?\(F=G \frac{m_{1} m_{2}}{d^{2}}\) Calculate the force of gravity between a newborn baby

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.

Shruti Kumar projects a ball at an angle of \(30^{\circ}\) above the horizontal. Which component of initial velocity is larger: the vertical or the horizontal? Which of these components undergoes the least change while the ball is airborne? Defend your answer. Text Transcription: 30^circ

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 \(1 / 2 g t^{2}\) as soon as they leave the barrel and that the curved path is apparent for low velocities and less apparent for high velocities. Now it’s your turn: Do all bullets drop the same vertical distance in equal times? Explain. Text Transcription: 1 / 2 gt^2

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.

Which requires more fuel: a rocket going from Earth to the Moon or a rocket returning from the Moon to Earth? Why?

Two facts: A freely falling object at Earth’s surface drops vertically 5 m in 1 s. Earth’s curvature “drops” 5 m for each 8-km tangent. Discuss how these two facts are related to the 8-km/s orbital speed necessary to orbit Earth.

A new member of your discussion group says that, because Earth’s gravity is so much stronger than the Moon’s gravity, rocks on the Moon could be dropped to Earth. What is wrong with this assumption?

A friend says that astronauts inside the International Space Station (ISS) are weightless because they’re beyond the pull of Earth’s gravity. Correct your friend’s reasoning.

Another new member of your discussion group says the primary reason why astronauts in orbit feel weightless is that they are being pulled by other planets and stars. Why do you agree or disagree?

Occupants inside future donut-shaped rotating habitats in space will be pressed to their floors by rotational effects. Their sensation of weight feels as real as that due to gravity. Does this indicate that weight need not be related to gravity?

A satellite can orbit at 5 km above the Moon’s surface, but not at 5 km above Earth’s surface. Why?

As part of their training before going into orbit, astronauts experience weightlessness when riding in an airplane that is flown along the same parabolic trajectory as a freely falling projectile. A classmate says that gravitational forces on everything inside the plane during this maneuver cancel to zero. Another classmate looks to you for confirmation. What is your response?

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

A communications satellite with a 24-h period hovers over a fixed point on Earth. Why is it placed in orbit only in the plane of Earth’s equator? (Hint: Think of the satellite’s orbit as a ring around Earth.

This situation should elicit good discussion: 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? (Hint: Think momentum conservation.)

(Here’s a Chapter 2-type question): When the brakes are applied on a vehicle moving to the right, the horizontal net force on the vehicle is to the left. A friend says that the velocity and acceleration of the vehicle are in opposite directions. Do you agree or disagree? Defend your answer.

(Here’s a Chapter 4-type question): The first stage of each SpaceX rocket that services the ISS no longer is dumped into the sea, but is returned for recycling (when all goes well). As the empty first stage falls back to Earth, one of its main engines slows its descent velocity to zero at the moment of touchdown. Is it correct to say that during this maneuver, the velocity and the acceleration of the first stage are in opposite directions? Defend your answer.

Here’s a situation to challenge you and your friends: A rocket coasts in an elliptical orbit around Earth. To attain the greatest amount of KE for escape using a given amount of fuel, should it fire its engines at the apogee (the point at which it is farthest from Earth) or at the perigee (the point at which it is closest to Earth)? (Hint: Let the formula \(F d=\Delta \mathrm{KE}\) guide your thinking. Suppose the thrust F is brief and of the same duration in either case. Then consider the distance d that the rocket would travel during this brief burst at the apogee and at the perigee.) Text Transcription: Fd=Delta KE

Fast-Moving Projectiles-Satellites Hawaii presents the most efficient launching site in the United States for nonpolar satellites. Why is this so? (Hint: Look at the spinning Earth from above either pole, and compare it to a spinning turntable.)

Circular Satellite Orbits Does the speed of a falling object depend on its mass? (Recall the answer to this question in earlier chapters.) Does the speed of a satellite in orbit depend on its mass? Defend your answers.

Circular Satellite Orbits If a space vehicle circled Earth at a distance equal to the Earth–Moon distance, how long would it take for it to make a complete orbit? In other words, what would be its period?

