Gravity, Projectile Motion, and Orbital Mechanics (Lesson 5 - Chapters 9 and 10)

According to Kelper's laws, the paths of planets about the sun are a. Parabolas b. Circles c. Straight lines d. Ellipses e. None of these.

d. Ellipses

*According to Newton, the greater the masses of interacting objects, the A) greater the force of gravity, by the product of the masses B) less the force of gravity C) greater the force of gravity, by the square of the masses D) less the force of gravity, inversely as the square of the masses

A) greater the force of gravity, by the product of the masses F = G M m / d2

If the mass of the earth somehow increased with no change in radius, your weight would A) increase B) decrease C) stay the same

A) increase F = G M m / d2

If the radius of Earth somehow decreased with no change in mass, your weight would A) increase B) decrease C) stay the same

A) increase F = G M m / d2

A woman who normally weighs 400 N stands on top of a very tall ladder so she is one earth radius above the earth's surface. How much would she weigh there? A) zero B) 100 N C) 200 N D) 400 N

B) 100 N F = G M m / d2 If d is made twice as large, then d2 will be four times as large. Since we are dividing by d2, this means the Force -- her weight -- will be only one-fourth as much.

If Earth's mass decreased to one-half its original mass with no change in radius, then your weight would A) decrease to one-quarter its original value B) decrease to one-half its original value C) remain the same D) increase to twice its original value

B) decrease to one-half its original value F = G M m / d2

The force of gravity acting on the Space Shuttle in orbit is nearly A) zero B) equal to the weight of the Space Shuttle at Earth's surface C) about one-tenth its weight at Earth's surface D) about one-one hundredth its weight at Earth's surface

B) equal to the weight of the Space Shuttle at Earth's surface F = G M m / d2 In a low-Earth orbit, the Space Shuttle's distance from the center of Earth is nearly the same as it was at Earth's surface.

*What is the force of gravity on a 500-newton woman standing on the earth's surface? A) 9.8 N B) 50 N C) 500 N D) 5,000 N

C) 500 N

The planet Jupiter is about 300 times as massive as Earth, yet on its surface you would weigh only about 3 times as much. This is because A) your mass is 100 times less on Jupiter. B) Jupiter is significantly farther from the sun. C) Jupiter's radius is 10 times Earth's radius. D) you are 100 times more weightless there.

C) Jupiter's radius is 10 times Earth's radius.

*According to Kepler's laws, the paths of planets about the Sun are A) straight lines B) parabolas C) ellipses D) hyperbolas

C) ellipses

The force of gravity acts on all apples on an apple tree. Some apples are twice as far from the ground as others. These twice- as-high apples, for the same mass, have practically A) one-fourth the weight B) one-half the weight C) the same weight D) twice the weight

C) the same weight F = G M m / d2 Being twice as far above the ground has hardly any effect on d, the distance from the center of Earth to the apple.

According to Newton, the greater the distance between masses of interacting objects, the A) greater the force of gravity, proportional to the distance B) less the force of gravity, inversely as the distance C) greater the force of gravity, proportional to the square of the distance D) less the force of gravity, inversely as the square of the distance

D) less the force of gravity, inversely as the square of the distance F = G M m / d2

How far must one travel to get away from the Earth's gravitational field? a. To a region above the Earth's atmosphere b. To a region well beyond the moon c. To a region beyond the solar system d. Forget it; you can't travel far enough.

Reasoning: Gravitation is a long range force. Its range is infinite.

The weight of an apple near the surface of the earth is 1 N. What is the weight of the earth in the gravitational field of the apple? a) 1 N b) 6 x 1024 N c) 0 N d) millions of millions of tons

a) 1 N Reasoning: Newton's third law.

