b) Determine the altitude of the satellite above the Earth's surface.

Question 31

Ordinary forces, such as pushes, pulls, normal forces and friction, are considered to be due to the

A)gravitational force.
B)electromagnetic force.
C)strong nuclear force.
D)weak nuclear force.
E)contact force.

Question 32

The hydrogen atom consists of a proton of mass 1.67 × 10^-27 kg and an orbiting electron of mass 9.11 × 10^-31 kg. In one of its orbits, the electron is 5.3 × 10^-11 m from the proton. What is the mutual attractive gravitational force between the electron and proton?

A)1.8 × 10^-47 N
B)3.6 × 10^-47 N
C)5.4 × 10^-47 N
D)7.0 × 10^-47 N
E)9.3 × 10^-47 N

Question 33

The International Space Station is orbiting at an altitude of about 370 km above the earth's surface. The mass of the earth is 5.976 × 10²⁴ kg and the radius of the earth is 6.378 × 10⁶ m.
(a) Assuming a circular orbit, what is the period of the International Space Station's orbit?
(b) Assuming a circular orbit, what is the speed of the International Space Station in its orbit?

Question 34

What is the force exerted by the Sun on the earth? The mass of the Sun is 1.99 × 10³⁰ kg, the mass of the earth is 5.97 × 10²⁴ kg, the Earth-Sun distance is 1.50 × 10¹¹ m, and G = 6.67 × 10^-11 N m2/kg2.

A)5.28 × 10³³ N
B)3.52 × 10²² N
C)8.85 × 10⁸ N
D)7.25 × 10¹⁹ N
E)9.32 × 10¹¹ N

Question 35

A satellite orbits just above the Earth's surface. (a) Calculate the period of the satellite. (b) Calculate the speed of the satellite.

Question 36

You ride on an elevator that is moving upward with constant speed while standing on a bathroom scale. The reading on the scale is

A)equal to your true weight, mg.
B)more than your true weight, mg.
C)less than your true weight, mg.
D)zero.
E)could be more or less than your true weight, mg, depending on the value of the speed.

Question 37

During a lunar eclipse, the Moon, Earth, and Sun all lie on the same line, with the Earth between the Moon and the Sun. The Moon has a mass of 7.36 × 10²² kg; the Earth has a mass of 5.98 × 10²⁴ kg; and the Sun has a mass of 1.99 × 10³⁰ kg. The separation between the Moon and the Earth is given by 3.84 × 10⁸ m; the separation between the Earth and the Sun is given by 1.496 × 10¹¹ m.
(a) Calculate the force exerted on the Earth by the Moon.
(b) Calculate the force exerted on the Earth by the Sun.
(c) Calculate the net force exerted on the Earth by the Moon and the Sun.

Question 38

A spherical shell of inner diameter R and outer diameter 3R has a uniform density ρ. What is the magnitude of the gravitational acceleration a distance 2R from the center of the spherical shell?

A)15πGρR/7
B)32πGρR/5
C)25πGρR/12
D)7πGρR/6
E)7πGρR/3

Question 39

Because Earth's orbit is slightly elliptical, Earth actually gets closer to the Sun during part of the year. When Earth is closer to the Sun its orbital speed is

A)less than when Earth is farthest away from the Sun.
B)the same as when Earth is farthest away from the Sun.
C)greater than when Earth is farthest away from the Sun.
D)sometimes greater sometimes smaller than when Earth is farthest away from the Sun.

Question 40

An object with mass m is located halfway between an object of mass M and an object of mass 3M that are separated by a distance d. What is the magnitude of the force on the object with mass m?

A)8GMm/d²
B)4GMm/d²
C)3GMm/2d²
D)GMm/(2d²)
E)GMm/(4d²)

Question 41

Uranus completes one revolution about its own axis every 17.24 hours. What is the radius of the orbit required for a satellite to revolve about Uranus with the same period? Uranus has a mass of 8.69 × 10²⁵ kg and G = 6.67 x 10^-11 N•m²/kg².

A)8.27 × 10⁷ m
B)3.41 × 10⁸ m
C)2.56 × 10⁸ m
D)9.03 × 10⁷ m
E)1.04 × 10⁷ m

Question 42

The mass of the Moon is 7.4 × 10²² kg and its mean radius is 1.75 × 10³ km. What is the acceleration due to gravity at the surface of the Moon?

