# Chapter 4 Part 2

## Unlock all answers in this set

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According to the universal law of gravitation, the force due to gravity is
inversely proportional to the square of the distance between objects.
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According to the universal law of gravitation, if you triple the distance between two objects, then the gravitational force between them will
decrease by a factor of 9.
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According to the universal law of gravitation, if you double the masses of both attracting objects, then the gravitational force between them will
increase by a factor of 4.
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According to what we now know from Newton's laws, which of the following best explains why Kepler's second law is true?
A planet's angular momentum must be conserved as it moves around its orbit.
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The center of mass of a binary star system is
the balance point of the system, around which the two objects would revolve.
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The mass of Jupiter can be calculated by
measuring the orbital period and distance of one of Jupiter's moons.
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The Moon is constantly falling toward Earth.
True
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The center of mass for Earth orbiting the Sun lies inside the Sun.
True
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There is no gravity in space.
False
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Doubling the distance between two objects halves the gravitational force between them.
False
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Process of Science: Gravity only affects very massive objects and we can therefore only test theories about it when looking at the orbits of planets.
False
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Why is Newton's version of Kepler's third law so useful to astronomers?
It can be used to determine the masses of many distant objects.
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If an astronaut goes on a space walk outside the Space Station, she will quickly float away from the station unless she has a tether holding her to the station.
This statement is false. She and the Space Station share the same orbit and will stay together unless they are pushed apart.
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If Earth were twice as far from the Sun, the force of gravity attracting Earth to the Sun would be
one-quarter as strong.
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According to the law of universal gravitation, what would happen to Earth if the Sun were somehow replaced by a black hole of the same mass?
Earth's orbit would not change.
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Each diagram shows a single experimental trial in which you will drop a ball from some height. In each case, the ball's size, mass, and height are labeled. Note that two diagrams show a basketball, one diagram shows a bowling ball of the same size but larger mass, and one diagram shows a much smaller marble with the same mass as the basketball. You have a timer that allows you to measure how long it takes the ball to fall to the ground. Which pair of trials will allow you to test the prediction that an object's mass does not affect its rate of fall?
1. mass = 5.0kg, size = bowling ball, height = 20m 2. mass = 0.5kg, size = basketball, height = 20m
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Assume you have completed the two trials chosen in Part A. Which of the following possible outcomes from the trials would support Newton's theory of gravity? Neglect effects of air resistance.
Both balls fall to the ground in the same amount of time.
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Consider again the experimental trials from Part A. This time, you wish to test how the size of an object affects the rate of its fall. Which pair of trials should you compare?
1. mass = 0.5kg, size = basketball, height = 30m 2. mass = 0.5kg, size = marble, height = 30m
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If you actually performed and compared the two trials chosen in Part C, you would find that, while the basketball and marble would hit the ground at almost the same time, it would not quite be exact: The basketball would take slightly longer to fall to the ground than the marble. Why?
Because air resistance has a greater effect on the larger ball.
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Einstein's theory, like Newton's, predicts that, in the absence of air resistance, all objects should fall at the same rate regardless of their masses. Consider the following hypothetical experimental results. Which one would indicate a failure of Einstein's theory?
Scientists dropping balls on the Moon find that balls of different mass fall at slightly different rates.
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Part A: The following five diagrams show pairs of astronomical objects that are all separated by the same distance d. Assume the asteroids are all identical and relatively small, just a few kilometers across. Considering only the two objects shown in each pair, rank the strength, from strongest to weakest, of the gravitational force acting on the asteroid on the left.
From strongest force to weakest force: sun, earth, moon, asteroid, hydrogen atom
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Part B: The following diagrams are the same as those from Part A. Again considering only the two objects shown in each pair, this time rank the strength, from strongest to weakest, of the gravitational force acting on the object on the right.
From strongest force to weakest force: sun, earth, moon, asteroid, hydrogen atom
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Part C: The following diagrams are the same as those from Part A. This time, rank the pairs from left to right based on the size of the acceleration the asteroid on the left would have due to the gravitational force exerted on it by the object on the right, from largest to smallest.
From strongest force to weakest force: sun, earth, moon, asteroid, hydrogen atom
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Part D: 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
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Part A: Each of the following diagrams shows a spaceship somewhere along the way between Earth and the Moon (not to scale); the midpoint of the distance is marked to make it easier to see how the locations compare. Rank the five positions of the spaceship from left to right based on the strength of the gravitational force that Earth exerts on the spaceship, from strongest to weakest. (Assume the spaceship has the same mass throughout the trip; that is, it is not burning any fuel.)
From Strongest force to weakest force rank the positions in ascending order from earth to the moon. Beginning with the spaceship closest to earth, ending with the spaceship closest to the moon.
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Part B: The following diagrams are the same as those from Part A. This time, rank the five positions of the spaceship from left to right based on the strength of the gravitational force that the Moon exerts on the spaceship, from strongest to weakest.
From Strongest force to weakest force rank the positions in descending order from moon to earth. Beginning with the spaceship closest to the moon, ending with the spaceship closest to earth (aka the opposite of part A).
