Chapter 4 Homework

Chapter 4 Homework Problem 4.28 Consider the statement "There's no gravity in space." This statement is: - Completely false. - False if you are close to a planet or moon, but true in between the planets. - Completely true.

- Completely false. Correct

Chapter 4 Homework Key Concept: Understanding Tides Most people are familiar with the rise and fall of ocean tides. Do tides also affect land? Part B - Yes, though land rises and falls by a much smaller amount than the oceans. - No, tides only affect the oceans. - Yes, land rises and falls with tides equally as high (and low) as the oceans. - No, tides can only affect liquids and gases, not solids.

- Yes, though land rises and falls by a much smaller amount than the oceans. Correct 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 about 1 centimeter with the tides.

Chapter 4 Homework Prelecture Concept Question 4.6 The planets never travel in a straight line as they orbit the Sun. According to Newton's second law of motion, this must mean that _________. - a force is acting on the planets - the planets are always accelerating - the planets will eventually fall into the Sun - the planets have angular momentum

- a force is acting on the planets Correct Because the planets are not traveling in straight lines, the planets are always accelerating, and Newton's second law tells us that a force must be acting to cause the acceleration

Chapter 4 Homework Visual Activity: Weight and Weightlessness in a Moving Elevator 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 __________. Part A - greater than your normal weight at rest - less than your normal weight at rest - equal to your normal weight at rest

- greater than your normal weight at rest Correct 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.

Chapter 4 Homework Process of Science: Testing the Law of Gravity 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. - Because gravity has a greater effect on the larger ball. - Because gravity has a greater effect on the smaller ball. - Because air resistance has a greater effect on the smaller ball.

- Because air resistance has a greater effect on the larger ball. Correct 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.

Chapter 4 Homework Visual Activity: Weight and Weightlessness in a Moving Elevator Suppose you are in an elevator car when the elevator cable breaks. Which of the following correctly describes what happens and why. - You will crash your head into the elevator car ceiling because the car will be falling rapidly away from you. - You float weightlessly within the elevator car because Earth's gravity is no longer tugging on you. - You float weightlessly within the elevator car because you and the elevator both begin to accelerate downward at the same rate. - You will remain stuck to the elevator floor as you and the elevator plunge downward toward a horrific crash. - You will crash your head into the elevator car ceiling because Earth's gravity will be pulling the car down faster than it pulls you down.

- You float weightlessly within the elevator car because you and the elevator both begin to accelerate downward at the same rate. Correct Once the cable breaks, you and the elevator car both fall with the acceleration of gravity. This means you are no longer pressing against the scale or the elevator floor, so you float weightlessly within the car -- though only until you and the car hit the ground!

Chapter 4 Homework Problem 4.34 If the Moon were closer to Earth, high tides would: - be higher than they are now. - be lower than they are now. - occur three or more times a day rather than twice a day.

- be higher than they are now. Correct

Chapter 4 Homework Key Concept: Making Predictions with Physical Laws As the cloud shrinks in size, its central temperature __________ as a result of its __________. Drag words indicating what happens to the first blank and indicating the reason to the second blank.

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

Chapter 4 Homework Visual Activity: Weight and Weightlessness in a Moving Elevator In Part A, you found that your weight will be greater than normal when the elevator is moving upward with increasing speed. For which of the following other motions would your weight also be greater than your normal weight? Part C - The elevator moves upward while slowing in speed. - The elevator moves upward with constant velocity. - The elevator moves downward with constant velocity. - The elevator moves downward while increasing in speed. - The elevator moves downward while slowing in speed.

- The elevator moves downward while slowing in speed. Correct In a downward-moving elevator, the elevator can be slowing only if it has an upward acceleration. As you know from Part A, an upward acceleration will give you an increased weight. Therefore, in an elevator that moves downward while slowing in speed, the acceleration is upward and your weight is greater than normal.

Chapter 4 Homework Visual Activity: Weight and Weightlessness in a Moving Elevator Which person is weightless? - A child in the air as she plays on a trampoline. - A scuba diver exploring a deep-sea wreck. -An astronaut on the Moon.

- A child in the air as she plays on a trampoline.

Chapter 4 Homework Key Concept: Making Predictions with Physical Laws 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? - Both the total amount of energy and the rotation rate would remain the same. - A tremendous amount of gravitational potential energy would be converted into other forms of energy, and the Sun would spin much more rapidly. - A tremendous amount of gravitational potential energy would be converted into other forms of energy, and the Sun would spin much more slowly. - The Sun would gain more energy and more angular momentum.

- A tremendous amount of gravitational potential energy would be converted into other forms of energy, and the Sun would spin much more rapidly. Correct 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.

Chapter 4 Homework Problem 4.33 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 would be quickly sucked into the black hole. - Earth would slowly spiral in to the black hole. - Earth's orbit would not change.

- Earth's orbit would not change. Correct

Chapter 4 Homework Problem 4.29 If you want to make a rocket turn left, you need to: - Fire an engine that shoots out gas to the left. - Fire an engine that shoots out gas to the right. - Spin the rocket clockwise.