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

Circular Satellite Orbits If a flight mechanic drops a box of tools from a highflying jumbo jet, it crashes to Earth. If an astronaut in an orbiting space vehicle drops a box of tools, does it crash to Earth also? Defend your answer.

Circular Satellite Orbits How could an astronaut in a space vehicle “drop” an object vertically to Earth?

Circular Satellite Orbits If you stopped an Earth satellite dead in its tracks-that is, if you reduced its tangential velocity to zero-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?

Circular Satellite Orbits The orbital velocity of Earth about the Sun is 30 km/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?

Elliptical Orbits At what point in Earth’s elliptical orbit about the Sun is the acceleration of Earth toward the Sun a maximum? At what point is it a minimum? Defend your answers.

Elliptical Orbits The force of gravity on an Earth satellite in circular orbit remains constant at all points along the orbit. Why is this not the case for a satellite in an elliptical orbit?

Elliptical Orbits Earth is farthest away from the Sun in July and closest in January. In which of these two months is Earth moving faster around the Sun?

Escape Speed In the 2014 Rosetta mission, when a probe from Earth landed on the low-mass comet, the probe bounced. Why were scientists overseeing the mission concerned about the comet’s escape speed?

Escape Speed An object tossed vertically will reach a maximum height. An object dropped from that same height would land with the same speed at which the first object was thrown. How fast would an object hit Earth if it were dropped from a distance beyond Neptune, falling only because of Earth gravity?

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. Newton tells us that gravitational force acts on all bodies in proportion to their masses. Why, then, doesn’t a heavy body fall faster than a light body?

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. “Okay,” a friend says, “gravitational force is proportional to mass. Is gravitation then stronger on a crumpled piece of aluminum foil than on an identical piece of foil that has not been crumpled? Isn’t that why the crumpled one falls faster when they are dropped together?” Defend your answer and explain why the two fall differently.

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. An apple falls because of its gravitational attraction to Earth. How does the gravitational attraction of Earth to the apple compare? (Does force change when you interchange \(m_{1}\) and \(m_{2}\) in the equation for gravity-\(m_{2} m_{1}\) instead of \(m_{1} m_{2}\)?) Text Transcription: m_1 m_2 m_2 m_1 m_1 m_2

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. 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 weigh scarcely three times as much on the surface of Jupiter as it would on the surface of Earth. Discuss why this is so. (Hint: Let the terms in the equation for gravitational force guide your thinking.)

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. When will the gravitational force between you and the Sun be greater: today at noon or tomorrow at midnight? Defend your answer.

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. 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.”

What did Newton discover about gravity?

The Universal Law of Gravity In what sense does the Moon “fall”?

The Universal Law of Gravity State Newton’s law of universal gravitation in words. Then express it in one equation.

The Universal Law of Gravity What is the magnitude of gravitational force between two 1-kg bodies that are 1 m apart?

The Universal Law of Gravity What is the magnitude of the gravitational force between Earth and a 1-kg body at its surface?

Gravity and Distance: The Inverse-Square Law How does the force of gravity between two bodies change when the distance between them is tripled?

Gravity and Distance: The Inverse-Square Law Where do you weigh more-at sea level or atop one of the peaks of the Rocky Mountains? Defend your answer.

Weight and Weightlessness Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that accelerated upward? Accelerated downward?

Weight and Weightlessness Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that moved upward at constant velocity? In an elevator that moved downward at constant velocity?

Weight and Weightlessness Explain why occupants of the International Space Station are firmly in the grip of Earth’s gravity, even though they have no weight.

Weight and Weightlessness Under what conditions is your weight equal to mg?

Universal Gravitation What was the cause of perturbations discovered in the orbit of planet Uranus?

Universal Gravitation The perturbations of Uranus led to what greater discovery?

Universal Gravitation What is the status of Pluto in the family of planets?

Universal Gravitation Which is thought to be more prevalent in the universe, dark matter or dark energy?

Projectile Motion A stone is thrown upward at an angle. Neglecting air resistance, what happens to the horizontal component of its velocity along its trajectory?

Projectile Motion A stone is thrown upward at an angle. Neglecting air resistance, what happens to the vertical component of its velocity along its trajectory?

Projectile Motion A projectile is launched upward at an angle of 75° from the horizontal and strikes the ground a certain distance downrange. For what other angle of launch at the same speed would this projectile land just as far away?

