Combo with "Astronomy Ch04.2: Key Concept: Understanding Tides" and 7 others

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.

- d = 2; m = 2; m = 2 - d= 1; m = 1; m = 2 - d = 1; m = 1; m = 1 - d = 2; m = 1; m = 2 - d = 2; m = 1; m = 1

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.

According to Newton's second law, the asteroid with the largest acceleration will be the one that has the strongest gravitational force exerted on it by the object on the right. That is why the ranking here is the same as the ranking for Part A.

Part E As you watch the animation, 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.

As the animation shows, the tidal bulges are largest and the tidal minima are smallest at full moon and new moon, because those are the times when the tidal forces due to the Sun and Moon are aligned (and therefore add to one another). Therefore, high tides are higher and low tides are lower at these times, which are called spring tides. (In contrast, we have neap tides at first- and third-quarter moons, when high tides are not as high and low tides are not as low.)

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. - asteroid:sun - asteroid:earth - asteroid:moon - asteroid:asteroid - asteroid:hydrogen atom

Because the distance is the same for all five cases, the gravitational force depends only on the product of the masses. And because the same asteroid is on the left in all five cases, the relative strength of gravitational force depends on the mass of the object on the right. Continue to Part B to explore what happens if we instead ask about the gravitational force acting on the object on the right.

Part E 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.

Dropping the balls on the Moon removes any potential effects due to air resistance, so a result in which mass affects the rate of fall would directly contradict the prediction of Einstein's theory.

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. Assume the spaceship has the same mass throughout the trip (that is, it is not burning any fuel). 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.

Gravity follows an inverse square law with distance, which means the force of gravity between Earth and the spaceship weakens as the spaceship gets farther from Earth.

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

The Sun exerts a stronger gravitational force on Earth, which is why Earth orbits the Sun. However, tides are caused by the variation in the gravitational attraction across Earth. Even though the gravitational attraction between Earth and the Moon is smaller than the attraction between Earth and the Sun, the Moon's much closer distance makes this attraction vary more across Earth. That is why tides are due primarily to the Moon, with only a secondary effect from the Sun.

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.

The dramatic shrinkage of the Sun would mean the loss of a huge amount of gravitational potential energy. Because energy is always conserved, this "lost" gravitational potential energy must reappear in other forms, such as heat (thermal energy) and light (radiative energy). Meanwhile, conservation of angular momentum would ensure that the collapsed Sun would spin much faster.

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.

Tides are created by gravity, and the tidal force is caused by the fact that gravity weakens with distance. Therefore, the parts of Earth that are closer to the Moon feel a stronger gravitational attraction to the Moon, and the parts of Earth that are farther away feel a weaker gravitational attraction to the Moon. This varying gravitational attraction essentially stretches Earth along the Earth-Moon line, creating tidal bulges on both sides.

Part D If you are standing on a scale in an elevator, what exactly does the scale measure? - the force you exert on the scale

You probably recognize that neither your mass nor the gravitational force exerted on you change when you are in an elevator. The scale measures the force that is exerted on it, which in an elevator is a combination of the force due to your normal weight and a force due to the elevator's acceleration.

An apple contains ______ energy that your body can convert into other forms energy.

chemical potential

An asteroid that is moving farther from the Sun is gaining ______ energy.

gravitational potential

Rapidly moving comets have more ______ energy than slowly moving ones.

kinetic

Nuclear fusion in stars converts some of the ______ energy of hydrogen nuclei into light and heat.

mass-

The light from Polaris travels through space in the form of ______ energy.

radiative

Due to its much higher density, water heated to 80 degrees (Celsius) contains more ______ energy than air at the same temperature.

thermal

Part C As the cloud shrinks in size, its central temperature __________ as a result of __________. - increases - gravitational potential energy being converted to thermal energy

As the cloud shrinks in size, its gravitational potential energy decreases. Because energy cannot simply disappear, the "lost" gravitational potential energy must be converted into some other form. Some of it is converted into thermal energy, which raises the temperature of the gas cloud. The rest is mostly converted into radiative energy, which is released into space as light.

Part B 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

Even though the elevator is still moving upward, the fact that its speed is slowing means that the acceleration is downward; the situation is rather like that of a ball that is still on its way up after you throw it, even though it is being pulled downward with the acceleration of gravity. Because the acceleration of the elevator is downward, your weight is lower than normal.

