Conceptual Physics Fundamentals

Paul G. Hewitt

Chapter 7

Gravity, Projectiles, and Satellites - all with Video Answers

Educators

Chapter Questions

Problem 1

Comment on whether or not the following label on a consumer product should be cause for concern.
CAUTION: The mass of this product pulls on every other mass in the universe, with an attracting force that is proportional to the product of the masses and inversely proportional to the square of the distance between them.

Mathis Ernst

Mathis Ernst

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Problem 2

Gravitational force acts on all bodies in proportion to their masses. Why, then, doesn't a heavy body fall faster than a light body?

Km Neeraj

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Problem 3

Is the force of gravity stronger on a piece of iron than it is on a piece of wood if both have the same mass? Defend your answer.

Salamat Ali

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Problem 4

Is the force of gravity stronger on a crumpled piece of paper than on an identical piece of paper that has not been crumpled? Defend your answer.

Mathis Ernst

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Problem 5

A friend says that astronauts in orbit are weightless because they're beyond the pull of Earth's gravity. Correct your friend's ignorance.

Km Neeraj

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Problem 6

Somewhere between Earth and the Moon, gravity from these two bodies on a space pod would cancel. Is this location nearer to Earth or to the Moon?

Salamat Ali

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Problem 7

Is the acceleration due to gravity more or less atop $\mathrm{Mt}$. Everest than it is at sea level? Defend your answer.

Luis Rios

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Problem 8

An astronaut lands on a planet that has the same mass as Earth but twice the diameter. How does the astronaut's weight differ from that on Earth?

Km Neeraj

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Problem 9

An astronaut lands on a planet that has twice Earth's and twice Earth's diameter. How does the astronaut's weight differ from that on Earth?

Km Neeraj

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Problem 10

If Earth somehow expanded to a larger radius, with no change in mass, how would your weight be affected? How would it be affected if instead Earth shrunk?

Salamat Ali

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Problem 11

A small light source located $1 \mathrm{~m}$ in front of a $1-\mathrm{m}^{2}$ opening illuminates a wall behind. If the wall is $1 \mathrm{~m}$ behind the opening $(2 \mathrm{~m}$ from the light source), the illuminated area covers $4 \mathrm{~m}^{2}$. How many square meters will be illuminated if the wall is $3 \mathrm{~m}$ from the light source? $5 \mathrm{~m} ? 10 \mathrm{~m} ?$

Salamat Ali

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Problem 12

The intensity of light from a central source varies inversely as the square of the distance. If you lived on a planet only half as far from the Sun as our Earth, how would the light intensity compare with that on Earth? How about a planet ten times farther away than Earth?

Mathis Ernst

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Problem 13

The planet Jupiter is more than 300 times as massive as Earth, so it might seem that a body on the surface of Jupiter would weigh 300 times as much as it would weigh on Earth. But it so happens that a body would scarcely weigh three times as much on the surface of Jupiter as it would on the surface of Earth. Can you think of an explanation for why this is so?

Km Neeraj

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Problem 14

Why do the passengers in high-altitude jet planes feel the sensation of weight while passengers in an orbiting space vehicle, such as a space shuttle, do not?

Salamat Ali

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Problem 15

If you were in a car that drove off the edge of a cliff, why would you be momentarily weightless? Would gravity still be acting on you?

Salamat Ali

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Problem 16

What two forces act on you while you are in a moving elevator? When are these forces of equal magnitude and when are they not?

Benjamin Arndell

Benjamin Arndell

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Problem 17

If you were in a freely falling elevator and you dropped a pencil, it would hover in front of you. Is there a force of gravity acting on the pencil? Defend your answer.

Salamat Ali

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Problem 18

Your friend says that the primary reason astronauts in orbit feel weightless is that they are beyond the main pull of Earth's gravity. Why do you agree or disagree?

Km Neeraj

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Problem 19

Explain why the following reasoning is wrong. "The Sun attracts all bodies on Earth. At midnight, when the Sun is directly below, it pulls on you in the same direction as Earth pulls on you; at noon, when the Sun is directly overhead, it pulls on you in a direction opposite to Earth's pull on you. Therefore, you should be somewhat heavier at midnight and somewhat lighter at noon."

Km Neeraj

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Problem 20

Which requires more fuel- -a rocket going from Earth to the Moon or a rocket coming from the Moon to Earth? Why?

Km Neeraj

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Problem 21

Some people dismiss the validity of scientific theories by saying they are "only" theories. The law of universal gravitation is a theory. Does this mean that scientists still doubt its validity? Explain.

Benjamin Arndell

Benjamin Arndell

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Problem 22

Suppose you roll a ball off a tabletop. Will the time to hit the floor depend on the speed of the ball? (Will a faster ball take a longer time to hit the floor?) Defend your answer.

Susan Hallstrom

Susan Hallstrom

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Problem 23

A heavy crate accidentally falls from a high-flying airplane just as it flies directly above a shiny red Porsche smartly parked in a car lot. Relative to the Porsche, where will the crate crash?

Prabhu Ramji

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Problem 24

In the absence of air resistance, why does the horizontal component of a projectile's motion not change, while the vertical component does?

Zulfiqar Ali

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Problem 25

At what point in its trajectory does a batted baseball have its minimum speed? If air resistance can be neglected, how does this compare with the horizontal component of its velocity at other points?