- Fire an engine that shoots out gas to the right. Correct

Chapter 4 Homework Key Concept: Understanding Tides 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? Part E - Low tides are highest at both full moon and new moon. - High tides are highest at both full moon and new moon. - Low tides are highest at full moon and lowest at new moon. - High tides are highest at full moon and lowest at new moon. - High tides are highest at first- and third-quarter moon. - Low tides are lowest at both full moon and new moon.

- High tides are highest at both full moon and new moon. - Low tides are lowest at both full moon and new moon. Correct As the video shows, the tidal bulges are largest and the tidal minima are smallest at full moon and new moon. Those are the times when the tidal forces of the Sun and Moon align (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.)

Chapter 4 Homework Prelecture Reading Question 4.10 When a spinning ice skater pulls in his arms, he spins faster because __________. - His angular momentum must be conserved, so reducing his radius must increase his speed of rotation. - There exists an unbalanced reaction force. - There is less friction with the air. - There is less friction with the ice.

- His angular momentum must be conserved, so reducing his radius must increase his speed of rotation. Correct Remember that angular momentum is related to an objects mass × velocity × radius. The skater's mass stays the same but pulling in his arms reduces his "radius," so his velocity or rotation must increase to keep his angular momentum constant.

Chapter 4 Homework Prelecture Reading Question 4.19 Why is Newton's version of Kepler's third law so useful to astronomers? - It tells us that more-distant planets orbit the Sun more slowly. - It can be used to determine the masses of many distant objects. - It allows us to calculate distances to distant objects. - It explains why objects spin faster when they shrink in size.

- It can be used to determine the masses of many distant objects. Correct We can apply Newton's version of Kepler's third law whenever we observe one object orbiting another; this is the primary way that we measure masses throughout the universe.

Chapter 4 Homework Prelecture Reading Question 4.21 Which statement must be true for a rocket to travel from Earth to another planet? - It must carry a lot of extra fuel. - It must attain escape velocity from Earth. - It must have large engines. - It must be launched from space, rather than from the ground

- It must attain escape velocity from Earth. Correct If it does not have escape velocity, it will either fall back down or orbit Earth.

Chapter 4 Homework Key Concept: Making Predictions with Physical Laws 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? Part E - It will also end up on an orbit that is closer to the Sun. - It will stay on its original orbit. - It will end up on an orbit that is farther from the Sun. - It will become much cooler.

- It will end up on an orbit that is farther from the Sun. Correct 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.

Chapter 4 Homework Prelecture Reading Question 4.22 Approximately where is it currently high tide on Earth? Part A - Wherever it is currently noon - On the portion of Earth facing directly toward the Moon and on the portion of Earth facing directly away from the Moon - Only on the portion of the Earth facing directly toward the Moon - Anywhere that ocean water laps up on the shore

- On the portion of Earth facing directly toward the Moon and on the portion of Earth facing directly away from the Moon Correct These are the approximate locations of the two tidal bulges. (Approximate because Earth's rotation pulls the bulge slightly ahead of the Earth-Moon line.)

Chapter 4 Homework Key Concept: Understanding Tides As shown in the video, Earth has two tidal bulges at all times. Approximately where are these bulges located? Part A - One faces the Moon and one faces opposite the Moon. - One faces the Moon and one faces the Sun. - One is over the Atlantic Ocean, and one is over the Pacific Ocean. - Both are on lines perpendicular to the Earth-Moon line.

- One faces the Moon and one faces opposite the Moon. Correct 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. We'll ignore that detail for now.

Chapter 4 Homework Process of Science: Testing the Law of Gravity 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. - Scientists dropping balls from the Leaning Tower of Pisa find that balls of different mass but the same size fall at slightly different rates. - Scientists dropping balls from the Leaning Tower of Pisa find that balls of different size but the same mass fall at slightly different rates.

- Scientists dropping balls on the Moon find that balls of different mass fall at slightly different rates. Correct 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 (as well as Newton's) theory.

Chapter 4 Homework Key Concept: Understanding Tides 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? Part D - The second tidal bulge is created by the Sun's gravity. - The second tidal bulge is created by the centrifugal force caused by Earth's rapid rotation. - The second tidal bulge arises because gravity weakens with distance, essentially stretching Earth along the Earth-Moon line. - The second tidal bulge is a rebound effect, created when water on the side facing the Moon falls back down and thereby pushes up the water on the opposite side of Earth.

- The second tidal bulge arises because gravity weakens with distance, essentially stretching Earth along the Earth-Moon line. Correct 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.

Chapter 4 Homework Prelecture Reading Question 4.07 Which of the following statements is not one of Newton's Laws of Motion? - What goes up must come down. - For any force, there always is an equal and opposite reaction force. - The rate of change of momentum of an object is equal to the net force applied to the object. - In the absence of a net force acting on it, an object moves with constant velocity.

- What goes up must come down. Correct This is not one of Newton's laws, and it's not even true. Objects with escape velocity can go up without coming back down.