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.

Gravity follows an inverse square law with distance, which means the force of gravity between the Moon and the spaceship increases as the spaceship approaches the Moon. Now continue to Part C for activities that look at the effects of both distance and mass on gravity.

Part A 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

Increasing speed means acceleration, and when the elevator is accelerating upward you will feel a force pressing you to the floor, making your weight greater than your normal (at rest) weight.

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

Newton's second law of motion, F=ma, means that for a particular force F, the product mass x acceleration must always be the same. Therefore if mass is larger, acceleration must be smaller, and vice versa.

Part B 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.

Newton's theory of gravity predicts that, in the absence of air resistance, all objects on Earth should fall with the same acceleration of gravity, regardless of mass. This means that balls dropped from the same height should take the same amount of time to reach the ground.

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.

Newton's third law tells us that the gravitational force exerted on the asteroid on the left by the object on the right will be equal in magnitude, but opposite in direction to the gravitational force exerted on the object on the right by the asteroid on the left. That is why the ranking here is the same as the ranking for Part A.

Part C Any particular location on Earth experiences __________. - two high tides and two low tides each day

The animation shows that any location on Earth passes through both tidal bulges and both tidal minima (the places where the tides are smallest) each day, which means two high tides and two low tides. Again, recall that this is true both of land and oceans, though tides are more noticeable in the oceans because water flows so much more readily than land.

Part A The animation shows a collapsing cloud of interstellar gas. As the cloud collapses, the force of gravity drawing the cloud inward __________ because __________. - gradually becomes stronger - the strength of gravity follows an inverse square law with distance

The force of gravity between any two particles increases as the particles come closer together. Therefore, as the cloud shrinks and particles move closer together, the force of gravity strengthens. This will tend to accelerate the collapse as long as no other force resists it—which is the case during the early stages of the collapse before the internal gas pressure builds up. (Once the gas pressure builds up, the outward push of the pressure can counteract the inward pull of gravity, which is why the cloud eventually stops contracting.)

Part D 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.

The larger size and lower density of the basketball means it will encounter more air resistance than the marble, so it will take slightly longer to reach the ground.

Part A 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? - mass:5.0kg ; size:bowling ball ; height:20m - mass:5.0kg ; size:basketball ; height:20m

The simplest way to test the effects of mass is to compare the results of two trials that are identical except for the mass of the balls. In the language of experimental design, we say that the mass is the "variable of interest" for this experiment, and we therefore hold the other variables (size and height) constant so that they cannot affect the results.

Part A As shown in the animation, Earth has two tidal bulges at all times. Approximately where are these bulges located? - One faces the Moon, and one faces opposite the Moon.

The tidal bulges face toward and away from the Moon, because they are caused primarily by the gravitational attraction between Earth and the Moon. (Friction explains why the bulges are slightly ahead of the Earth-Moon line, rather than directly on the Earth-Moon line; but we'll ignore that detail for now.)

Part C 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? - mass:0.5kg ; size:marble ; height:30m - mass:0.5kg ; size:basketball ; height:30m

The variable of interest is now size, so appropriate trials to compare are those in which size differs but other variables are constant.

Part B Most people are familiar with the rise and fall of ocean tides, but do tides also affect land? - Yes, though land rises and falls by a much smaller amount than the oceans.

Tides affect the entire Earth, but they are much more noticeable for the oceans because water flows so much more easily than land. Still, the land rises and falls measurably (by about 1 centimeter) with the tides.

Part B As the cloud shrinks in size, its rate of rotation __________ because __________. - speeds up - its total angular momentum is conserved

Total angular momentum is always conserved. In this case, because nothing is carrying angular momentum into or out of the cloud, the cloud's angular momentum stays constant. Maintaining constant angular momentum as the cloud shrinks requires that its rate of rotation increase, because angular momentum depends on the product of rotation rate and radius.

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.

Total energy must be conserved, so if one asteroid loses energy and moves to a closer orbit, the other must gain energy and move to a more distant orbit.

Part C 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.

When the elevator is moving downward, a downward acceleration would mean an increasing downward speed. Therefore, as your answer correctly states, an upward acceleration would mean a decreasing downward speed.