A)2.8 × 10⁶ m/s²
B)9.8 m/s²
C)4.9 m/s²
D)1.6 m/s²
E)0.80 m/s²

Question 43

Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

A)20 days
B)40 days
C)80 days
D)160 days
E)320 days

Question 44

Jupiter completes one revolution about its own axis every 9.92 hours. What is the radius of the orbit required for a satellite to revolve about Jupiter with the same period? Jupiter has a mass of 1.90 × 10²⁷ kg and G = 6.67 x 10^-11 N•m²/kg².

A)1.04 × 10⁷ m
B)2.26 × 10⁹ m
C)1.60 × 10⁸ m
D)3.41 × 10⁸ m
E)7.45 × 10⁸ m

Question 45

The moons of Mars, Phobos (Fear) and Deimos (Terror), are very close to the planet compared to Earth's Moon. Their orbital radii are 9,378 km and 23,459 km respectively. What is the ratio of the orbital speed of Phobos to that of Deimos?

A)0.2528
B)0.3998
C)1.582
D)2.858
E)3.956

Question 46

At what altitude should a satellite be placed into circular orbit so that its orbital period is 48.0 hours? The mass of the earth is 5.976 × 10²⁴ kg and the radius of the earth is 6.378 × 10⁶ m.

A)4.22 × 10⁷ m
B)7.58 × 10⁷ m
C)8.22 × 10⁷ m
D)6.07 × 10⁷ m
E)6.71 × 10⁷ m

Question 47

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 10⁷ m. The second planet has an orbital radius 3.00 × 10⁷ m. What is the period of the second satellite?

A)60.8 hours
B)12.0 hours
C)33.1 hours
D)9.80 hours
E)27.0 hours

Question 48

The gravitational acceleration on a planet's surface is 16.00 m/s². What is the gravitational acceleration at distance of one planet diameter above the surface of the planet?

A)5.33 m/s²
B)1.78 m/s²
C)1.60 m/s²
D)4.00 m/s²
E)8.00 m/s²

Question 49

The radius of the Earth is R. At what distance above the Earth's surface will the acceleration of gravity be 4.9 m/s²?

A)0.41 R
B)0.50 R
C)1.0 R
D)1.4 R
E)2.0 R

Question 50

By how many newtons does the weight of a 100-kg person change when he goes from sea level to an altitude of 5000 m? (The mean radius of the Earth is 6.38 × 10⁶ m.)

A)0.6 N
B)1.6 N
C)2.6 N
D)3.6 N
E)5.2 N

Question 51

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 10⁷ m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite?

A)4.50 × 10⁷ m
B)3.90 × 10⁷ m
C)9.24 × 10⁷ m
D)8.00 × 10⁷ m
E)7.27 × 10⁷ m

Question 52

A 2.00 × 10⁸-kg mass is located at x = 100 m, y = 0.00 m. A 5.00 × 10⁸-kg mass is located at x = 0.00 m, y = 200 m. Determine the gravitational force on a 3.00-kg mass located at x = 0.00 m, y = 0.00 m.

A)4.00 × 10^-4 N - 5.00 × 10^-4 N

B)4.00 × 10^-4 N + 5.00 × 10^-4 N

C)-4.00 × 10^-4 N + 5.00 × 10^-4 N

D)4.00 × 10^-6 N - 2.50 × 10^-6 N

E)4.00 × 10^-6 N + 2.50 × 10^-6 N

Question 53

The moons of Mars, Phobos (Fear) and Deimos (Terror), are very close to the planet compared to Earth's Moon. Their orbital radii are 9,378 km and 23,459 km respectively. What is the ratio of the period of revolution of Phobos to that of Deimos?

A)0.2528
B)0.3998
C)1.582
D)2.858
E)3.956

Question 54

You are on an airplane traveling with a constant velocity at an altitude of 20,000 m. What is the acceleration of gravity at that altitude? The radius of Earth is 6.37 × 10⁶ m.

