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An asteroid exerts a 360-N gravitational force on a nearby spacecraft. If the spacecraft moves to a point 3 times as far from the center of the asteroid, what is the gravitational force?

40 N

A weight watcher 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?

100 N

If the Earth's mass decreased to one-half its original mass with no change in radius, how will your weight change?

decrease to one half your original weight

An object is placed exactly halfway between the Earth and moon. What will the object will move towards?

earth

If the mass of the Earth somehow increased with no change in radius, how would your weight change?

increase also

gravitational forces act on all bodies in proportion to their masses. Why, then, doesn't a heavy body fall faster than a light body?

The reason that a heavy body doesn't fall faster than a light body is because the greater gravitational force on the heavier body (its weight), acts on a correspondingly greater mass (inertia). The ratio of gravitational force to mass is the same for every body—hence all bodies in free fall accelerate equally. And it's true not just near the Earth, but anywhere. (This is illustrated in Figures 4.11 and 4.12.)

A friend says that, since earth's gravity is so much stronger than the moons gravity, rocks on the moon could be dropped to earth. What is wrong with this assumption?

The force of gravity on moon rocks at the Moon's surface is considerably stronger than the force of gravity of the distant Earth. Rocks dropped on the Moon fall onto the Moon surface. (The force of the Moon's gravity is about 1/6 of the weight the rock would have on Earth; the force of the Earth's gravity at that distance is only about 1/3600 of the rock's Earth-weight.)

A friend says that the international space station shown on the cover of this book is beyond the pull of earths gravity. Correct your friends statement.

Astronauts are weightless because they lack a support force, but they are well in the grips of Earth gravity, which accounts for them circling the Earth rather than going off in a straight line in outer space.

Larry weighs 300 N at the surface of earth. What is the weight of earth in the gravitational field of Larry?

In accord with Newton's 3rd law, the weight of the Earth in the gravitational field of the apple is 1 N; the same as the weight of the apple in the Earth's gravitational field.

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

Letting the equation for gravitation guide your thinking, twice the diameter is twice the radius, which corresponds to 1/4 the astronaut's weight at the planet's surface.

Why does a person in free fall experience weightlessness, while a person falling at terminal velocity does not?

A person is weightless when the only force acting is gravity, and there is no support force. Hence the person in free fall is weightless. But more than gravity acts on the person falling at terminal velocity. In addition to gravity, the falling person is "supported" by air drag.

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

The two forces are the normal force and mg, which are equal when the elevator doesn't accelerate, and unequal when the elevator accelerates.

Suppose you stood atop a ladder so tall that you were 3 times as far from earths center as you presently are. Show that your weight would be one ninth of its present value.

From , F= G m1 m2 / d^2--3 times d squared is 9d2, which means the force is one ninth of surface weight

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.

In accord with the inverse-square law, four times as far from the Earth's center diminishes the value of g to g/42, or g/16, or 0.6 m/s2.

Find the change in the force of gravity between two planets when distance between them is decreased by 10.

It is g = GM/r2 = (6.67 x 10-11) (3.0 x 1030)/(8.0 x 103)2 = 3.1 x 10^12 m/s2, 300 billion times g on Earth.

The moon falls around the earth rather than straight into it, if the moon 's tangential velocity were zero, how would it more?

if the moons tangential velocity were zero, it would fall straight down and crash into earth

According to the equation for gravitational force, what happens to the force between two bodies if the mass of one of the bodies is doubled? If both masses are doubled?

When one mass is doubled, the force between it and the other one doubles. If both masses double, the force is 4 times as much.

By how much does the gravitational force between two objects decrease when the distance between their centers is doubled? Tripled? Increased tenfold?

It decreases to 1/4, 1/9, and 1/100 to the original value.

Consider an apple at the top of a tree that is pulled by earths gravity with a force 1 N. If the tree were twice as tall, would the force of gravity be 1/4 as strong?

No, because an apple at the top of the twice-as tall apple tree is not twice as far from earths center. The taller tree would need a height equal to the earths radius for the apple's weight at its top to reduce 1/4 N. Before its weight decreases by 1%, an apple or any object must be raised 32 km--nearly 4 times the height of Mt. Everest. So, as a practical matter we disregard the effects of everyday changes in elevation.

Halfway to the center of earth, would the force of gravity on you be less than at the surface of earth?

Gravitational force, on you would be less, because there is less mass of earth below you, which pulls you with less force.