If you were in a freely falling elevator and you dropped a pencil, you'd see the pencil hovering. Is the pencil falling? a) yes: it is falling at the same rate as the elevator b) yes: it is falling, but it has much smaller acceleration because of its small mass c) no: it is basically standing still exactly at the location it was released d) no: it is actually going upward compared to the elevator

a) yes: it is falling at the same rate as the elevator

If the radius of the Earth somehow decreased with no change in mass, your weight would a. Increase b. Not change c. Decrease.

a. Increase Reasoning: The decrease in radius will produce a much larger acceleration of gravity at the surface. This means your weight will increase.

and her weight would be a. Less than 686 N b. 686 N c. More than 686 N. Reasoning: Mass is independent of locations. Thus her mass does not change. However, weight depends on the force of the gravity of the Earth and inside the space station, there is a smaller force of gravity acting on the woman.

a. Less than 686 N

The body chiefly responsible for ocean tides is the a. Moon b. Sun

a. Moon

An asteroid exerts a 360-N gravitational force on a nearby spacecraft. This force is directed a. Toward the asteroid b. Away from the asteroid c. Toward the sun.

a. Toward the asteroid Reasoning: The gravitational force is an attractive force. Thus the astroid pulls the spacecraft toward itself.

Consider a ball thrown from a level surface with an initial upward velocity of 10 m/s and an initial horizontal velocity of 5 m/s. Where does it land? That is, measured from its initial position, where does it come back to and strike the level surface? a) 5 m b) 10 m c) 15 m d) 20 m

b) 10 m From the previous question, we already know the ball is in the air for t = 2 sec x = vx t = (5 m/s) ( 2 s) = 10 m

The planet Jupiter is about 300 times more massive than the earth is. However, an object on the Jupiter weighs only about three times as much as the earth. The explanation for this is that a) the Jupiter is 100 times smaller in radius than the earth is b) the radius of Jupiter is about 10 times larger than the earth radius c) the Jupiter being gaseous does not apply a full force on objects near its surface d) the high temperature at the surface makes the force less effective

b) the radius of Jupiter is about 10 times larger than the earth radius

A 400-N person stands on the surface of the Earth. If he were somehow able to stand on a ladder so that he was twice as far from the center of the Earth, he would weight a. 0 N b. 100 N c. 200 N d. 400 N

b. 100 N Reasoning: As shown in the text (pages157-158), and in the computer lessons for the review of gravity, the force of gravity falls with distace squared. Thus doubling the distance to the center of the earth causes the force of gravity to become 1/4 compared to the surface of the earth. The 400-N person now weighs 1/4 as much or 100 N.

A woman standing on the surface of the Earth has a mass of 70 kilograms and a weight of 686 N. If instead she is floating freely inside a nonrotating space habitat far from the Earth, her mass would be a. Less than 70 kg b. 70 kg c. More than 70 kg.

b. 70 kg

Inside a freely-falling elevator, there would be no a. Gravitational force on you b. Apparent weight for you c. Both of these d. None of these.

b. Apparent weight for you

According to Newton, the greater the masses of interacting objects, the a. Less the gravitational force between them b. Greater the gravitational force between them c. Greater the force between them by the square of the masses.

b. Greater the gravitational force between them

Because a. Of rotation of the Earth and moon about the sun b. The moon pulls with a significantly greater force on the closer side of the Earth than on the side farther away. c. The sun pulls the Earth with a force 200 times stronger than the gravitational pull of the moon.

b. The moon pulls with a significantly greater force on the closer side of the Earth than on the side farther away.

Which pulls on the oceans of the Earth with the greater force? a. The moon b. The sun c. Both pull the same.

b. The sun Reasoning: Sun applies a stronger force on the earth than the moon does. However, this does not mean that the sun creates bigger tidal effects.