Projectile Motion A projectile is launched vertically at 100 m/s. If air resistance can be neglected, at what speed does it return to its initial level?

Fast-Moving Projectiles-Satellites What connection does Earth’s curvature have with the speed needed for a projectile to orbit Earth?

Fast-Moving Projectiles-Satellites Why is it important that a satellite remain above Earth’s atmosphere?

Fast-Moving Projectiles-Satellites When a satellite is above Earth’s atmosphere, is it also beyond the pull of Earth’s gravity? Defend your answer.

Fast-Moving Projectiles-Satellites If a satellite were beyond Earth’s gravity, what path would it follow?

Circular Satellite Orbits Why doesn’t the force of gravity change the speed of a bowling ball as it rolls along a bowling lane?

Circular Satellite Orbits Why doesn’t the force of gravity change the speed of a satellite in circular orbit?

Circular Satellite Orbits Is the period longer or shorter for orbits of greater altitude?

Elliptical Orbits Why does the force of gravity change the speed of a satellite in an elliptical orbit?

Elliptical Orbits At what part of an elliptical orbit does an Earth satellite have the greatest speed? The least speed?

Escape Speed What happens to an object close to Earth’s surface if it is given a speed exceeding 11.2 km/s?

Escape Speed A space vehicle can outrun Earth’s gravity, but can it get entirely beyond Earth’s gravity?

With a ballpoint pen, write your name on a piece of paper on your desk. No problem. Now try it with the pen upside down-for example, with the paper held against a book above your head. Note the pen “doesn’t work.” Now you see that gravity acts on the ink in the barrel through which the ink flows!

Hold your hands outstretched in front of you, one twice as far from your eyes as the other, and make a casual judgment as to which hand looks bigger. Most people see them to be about the same size, and many see the nearer hand as slightly bigger. Almost no one, upon casual inspection, sees the nearer hand as four times as big. But by the inverse-square law, the nearer hand should appear to be twice as tall and twice as wide, and therefore it should seem to occupy four times as much of your visual field as the farther hand. Your belief that your hands are the same size is so strong that it overrules this information. However, if you overlap your hands slightly and view them with one eye closed, you’ll see the nearer hand as clearly bigger. This raises an interesting question: What other illusions do you have that are not so easily checked?

Repeat the eyeballing experiment, only this time use two one-dollar bills: one unfolded and flat, and the other folded along its middle lengthwise, and again widthwise, so that it has \(\frac{1}{4}\) the area. Now hold the two bills in front of your eyes. Where do you hold the folded dollar bill so that it looks the same size as the unfolded one? Nice? Text Transcription: 1/4

With stick and strings, make a “trajectory stick” as shown in the Doing Physical Science feature “Hands-On Hanging Beads” on page 103.

With your friends, whirl a bucket of water in a vertical circle fast enough so the water doesn’t spill out. As it happens, the water in the bucket is falling, but with less speed than you give to the bucket. Tell them how your bucket swing is linked to satellite motion-that satellites in orbit continually fall toward Earth, but not with enough vertical speed to get closer to the curved Earth below. Remind your friends that physics is about finding the connections in nature!

\(F=G \frac{m_{1} m_{2}}{d^{2}}\) Using the formula for gravity, show that the force of gravity on a 1-kg mass at Earth’s surface is 9.8 N. You need to know that the mass of Earth is \(6 \times 10^{24} \mathrm{~kg}\), and its radius is \(6.4 \times 10^{6} \mathrm{~m}\). Text Transcription: F=G m_1 m_2/d^2 6 times 10^24 kg 6.4 times 10^6 m

\(F=G \frac{m_{1} m_{2}}{d^{2}}\) Calculate the force of gravity on the same 1-kg mass if it were \(6.4 \times 10^{6} \mathrm{~m}\) above Earth’s surface (that is, if it were two Earth radii from Earth’s center). Text Transcription: F=G m_1 m_2/d^2 6.4 times 10^6 m

