Conceptual Physics - Chapter 13: Gravitational Interactions (Review)

What would be the weight of a 1-kg mass on the surface of Mars? The mass of Mars is 0.11 that of the earth, and its radius 0.53 that of the earth.

0.39 kg

On the small and good planet Ballonius in a distant solar system, suppose we find the radius of the good planet to be 200,000 m. We also drop a rock and find that it travels 1.5 m in the first second of free fall, which means it accelerates at 3 m/s^2. Estimate the mass of Ballonius.

2.04 x 10^21 kg

Many people mistakenly believe that the astronauts that orbit the earth are "above gravity." Calculate g for space shuttle territory, 200 km above the earth's surface. Assume the earth's mass is 6.0 x 10^24 kg, and its radius 6.38 x 10^6 m. Your answer is what percentage of 9.8 m/s^2?

9.18 N; 93.6 percent

Distinguish between a stellar black dwarf and a black hole.

A black dwarf is a star that has cooled because of the lack of helium and will cease giving off heat. A black hole is a heavier star that has collapsed, creating an abyss that has infinite density, engulfing everything

Gravitational field

A force field that exists in the space around every mass or group of masses.

Spring tide

A high or low tide that occurs when the sun, earth, and moon are all lined up so that the tides due to the sun and moon coincide, making the high tides higher than average, and the low tides lower than average.

Black hole

A mass that has collapsed to so great a density that its enormous local gravitational field prevents light from escaping.

Neap tide

A tide that occurs when the moon is halfway between a new moon and a full moon, in either direction. The tides due to the sun and the moon partly cancel, so that the high tides are lower than average, and the low tides are not as low as average.

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?

According to Newton's Third Law, the weight of the Earth in the gravitational field of the apple is 1 N, the same weight as the apple.

What is the value of the gravitational field at the center of the earth?

At the center of the earth, the value of the gravitation field is zero.

We can think of a force field as a kind of extended aura that surrounds a body, spreading its influence to affect things. As later chapters will show, an electric field affects electric charges, and a magnetic field affect magnetic poles. What does a gravitational field affect?

Gravitational fields affect the strength of attraction between two masses.

What would be the effect on the earth's tides if the diameter of the earth were larger than it is? If the earth were as it presently is, but the moon were larger - with the same mass?

If the diameter of the earth were larger than it is, the earth's tides would increase as well. If the earth were as it presently is, but the moon were larger, there would be no effect on the tides.

If the radius of the earth somehow shrunk by half without any change in the earth's mass, what would be the value of g at the new surface? What would be the value of g above the new surface at a distance equal to the present radius?

If the radius of the Earth shrank by half, g would increase by a factor of four to 39.2 N. At a distance equal to the present radius, the value of g would be 9.8 N (exactly what it is currently).

If you stand on a shrinking planet, so that in effect you get closer to its center, your weight will increase. But if you instead burrow into the planet and get closer to its center, your weight will decrease. Explain.

If you burrow into the earth, the matter above you (that you already tunneled through) also exerts a gravitational force on you, lowering the total force.

When would the moon be its fullest - just before a solar eclipse or just before a lunar eclipse? Defend your answer.

Just before a lunar eclipse, because the moon is always full at that time.

If the gravitational pull of the moon on the earth were the same over all parts of the earth, would there be any tides? Defend your answer.

No, there would not be any tides. This is because tides form when the moon's pull is stronger in one ocean and smaller in the next due to the orientation of the Earth. If this pull was the same everywhere, there would be no tides.

Why is "difference" a key word in explaining tides?

Ocean tides are caused by "differences" in the gravitational pull of the moon on opposite sides of the earth.

If the earth were the same size but twice as massive, how would the value of G change, if at all? How would the g change, if at all? (Why are your answers different? In this and the following question, let the equation g = GM/R^2 guide your thinking.)

Since it is a universal constant, the value of G never changes, no matter where it is in the universe. Doubling the mass of the earth would also double the value of g, the gravitational force.

Distinguish between spring tides and neap tides.

Spring tides are when the sun and moon are in alignment and produce larger tides. Neap tides are when the sun and moon are in non-alignment and produce smaller tides.