Prabhu Ramji

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Problem 26

A friend claims that bullets fired by some high-powered rifles travel for many meters in a straight-line path before they start to fall. Another friend disputes this claim and states that all bullets from any rifle drop beneath a straight-line path a vertical distance given by $\frac{1}{2} g t^{2}$ and that the curved path is apparent for low velocities and less apparent for high velocities. Now it's your turn: Will all bullets drop the same vertical distance in equal times? Explain.

Prabhu Ramji

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Problem 27

Two golfers each hit a ball at the same speed, but one at $60^{\circ}$ with the horizontal and the other at $30^{\circ} .$ Which ball goes farther? Which hits the ground first?

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

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Problem 28

A park ranger shoots a monkey hanging from a branch of a tree with a tranquilizing dart. The ranger aims directly at the monkey, not realizing that the dart will follow a parabolic path and thus will fall below the monkey. The monkey, however, sees the dart leave the gun and lets go of the branch to avoid being hit. Will the monkey be hit anyway? Does the velocity of the dart affect your answer, assuming that it is great enough to travel the horizontal distance to the tree before hitting the ground? Defend your answer.

Prabhu Ramji

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Problem 29

A projectile is fired straight upward at $141 \mathrm{~m} / \mathrm{s}$. How fast is it moving at the instant it reaches the top of its trajectory? Suppose instead that it were fired upward at $45^{\circ} .$ What would be its speed at the top of its trajectory?

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

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Problem 30

When you jump upward, your hang time is the time your feet are off the ground. Does hang time depend on your vertical component of velocity when you jump, your horizontal component of velocity, or both? Defend your answer.

Zulfiqar Ali

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Problem 31

The hang time of a basketball player who jumps a vertical distance of 2 feet $(0.6 \mathrm{~m})$ is about $2 / 3$ second. What will be the hang time if the player reaches the same height while jumping 4 feet $(1.2 \mathrm{~m})$ horizontally?

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

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Problem 32

Since the Moon is gravitationally attracted to Earth, why doesn't it simply crash into Earth?

Prabhu Ramji

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Problem 33

Does the speed of a falling object depend on its mass? Does the speed of a satellite in orbit depend on its mass? Defend your answers.

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

Numerade Educator

Problem 34

If you have ever watched the launching of an Earth satellite, you may have noticed that the rocket starts vertically upward, then departs from a vertical course and continues its climb at an angle. Why does it start vertically? Why does it not continue vertically?

Prabhu Ramji

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Problem 35

If a cannonball is fired from a tall mountain, gravity changes its speed all along its trajectory. But if it is fired fast enough to go into circular orbit, gravity does not change its speed at all. Explain.

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

Numerade Educator

Problem 36

A satellite can orbit at $5 \mathrm{~km}$ above the Moon, but not at $5 \mathrm{~km}$ above Earth. Why?

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

Numerade Educator

Problem 37

Would the speed of a satellite in close circular orbit about Jupiter be greater than, equal to, or less than $8 \mathrm{~km} / \mathrm{s} ?$

Prabhu Ramji

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Problem 38

Why are satellites normally sent into orbit by firing them in an easterly direction, the direction in which Earth spins?

Prabhu Ramji

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Problem 39

Of all the United States, why is Hawaii the most efficient launching site for nonpolar satellites?

Prabhu Ramji

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Problem 40

Earth is closer to the Sun in December than it is in June. In which of these two months is Earth moving faster around the Sun?

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

Numerade Educator

Problem 41

What is the shape of the orbit when the velocity of the satellite is everywhere perpendicular to the force of gravity?

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

Numerade Educator

Problem 42

A communications satellite with a 24 -hour period hovers over a fixed point on Earth. Why is it placed in orbit only in the plane of Earth's equator?

Prabhu Ramji

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Problem 43

If a flight mechanic drops a wrench from a high-flying jumbo jet, it crashes to Earth. If an astronaut on the orbiting space shuttle drops a wrench, does it crash to Earth also? Defend your answer.

Prabhu Ramji

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Problem 44

How could an astronaut in a space shuttle "drop" an object vertically to Earth?

Zulfiqar Ali

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Problem 45

If you stopped an Earth satellite dead in its tracks, it would simply crash into Earth. Why, then, don't the communications satellites that "hover motionless" above the same spot on Earth crash into Earth?

Zulfiqar Ali

Numerade Educator

Problem 46

The orbital velocity of Earth about the Sun is $30 \mathrm{~km} / \mathrm{s}$. If Earth were suddenly stopped in its tracks, it would simply fall radially into the Sun. Devise a plan whereby a rocket loaded with radioactive wastes could be fired into the Sun for permanent disposal. How fast and in what direction with respect to Earth's orbit should the rocket be fired?

Prabhu Ramji

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Problem 47

In an accidental explosion, a satellite breaks in half while in circular orbit about Earth. One half is brought momentarily to rest. What is the fate of the half brought to rest? What happens to the other half?

Zulfiqar Ali

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Problem 48

If Pluto were somehow stopped short in its orbit, it would fall into, rather than around, the Sun. How fast would it be moving when it hit the Sun?

Prabhu Ramji

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Problem 49

At which of the indicated positions does the satellite in elliptical orbit experience the greatest gravitational force? Have the greatest speed? The greatest velocity? The greatest momentum? The greatest kinetic energy? The greatest gravitational potential energy?

Sri Datta Vikas Buchemmavari

Sri Datta Vikas Buchemmavari

Numerade Educator

Problem 50

A rocket coasts in an elliptical orbit around Earth. To attain the greatest amount of $\mathrm{KE}$ for escape using a given amount of fuel, should it fire its engines at the apogee or at the perigee?

Prabhu Ramji

Numerade Educator