\(F=G \frac{m_{1} m_{2}}{d^{2}}\) Show that the average force of gravity between Earth (\(\text { mass }=6.0 \times 10^{24} \mathrm{~kg}\)) and the Moon (\(\text { mass }=7.4 \times 10^{22} \mathrm{~kg}\) is \(2.1 \times 10^{20} \mathrm{~N}\). (The average EarthMoon distance is \(3.8 \times 10^{8} \mathrm{~m}\). Text Transcription: F=G m_1 m_2/d^2 mass=6.0 times 10^24 kg mass=7.4 times 10^22 2.1 times 10^20 N 3.8 times 10^8 m

\(F=G \frac{m_{1} m_{2}}{d^{2}}\) Show that the force of gravity between Earth (\(\text { mass }=6.0 \times 10^{4} \mathrm{~kg}\)) and the Sun (\(\text { mass }=2.0 \times 10^{30} \mathrm{~kg}\)) is \(3.6 \times 10^{22} \mathrm{~N}\). (The average Earth-Sun distance is \(1.5 \times 10^{11} \mathrm{~m}\).) Text Transcription: F=G m_1 m_2/d^2 mass=6.0 times 10^24 kg mass=2.0 times 10^30 kg 3.6 times 10^22 N 1.5 times 10^11 n

\(F=G \frac{m_{1} m_{2}}{d^{2}}\) Show that the force of gravity between a newborn baby (mass 3.0 kg) and planet Mars (\(\text { mass }=6.4 \times 10^{23} \mathrm{~kg}\)) is \(4.0 \times 10^{-8} \mathrm{~N}\) when Mars is at its closest to Earth (\(\text { distance }=5.6 \times 10^{10} \mathrm{~m}\)). Text Transcription: F=G m_1 m_2/d^2 mass=6.4 times 10^23 kg 4.0 times 10^-8 N distance=5.6 times 10^10 m

\(F=G \frac{m_{1} m_{2}}{d^{2}}\) Calculate the force of gravity between a newborn baby of mass 3.0 kg and the obstetrician of mass 100 kg who is 0.5 m from the baby. Which exerts more gravitational force on the baby, Mars or the obstetrician? By how much?

Suppose you stood atop a ladder that was so tall that you were three times as far from Earth’s center as you presently are. Show that your weight would be one-ninth of its present value.

Show that the gravitational force between two planets is quadrupled if the masses of both planets are doubled but the distance between them stays the same.

Show that there is no change in the force of gravity between two objects when their masses are doubled and the distance between them is also doubled.

Find the change in the force of gravity between two planets when their distance apart is decreased by a factor of 10.

Consider a pair of planets in which the distance between them is decreased by a factor of 5. Show that the force between them becomes 25 times as strong.

Many people mistakenly believe that the astronauts who orbit Earth are "above gravity." Earth's mass is \(6 \times 10^{24} \mathrm{~kg}\), and its radius is \(6.38 \times 10^{6} \mathrm{~m}\) (6380 km). Use the inverse-square law to show that in "space shut- tle territory," 200 kilometers above Earth's surface, the force of gravity on a shuttle is about 94% that at Earth's surface. Text Transcription: 6 times 10^24 kg 6.38 times 10^6 m

Newton's universal law of gravity tells us that \(F=G \frac{m_{1} m_{2}}{d^{2}}\). Newton's second law tells us that \(a=\frac{F_{net}}{m}\). (a) With a bit of algebraic reasoning, show that your gravitational acceleration toward any planet of mass M a distance d from its center is \(a=\frac{G M}{d^{2}}\) (b) How does this equation tell you whether or not your gravitational acceleration depends on your mass? Text Transcription: F=G m_1m_2/d^2 a=F_net/m a=GM/d^2

An airplane is flying horizontally with speed 1000 km/h (280 m/s) when an engine falls off. Neglecting air resistance, assume that it takes 30 s for the engine to hit the ground. (a) Show that the altitude of the airplane is 4.4 km. (Use \(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\)) (b) Show that the horizontal distance that the airplane engine travels during its fall is 8.4 km. (c) If the airplane somehow continues to fly as though nothing had happened, where is the engine relative to the airplane at the moment the engine hits the ground? Text Transcription: g=9.8 m/s^2

A ball is thrown horizontally from a cliff at a speed of 10 m/s. Show that its speed one second later is about 14 m/s.

