Chapter 4

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?

100 m/s

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?

15

What is the magnitude of gravitational force between two 1−kg bodies that are 1 m apart?

6.67 × 10^−11 N

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?

Astronaut has four times as much weight as on Earth

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

At first it slows down, then reverses direction and speeds up.

Where do you weigh more—at sea level or atop one of the peaks of the Rocky Mountains? Defend your answer.

At sea level because your distance to the center of the Earth is least at sea level.

Find the force of gravity between Earth (mass = 6.0×10^24kg) and the Moon (mass = 7.4×10^22kg). The average Earth-Moon distance is 3.8×10^8m.

F = 2.1×10^20 N

Consider a pair of planets for which the distance between them is decreased by a factor of 3. How many times does the force between them increase?

F after/F before = 9

Why is it important that a satellite remain above Earth's atmosphere?

Friction with the air will exert forces on the satellite slowing it down.

Is the force of gravity half as much in Jean's workspace as in Phil's? Explain why or why not.

Gravitational force is measured with respect to distance from Earth's center; since the workplaces are practically the same distance from Earth's center any difference due to gravity is negligible.

Which component of initial velocity is larger: the vertical or the horizontal?

Horizontal

Which of these components undergoes the least change while the ball is airborne?

Horizontal

In what sense does the Moon "fall"?

It falls away from the straight line it would follow if there were no force on it.

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

It is constant

If the probe had been twice as massive, how would its weight on the comet surface have been affected?

Its weight would have been twice as high

A space vehicle can outrun Earth's gravity, but can it get entirely beyond Earth's gravity?

No, Earth's gravity extends to infinity, decreasing as the inverse square of the distance.

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?)

Since the ball leaves the table horizontally, its speed will not affect the time it takes to reach the floor.

Earth is farther away from the Sun in June and closest in December. In which of these two months is Earth moving faster around the Sun?

The Earth travels faster about the Sun in December than in June.

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?

The astronaut weighs one-quarter as much as on Earth.

As you found in Part A, your weight will be greater than normal when the elevator is moving upward with increasing speed. For what other motion would your weight also be greater than your normal weight?

The elevator moves downward while slowing in speed.

What did Newton discover about gravity?

The same laws of gravity apply on the Earth and in the heavens.

What connection does Earth's curvature have with the speed needed for a projectile to orbit Earth?

The speed has to be great enough that the distance the projectile falls each second matches the Earth's curvature.

Is there change in the force of gravity between two objects when their masses are doubled and the distance between them is also doubled?

There is no change.

Why doesn't the force of gravity change the speed of a bowling ball as it rolls along a bowling lane?

There is no component of the force in the direction of motion of the ball.

Why doesn't the force of gravity change the speed of a satellite in circular orbit?

There is no component of the force in the direction of motion of the satellite.

State Newton's law of universal gravitation in words. Then express it in one equation.

Two bodies attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. F ~ m1m2/d^2

Does the weight of Curiosity vary if it makes its way from a valley floor to the top of a tall hill? Explain.

Yes, in accord with the inverse-square law, the gravitational force on Curiosity at the higher location is less. So its weight is less at the top of the hill.

If a satellite were beyond Earth's gravity, what path would it follow?

a straight line

A satellite in elliptical orbit about Earth travels fastest when it moves _______.

close to Earth

Suppose you are in an elevator. As the elevator starts upward, its speed will increase. During this time when the elevator is moving upward with increasing speed, your weight will be __________.

greater than your normal weight at rest

In accord with the inverse-square law, ---- as far means ---- times the force.

half, four

Suppose you are in an elevator that is moving upward. As the elevator nears the floor at which you will get off, its speed slows down. During this time when the elevator is moving upward with decreasing speed, your weight will be __________.

less than your normal weight at rest

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

longer

When you toss a projectile sideways, it curves as it falls. It will be an Earth satellite if the curve it makes _______.

matches the curved surface of earth

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

nearer the Moon

A dropped ball accelerates as it falls. But a ball rolling on a horizontal surface has zero acceleration because _______.

no horizontal force acts on it

When an astronaut in orbit is weightless, he or she is _______.

still in the grips of Earth's gravity

Consider Earth and the Moon. As you should now realize, the gravitational force that Earth exerts on the Moon is equal and opposite to that which the Moon exerts on Earth. Therefore, according to Newton's second law of motion __________.

the Moon has a larger acceleration than Earth, because it has a smaller mass

Earth is gravitationally pulled toward _______.

the Sun, Mars, Jupiter

If you are standing on a scale in an elevator, what exactly does the scale measure?

the force you exert on the scale

In accord with the inverse-square law, ---- as far means ---- the force.

twice, one-quarter

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?

upward, more compressed; downward, less compressed

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? What about in an elevator that moved downward at constant velocity?

upward, no change; downward, no change.