A)9.81 m/s²
B)9.78 m/s²
C)9.75 m/s²
D)9.72 m/s²
E)9.69 m/s²

Question 55

Three identical 50-kg masses are held at the corners of an equilateral triangle, 30 cm on each side. If one of the masses is released, what is its initial acceleration, if the only forces acting on it are the gravitational forces due to the other two masses?

A)3.7 × 10^-8 m/s²
B)2.5 × 10^-8 m/s²
C)1.9 × 10^-8 m/s²
D)4.2 × 10^-8 m/s²
E)6.4 × 10^-8 m/s²

Question 56

What is the period of a satellite circling Mars 100 km above the planet's surface? The mass of Mars is 6.42 × 10²³ kg, its radius is 3.40 × 10⁶ m, and G = 6.67 × 10^-11 m³/kg/s².

A)1.75 hours
B)1.25 hours
C)1.15 hours
D)1.00 hours
E)1.45 hours

Question 57

A spherical shell of inner diameter R and outer diameter 3R has a uniform density ρ. What is the magnitude of the gravitational acceleration a distance 4R from the center of the spherical shell?

A)7πGρR/6
B)104πGρR/3
C)27πGρR/12
D)27πGρR/3
E)13πGρR/6

Question 58

Neptune circles the Sun at a distance of 4.50 × 10¹² m once every 164 years. Saturn circles the Sun at a distance of 1.43 × 10¹² m. What is the orbital period of Saturn?

A)304 years
B)121 years
C)109 years
D)88.6 years
E)29.4 years

Question 59

A 36.0-kg child steps on a scale in an elevator. The scale reads 400 N. What is the magnitude of the acceleration of the elevator?

A)4.91 m/s²
B)9.81 m/s²
C)46.9 m/s²
D)0.206 m/s²
E)1.30 m/s²

Question 60

You have discovered a new asteroid, which has a moon in an elliptical orbit around it. From a series of observations, you establish that the closest approach occurs when the moon is 49,000 m from the asteroid, the furthest separation is 98,000 m, and the speed of the moon at the point of closest approach is 7.50 m/s. What is the mass of the asteroid? G = 6.67 x 10^-11 N•m²/kg².

A)4.25 × 10¹⁶ kg
B)9.87 × 10¹⁶ kg
C)3.10 × 10¹⁶ kg
D)2.04 × 10¹⁶ kg
E)5.05 × 10¹⁶ kg

Question 61

A light beam traveling horizontally enters a hole in the side of a laboratory on planet X. The laboratory is 40.0 m wide. If the light beam hits the far wall a distance 0.20 mm below the height it entered the laboratory, what is the acceleration of gravity on planet X?

A)2.25 × 10¹⁰ m/s²
B)8.00 × 10⁶ m/s²
C)9.81 m/s²
D)4.50 × 10⁵ m/s²
E)3.75 × 10³ m/s²

Question 62

Assuming that the gravitational acceleration is constant and equal, in magnitude, to the acceleration of gravity at the surface of the earth, how far would light deflect from a straight line path as it travels one Earth diameter, 1.28 × 10⁷ m?

A)25.4 cm
B)8.94 mm
C)3.14 m
D)1.77 cm
E)12.7 cm

Question 63

A satellite is in a circular parking orbit 6.98 × 10⁶ m from the center of Earth. To initiate a Hohmann transfer, a rocket gives it an accelerating thrust so that its speed is increased to 8300 m/s. How far from the center of Earth will the satellite be when it reaches its apogee? The mass of Earth is 5.97 × 10²⁴ kg and G = 6.67 x 10^-11 N•m²/kg².

A)3.12 × 10⁷ m
B)2.48 × 10⁷m
C)1.06 × 10⁷m
D)6.73 × 10⁷m
E)4.75 × 10⁷m

Question 64

Sputnik I was launched into orbit around Earth in 1957. It had a perigee (the closest approach to Earth, measured from Earth's center) of 6.81 × 10⁶ m and an apogee (the furthest point from Earth's center) of 7.53 × 10⁶ m. What was its speed when it was at its perigee? The mass of Earth is 5.97 × 10²⁴ kg and
G = 6.67 x 10^-11 N•m²/kg².

A)7.18 × 10³ m/s
B)7.84 × 10³ m/s
C)8.23 × 10³ m/s
D)11.0 × 10³ m/s
E)13.4 × 10³ m/s