A satellite at a particular point along an elliptical orbit has a gravitational potential energy of 5000 MJ with respect to Earth’s surface and a kinetic energy of 4500 MJ. Later in its orbit the satellite’s potential energy is 6000 MJ. Use the conservation of energy to find its kinetic energy at that point.

A rock thrown horizontally from a bridge hits the water below. The rock travels a smooth parabolic path in time t. (a) Show that the height of the bridge is \(1 / 2 g t^{2}\) (b) What is the height of the bridge if the time the rock is airborne is 2 s? (c) To solve this problem, what information is assumed here that wasn't in Chapter 2 Text Transcription: 1/2gt^2

A baseball is tossed at a steep angle into the air and makes a smooth parabolic path. Its time in the air is t, and it reaches a maximum height h. Assume that air resistance is negligible. (a) Show that the height reached by the ball is \(\frac{g t^{2}}{8}\) (b) Show that if the ball is in the air for 4 s, it reaches a height of nearly 20 m. (c) If the ball reached the same height as it did when it was tossed at some other angle, would the time of flight be the same? Text Transcription: g t^2/8

A penny on its side moving at speed v slides off the horizontal surface of a table a vertical distance y from the floor. (a) Show that the penny lands a distance \(v \sqrt{\frac{2 y}{g}}\) from the base of the coffee table. (b) Show that if the speed is 3.5 m/s and the coffee table is 0.4 m tall, the distance the coin lands from the base of the table is 1.0 m. (Use \(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\).) Text Transcription: v sqrt 2y/g g=9.8m/s^2

Students in a lab measure the speed of a steel ball launched horizontally from a tabletop to be v. The tabletop is distance y above the floor. They place a tin coffee can of height 0.1y on the floor to catch the ball. (a) Show that the can should be placed a horizontal distance from the base of the table of \(v \sqrt{\frac{2(0.9) y}{g}}\) (b) Show that if the ball leaves the tabletop at a speed of 4.0 m/s, the tabletop is 1.5 m above the floor, and the can is 0.15 m tall, then the center of the can should be placed a horizontal distance of 2.1 m from the base of the table. Text Transcription: v=sqrt 2(0.9)y/g

The planet and its moon gravitationally attract each other. Rank, from greatest to least, the force of attraction between the members of each pair.

Consider the light of multiple candle flames, each of the same brightness. Rank, from brightest to dimmest, the light that enters your eye for the following situations. (a) 3 candles seen from a distance of 3 m. (b) 2 candles seen from a distance of 2 m. (c) 1 candle seen from a distance of 1 m.

Rank, from greatest to least, the average gravitational forces between: (a) The Sun and Mars. (b) The Sun and the Moon. (c) The Sun and Earth.

A ball is tossed off the edge of a cliff with the same speed, but at different angles as shown. Rank, from greatest to least: (a) The initial PEs of the balls relative to the ground below. (b) The initial KEs of the balls when tossed. (c) The KEs of the balls when hitting the ground below. (d) The times of flight while airborne.

The dashed lines show three circular orbits about Earth. Rank the following quantities from greatest to least: (a) Their orbital speed. (b) Their time to orbit Earth.

The positions of a satellite in elliptical orbit are indicated. Rank the following quantities from greatest to least: (a) Gravitational force. (b) Speed. (c) Momentum. (d) KE. (e) PE. (f) Total energy (KE + PE). (g)Acceleration.

The Universal Law of Gravity What would be the path of the Moon if somehow all gravitational acting forces on it sank to zero?

The Universal Law of Gravity Is the gravitational force greater on a 1-kg piece of iron or on a 1-kg piece of glass? Defend your answer.

The Universal Law of Gravity Consider a space pod somewhere between Earth and the Moon, at just the right distance so that gravitational attraction to Earth and gravitational attraction to the Moon are equal. Is this location nearer Earth or nearer the Moon?

The Universal Law of Gravity An astronaut lands on a planet that has the same mass as Earth but half the diameter. How does the astronaut’s weight differ from that on Earth?

The Universal Law of Gravity An astronaut lands on a planet that has the same mass as Earth and twice the diameter. How does the astronaut’s weight differ from her or his weight on Earth?