Force field

That which exists in the space surrounding a mass, electric charge, a magnet so that another mass, electric charge, or magnet introduced to this region will experience a force; examples of force fields are gravitational fields, electric fields, and magnetic fields.

Why would the earth not be sucked into the sun if it became a black hole?

The Earth would not be sucked into the sun if it became a black hole because the gravitational field of the black hole is the same as the gravitational field of the sun's, meaning that Earth would not be sucked into the black hole if it was nearby.

Which force-pair is greater - that between the moon and earth, or that between the sun and earth?

The force pair of the Earth and the moon are stronger because their masses and distances are closely related.

Weightlessness

The condition of free fall towards or around the earth, in which an object experiences no support force (and exerts no force on a scale).

Lunar eclipse

The cutoff of light from the full moon when the earth is directly below the sun and the moon, so that the earth's shadow is cast on the moon.

Solar eclipse

The cutoff of light from the sun to an observer on the earth when the moon is directly between the sun and the earth.

Upon which quantities does the acceleration of gravity on the surfaces of various planets depend?

The equation g = GM/R^2 describes gravitational fields, meaning that these factors depend on the mass and radius of various planets.

A black hole is no more massive than the star from which it collapsed. Why then, is gravitation so intense near a black hole?

The gravitational field around a black hole is strong because it is very dense, and its radius is almost zero.

How does the gravitational field strength at the surface of the earth compare with the acceleration of free fall?

The gravitational field strength at the surface of the earth is equal to the acceleration of free fall.

If you were unfortunate enough to be in a freely falling elevator, you might notice the bag of groceries you were carrying is hovering in front of you, apparently weightless. Cite the frames of reference in which the groceries are falling, and in which they are not falling.

The groceries are simply falling at the same speed as the elevator (and you).

Which is more effective in raising ocean tides - the moon or the sun? Why does this answer not contradict your previous answer?

The moon is more effective in raising ocean tides than the sun because the difference in the distance from one point of the Earth to the other is more relevant to the strength. This does not contradict the previous statement because the moon and the Earth have more direct effects on each other.

The human body is more than 50% water. Is it likely that the moon's gravitational pull causes any significant biological tides - cyclic changes in water flow among the body's fluid compartments? (Hint: Is any part of your body appreciably closer to the moon than any other part? Is there a difference in lunar pulls?)

The moon's gravity is not strong enough to cause any significant biological tide to occur. Any tide that does occur in your body is negligible.

What two major factors determine the size of a star?

The processes of gravitation and thermonuclear fusion

Which is correct - to say that a distant rocket interacts with the mass of the earth, or to say that it interacts with the gravitational field of the earth? Explain.

The rocket would interact with the gravitational field of the earth, not its mass, because the rocket is directed in the direction of the mass by a force and not by the mass directly.

How does the gravitational field surrounding the earth vary with increasing distance?

The strength of the earth's gravitational field weakens with increasing distance from the earth.

Why are tides greater at the times of the full and new moons and at the times of lunar and solar eclipses?

The strength of the moon and the sun are directly affecting the Earth at the optimal strength.

How does the support force of a floor you stand on relate to your weight?

The stronger the support force, the more you weigh due to the force that opposes your weight.

Do the sun and moon produce atmospheric tides on earth?

Yes, both the sun and the moon produce atmospheric tides on Earth.

A friend proposes an idea for launching space probes that consist of boring a hole completely through the earth. Your friend reasons that a probe dropped into such a hole would accelerate all the way through and shoot like a projectile out the other side. Defend or oppose the reasoning of your friend.

Your friend's reasoning is wrong - since the acceleration at the center of the Earth is zero, the satellite would fall to the center of the Earth and stay there.

Does your apparent weight change when you ride an elevator moving at constant speed? An accelerating elevator? Explain.

Your weight does not change when you ride an elevator moving at a constant speed because it is moving at a steady pace. However, if the elevator is accelerating, your weight would change drastically, depending on which direction it was going.

Why would your weight be less if you were deep beneath the earth's surface?

Your weight would be less because the force of the weight above you would cancel out the force of the gravitational field.

Where is your weight greatest - at the surface of the earth, deep below the surface, or above the surface?

Your weight would be the greatest at the surface of the earth.