*Consider a ball thrown from a level surface with an initial upward velocity of 10 m/s and an initial horizontal velocity of 5 m/s. How long is the ball in the air? a) 1.0 s b) 1.5 s c) 2.0 s d) 4.0 s

c) 2.0 s Time to top: v = 0 v = vi + a t = 10 m/s + ( - 10 m/s2) (ttop) = 0 0 = 10 - 10 t top t top = 1 sec Total time in the air ttotal = 2 ttop = 2 s

The value of g at the surface of the earth is 9.8m/s2. What is the value of g at a distance of twice the radius of the earth (from the center of the earth)? a) 9.8 m/s2 b) 4.9 m/s2 c) 2.45 m/s2 d) 0 m/s2

c) 2.45 m/s2

*When a ball or stone or other object is thrown or hit or fired, and air resistance can be neglected, the resulting motion is known as projectile motion The path of an object in projectile motion is a) a straight line b) a hyperbola c) a parabola d) a quadrant of a circle

c) a parabola

*Projectile motion is a combination of a) horizontal motion with constant, non-zero acceleration and vertical motion with constant velocity b) horizontal motion with constant non-zero acceleration and vertical motion with constant, non-zero acceleration c) horizontal motion with constant velocity and vertical motion with constant, non-zero acceleration d) horizontal motion with constant velocity and vertical motion with constant velocity

c) horizontal motion with constant velocity and vertical motion with constant, non-zero acceleration

What is the force of gravity on a 500-newton woman standing on the Earth's surface? a. 50 N b. 250 N c. 500 N d. 509.8 N e. None of these

c. 500 N Reasoning: A 500-N woman is acted upon by a force of 500 N from the earth. This is precisely the weight of the person.

A very massive object A and a less massive object B move toward each other under the influence of gravitation. Which force, if either, is greater? a. The force on A b. The force on B c. Both forces are the same.

c. Both forces are the same. Reasoning: Newton's third law.

High tides are predominately produced by the a. Strong gravitational pull of the sun b. Centrifugal force created by the Earth-moon orbit c. Differences in gravitational pulls of the moon on opposite sides of the Earth.

c. Differences in gravitational pulls of the moon on opposite sides of the Earth

According to Newton, doubling the distance between two interacting objects a. Divides by 2 the gravitational force between them b. Multiplies by 2 the gravitational force between them c. Divides by 4 the gravitational force between them d. Multiples by 4 the gravitational force between them.

c. Divides by 4 the gravitational force between them

This would be because a. He would be above the atmosphere b. His mass would be the same wherever he was c. Gravitational force obeys an inverse square law.

c. Gravitational force obeys an inverse square law.

The reason the moon does not crash into the Earth is that the a. Earth's gravitational field is weak at the moon b. Gravitational pull of other planets keeps the moon up c. Moon has a sufficient tangential speed d. Moon has less mass than the Earth e. None of these.

c. Moon has a sufficient tangential speed

chiefly because a. The moon is closer to the Earth than the sun b. Gravitational pull by the moon is less than that of the sun c. The difference between the moon's pull on the near and far sides of the Earth is appreciable.

c. The difference between the moon's pull on the near and far sides of the Earth is appreciable.

The Earth and the moon are attracted to each other by gravitational force. The larger Earth attracts the smaller moon with a force whose magnitude is a. Smaller than that of the force which the moon exerts on the Earth b. Greater than that of the force which the moon exerts on the Earth c. The same as that of the force which the moon exerts on the Earth.

c. The same as that of the force which the moon exerts on the Earth.

**Consider a ball that is thrown horizontally from the edge of a building with an initial velocity of 20 m/s. The building is 5 m above the driveway below. How far from the building does the ball strike the driveway? a) 5 m b) 10 m c) 15 m d) 20 m

d) 20 m y = (1/2) a t 2 - 5 m = (1/2) ( - 10 m/s 2) t 2 = (- 5 m/s2) t 2 1 s2 = t2 t = 1 s x = vx t = (20 m/s) (1 s) = 20 m

This is in accordance with a. The law of inertia b. Kepler's Law's c. The conservation of energy d. The fact that both moon and Earth orbit about a common point, the center of mass e. The law of action and reaction.

e. The law of action and reaction. Reasoning: Forces are the same, however, the results are different. The moon with a smaller mass than the earth will have a larger acceleration due to this forcethan the earth does. (Note: this acceleration is NOT the acceleration of gravity on the moon. This is referring to the acceleration of the moon as it revolves around the earth.)