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Part C: The following diagrams show five pairs of asteroids, labeled with their relative masses (M) and distances (d) between them. For example, an asteroid with M=2 has twice the mass of one with M=1 and a distance of d=2 is twice as large as a distance of d=1. Rank each pair from left to right based on the strength of the gravitational force attracting the asteroids to each other, from strongest to weakest.
Ordered from strongest force to weakest force. 1. m = 2, d = 1, m = 2 2. m = 1, d = 1, m = 2 3. m = 1, d = 1, m = 1 4. m = 1, d = 2, m = 2 5. m = 1, d = 2, m = 1
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The allowed shapes for orbits under the force of gravity are
ellipses, parabolas, and hyperbolas.
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Which of the following best describes the origin of ocean tides on Earth?
Tides are caused by the difference in the force of gravity exerted by the Moon across the sphere of the earth.
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At which lunar phase(s) are tides most pronounced (e.g., the highest high tides)?
both new and full Moons
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At which lunar phase(s) are tides least pronounced (e.g., the lowest high tides)?
both first and third quarters
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The Moon is slowly moving away from Earth.
True
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Part A: The video shows a collapsing cloud of interstellar gas, which is held together by the mutual gravitational attraction of all the atoms and molecules that make up the cloud. As the cloud collapses, the overall force of gravity that draws the cloud inward____because____.
- gradually becomes stronger - the strength of gravity follows an inverse square law with distance
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Part B: As the cloud shrinks in size, its rate of rotation____because____.
- speeds up - its total angular momentum is conserved
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Part C: As the cloud shrinks in size, its central temperature____as a result of its____.
- increases - gravitational potential energy being converted to thermal energy
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Part D: Suppose that the Sun were to collapse from its current radius of about 700,000 km to a radius of only about 6000 km (about the radius of Earth). What would you expect to happen as a result?
A tremendous amount of gravitational potential energy would be converted into other forms of energy, and the Sun would spin much more rapidly.
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Part E: Suppose that two asteroids are orbiting the Sun on nearly identical orbits, and they happen to pass close enough to each other to have their orbits altered by this gravitational encounter. If one of the asteroids ends up moving to an orbit that is closer to the Sun, what happens to the other asteroid?
It will end up on an orbit that is farther from the Sun.
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Part A: As shown in the video, Earth has two tidal bulges at all times. Approximately where are these bulges located?
One faces the Moon and one faces opposite the Moon.
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Part B: Most people are familiar with the rise and fall of ocean tides. Do tides also affect land?
Yes, though land rises and falls by a much smaller amount than the oceans.
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Part C: Any particular location on Earth experiences
two high tides and two low tides each day.
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Part D: One tidal bulge faces toward the Moon because that is where the gravitational attraction between Earth and the Moon is strongest. Which of the following best explains why there is also a second tidal bulge?
The second tidal bulge arises because gravity weakens with distance, essentially stretching Earth along the Earth-Moon line.
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Part E: As you watch the video, notice that the size of the tidal bulges varies with the Moon's phase, which depends on its orbital position relative to the Sun. Which of the following statement(s) accurately describe(s) this variation?
- Low tides are lowest at both full moon and new moon. - High tides are highest at both full moon and new moon.
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Part F: You have found that tides on Earth are determined primarily by the position of the Moon, with the Sun playing only a secondary role. Why does the Moon play a greater role in causing tides than the Sun?
Because the gravitational attraction between Earth and the Moon varies more across Earth than does the gravitational attraction between Earth and the Sun.
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Which person is weightless during the activity shown?
The diver is the only person that is in free-fall, and hence the only one that is weightless (aka the only person fully in the air.)
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Which of the following statements about the force attracting these two galaxies is true?
It is the same force that causes an apple to fall to the ground.
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The diagram shows a planet at four positions in its orbit. At which position does it have the greatest angular momentum?
The angular momentum is the same at all four points.
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The diagram shows a planet at four positions in its orbit. At which position does it have the greatest gravitational potential energy?
Position 3
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The diagram shows a planet at four positions in its orbit. At which position does it have the greatest total orbital energy? (Orbital energy is the sum of the planet's kinetic and gravitational potential energy.)
The total orbital energy is the same at all four positions.
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Which of the paths shown represent unbound orbits?
Both 2 and 3
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Suppose you are aboard a rocket that is orbiting Earth in the low, circular orbit shown. If you want to escape from Earth and head to the Moon or Mars along the "escape" path shown, what do you need to do?
Fire the rocket engine in your direction of travel, so that you gain speed.
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Which of the following correctly shows tidal bulges on Earth when the Moon is in the position shown?
two tidal bulges: one facing the Moon and one on the side of Earth opposite to the Moon
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In which position(s) of the Moon do we experience the highest high tides?
Positions 1 and 3
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In which position(s) of the Moon do we experience the lowest low tides?
Positions 1 and 3
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Part A: As a giant cloud of gas collapses due to gravity, you would expect its rate of rotation to
increase
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Part B: Which of the following represents a change from potential energy to kinetic energy?
A rock starting from rest on a high cliff, then moving faster and faster as it falls.
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Part C: Suppose two objects are attracting each other gravitationally. If you double the distance between them, the strength of their gravitational attraction
decreases by a factor of 4
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Part D: As a giant cloud of gas collapses due to gravity, you would expect its rate of rotation to