The Universal Law of Gravity 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 Earth instead shrunk? (Hint: Let the equation for gravitational force guide your thinking.)

Gravity and Distance: The Inverse-Square Law How would the force between a planet and its moon change if its moon were boosted to twice its distance from the center of the planet? If it were instead brought to half its distance from the center of the planet?

Gravity and Distance: The Inverse-Square Law Phil works on the 15th floor of an office building, and his wife Jean works on the 30th floor, which is twice as high as Phil’s workplace. Is the force of gravity half as much in Jean’s workspace as in Phil’s? Explain why or why not.

Gravity and Distance: The Inverse-Square Law In 2013, Curiosity landed on the surface of Mars. Does the weight of Curiosity vary if it makes its way from a valley floor to the top of a tall hill? Explain.

Gravity and Distance: The Inverse-Square Law Earth is not exactly a sphere but, rather, bulges outward at the equator. How does this bulge affect the relationship between a person’s weight in Singapore and his or her weight in Hong Kong?

Gravity and Distance: The Inverse-Square Law A small light source located 1 m in front of a \(1-m^{2}\) opening illuminates a wall behind. If the wall is 1 m behind the opening (2 m from the light source), the illuminated area covers \(4 m^{2}\). How many square meters are illuminated if the wall is 3 m from the light source? 5 m from the light source? 10 m from the light source? Text Transcription: 1-m^2 4 m^2

Gravity and Distance: The Inverse-Square Law 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 five times as far away as Earth?

Weight and Weightlessness Why do the passengers in high-altitude jet planes feel the sensation of weight, while passengers in the International Space Station do not?

Weight and Weightlessness To begin your wingsuit flight, you step off the edge of a high cliff. Why are you then momentarily weightless? At that point, is gravity acting on you?

Weight and Weightlessness In synchronized diving, divers remain in the air for the same time. With no air resistance, they would fall exactly together. But air resistance is appreciable, so how do they remain together in fall?

Weight and Weightlessness 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?

Weight and Weightlessness 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.

Universal Gravitation In the 2014 Rosetta mission, a probe from Earth landed on a comet of very low mass. If the probe had been twice as massive, how would its weight on the comet surface have been affected?

Universal Gravitation How does the size of Pluto compare with that of planets in the solar system?

Universal Gravitation Elements beyond the naturally occurring elements that have been discovered that are named Neptunium and Plutonium. How was the naming process related to discovery of new planets?

Universal Gravitation Earth and the Moon are gravitationally attracted to the Sun, but they don’t crash into the Sun. A friend says that is because Earth and the Moon are beyond the Sun’s main gravitational influence. Other friends look to you for a response. What is your response?

Projectile Motion Chuck Stone releases a ball near the top of a track and measures the ball’s speed as it rolls horizontally off the end of the table. Students make measurements to predict where a can must be placed to catch the ball. How will the ball’s speed affect the time it takes to reach the can once the ball leaves the end of the table? (Does a faster ball take a longer time to hit the floor?) Defend your answer.

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

Projectile Motion 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?

Projectile Motion A heavy crate accidentally falls from a high-flying airplane just as it flies directly above Mike’s shiny red Corvette defensively parked in a car lot. Relative to the Corvette, where does the crate crash?

Projectile Motion Two golfers each hit a ball at the same speed, but one hits it at \(60^{\circ}\) with the horizontal and the other at \(30^{\circ}\). Which ball goes farther? Which hits the ground first? (Ignore air resistance.) Text Transcription: 60 degrees 30 degrees

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

Projectile Motion The hang time of a basketball player who jumps a vertical distance of 2 feet (0.6 m) is about 0.6 s. What is the hang time if the player reaches the same height while jumping 4 ft (1.2 m) horizontally?

Fast-Moving Projectiles-Satellites If you’ve had the good fortune to witness 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?

Fast-Moving Projectiles-Satellites Newton knew that if a cannonball were fired from a tall mountain, gravity would change its speed all along its trajectory (Figure 4.29). But if it is fired fast enough to attain circular orbit, gravity does not change its speed at all. Explain.

Fast-Moving Projectiles-Satellites Satellites are normally sent into orbit by firing them in an easterly direction, the direction in which Earth spins. What is the advantage of this?