Chapter 4 Homework Key Concept: Understanding Tides 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? Part F - because the gravitational attraction between Earth and the Moon varies more across Earth than does the gravitational attraction between Earth and the Sun - because the Moon orbits Earth faster than Earth orbits the Sun - because the gravitational force between Earth and the Moon is stronger than the gravitational force between Earth and 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 Correct 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.

Chapter 4 Homework Prelecture Reading Question 4.16 According to the universal law of gravitation, if you triple the distance between two objects, then the gravitational force between them __________. - decreases by a factor of 9 - decreases by a factor of 3 - increases by a factor of 3 - increases by a factor of 9

- decreases by a factor of 9 Correct Gravity follows an inverse square law, so the force goes down with the square of the distance; in this case, increasing the distance by a factor of 3 causes the force to decrease by a factor of 3^2 = 9.

Chapter 4 Homework Problem 4.31 As an interstellar gas cloud shrinks in size, its gravitational potential energy: - stays the same at all times. - gradually transforms into other forms of energy. - gradually grows larger.

- gradually transforms into other forms of energy. correct

Chapter 4 Homework Visual Activity: Weight and Weightlessness in a Moving Elevator 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 __________. (Be sure to note that the video does not show a situation in which the elevator is slowing while moving upward, so you will need to decide which portion of the video is relevant to this situation; Hint 1 may be helpful.) Part B - equal to your normal weight at rest - less than your normal weight at rest - greater than your normal weight at rest

- less than your normal weight at rest Correct 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: the ball slows as it goes upward because of the downward acceleration of gravity. Because the acceleration of the elevator is downward, your weight is lower than normal.

Chapter 4 Homework Problem 4.32 If Earth were twice as far from the Sun, the force of gravity attracting Earth to the Sun would be: - twice as strong. - half as strong. - one-quarter as strong.

- one-quarter as strong. Correct

Chapter 4 Homework Prelecture Reading Question 4.14 What does temperature measure? - the total amount of heat in a substance - the average mass of particles in a substance - the total potential energy of particles in a substance - the average kinetic energy of particles in a substance

- the average kinetic energy of particles in a substance Correct For example, air molecules are moving faster on average on a hot day than on a cool day.

Chapter 4 Homework Visual Activity: Weight and Weightlessness in a Moving Elevator When you are standing on a scale in an elevator, what exactly does the scale measure? Part D - your mass - the force you exert on the scale - the gravitational force exerted on you by Earth

- the force you exert on the scale Correct Your presence in an elevator cannot change either your mass or the gravitational force exerted on you by Earth. The scale measures the force that is exerted on it, which in an elevator is a combination of the force due to gravity and a force due to the elevator's acceleration.

Chapter 4 Homework Key Concept: Understanding Tides Any particular location on Earth experiences __________. Part C - two sets of high and low tides in the ocean, but only one set on land - one high tide and one low tide each day - two high tides and two low tides each month - one high tide and one low tide each month - two high tides and two low tides each day

- two high tides and two low tides each day Correct The video 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 for both land and oceans, though tides are more noticeable in the oceans because water flows so much more readily than land.

Chapter 4 Homework Vocabulary in Context: Describing Forms of Energy Match the words in the left-hand column to the appropriate blank in the sentences in the right-hand column. Use each word only once.

1. The light from Polaris travels through space in the form of radiative energy. 2. Rapidly moving comets have more kinetic energy than slowly moving ones. 3. An apple contains chemical potential energy that your body can convert into other forms energy. 4. Nuclear fusion in stars converts some of the mass- energy of hydrogen nuclei into light and heat. 5. Due to its much higher density, water heated to 80 degrees (Celsius) contains more thermal energy than air at the same temperature. 6. An asteroid that is moving farther from the Sun is gaining gravitational potential energy.

Chapter 4 Homework Key Concept: Making Predictions with Physical Laws Drag words indicating what happens to the first blank and indicating the reason to the second blank.

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

Chapter 4 Homework Ranking Task: Pairs of Gravitationally Interacting Objects 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.

Correct 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.

Chapter 4 Homework Ranking Task: Pairs of Gravitationally Interacting Objects 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.

Correct 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.

Chapter 4 Homework Ranking Task: Pairs of Gravitationally Interacting Objects 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 and Earth both have equal accelerations, because the forces are equal - Earth has a larger acceleration than the Moon, because it has a larger mass - the Moon has a larger acceleration than Earth, because it has a smaller mass

Correct 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.

Chapter 4 Homework Process of Science: Testing the Law of Gravity 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. - The two balls take different amounts of time to reach the ground. - Both balls fall to the ground in the same amount of time. - The more massive ball takes longer to reach the ground. - The less massive ball takes longer to reach the ground.

Correct 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.

Chapter 4 Homework Ranking Task: Pairs of Gravitationally Interacting Objects 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.

Correct 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.

Chapter 4 Homework Process of Science: Testing the Law of Gravity 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?

Correct 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.

Chapter 4 Homework Process of Science: Testing the Law of Gravity 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?

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

Chapter 4 Homework Key Concept: Making Predictions with Physical Laws Drag words indicating what happens to the first blank and indicating the reason to the second blank.

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 gradually becomes stronger because the strength of gravity follows an inverse square law with distance. Correct 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. This 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.)