Chapter 4 Astronomy Homework

Which person is weightless? A. An astronaut on the Moon. B. A child in the air as she plays on a trampoline. C. A scuba diver exploring a deep-sea wreck.

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

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. M = 1, D = 2, M = 1. M = 1, D = 2, M = 2. M = 1, D = 1, M = 1. M = 1, D = 1, M = 2. M = 2, D = 1, M = 2.

(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. Correct. You have correctly taken into account both the masses of the asteroids and the distances between them.

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? Check exactly two of the following diagrams. A. Mass = 0.5 kg; size = basketball; height = 30 m. B. Mass = 0.5 kg; size = basketball; height = 20 m. C. Mass = 5.0 kg; size = bowling ball; height = 20 m. D. Mass = 0.5 kg; size = marble; height = 30 m.

A. Mass = 0.5 kg; size = basketball; height = 30 m. D. Mass = 0.5 kg; size = marble; height = 30 m. Correct. The variable of interest is now size, so appropriate trials to compare are those in which size differs but other variables are constant.

Process of Science: Testing the Law of Gravity. Learning Goal: To understand how different variables affect the design of experiments used to test the universal law of gravitation. Introduction. More than 400 years ago, Galileo claimed that all objects on Earth should fall with the same acceleration of gravity if we neglect air resistance. A few decades later, Newton showed this claim to be a consequence predicted by his theory of gravity. For the following questions, assume that you have been asked to test Newton's theory with experiments that involve dropping balls and timing their falls. 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? Check exactly two of the following diagrams. A. Mass = 5.0 kg; size = bowling ball; height = 20 m. B. Mass = 0.5 kg; size = marble; height = 30 m. C. Mass = 0.5 kg; size = basketball; height = 20 m. D. Mass = 0.5 kg; size = basketball; height = 30 m.

A. Mass = 5.0 kg; size = bowling ball; height = 20 m. C. Mass = 0.5 kg; size = basketball; height = 20 m. 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.

Newton's theory of gravity has been tested extensively, and while it passed many tests, it did not pass all of them. For example, its prediction for how Mercury's orbit changes with time disagrees slightly with observations. Einstein's general theory of relativity improves on Newton's theory: In most cases the two theories of gravity predict the same results, but in the situations where they differ, Einstein's theory works better than Newton's. --------------------------- 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? A. Scientists dropping balls on the Moon find that balls of different mass fall at slightly different rates. B. Scientists dropping balls from the Leaning Tower of Pisa find that balls of different size but the same mass fall at slightly different rates. C. Scientists dropping balls from the Leaning Tower of Pisa find that balls of different mass but the same size fall at slightly different rates.

A. 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 theory.

A car is accelerating when it is ____. A. going around a circular track at a steady 100 miles per hour. B. traveling on a straight, flat road at 50 miles per hour. C. traveling on a straight uphill road at 30 miles per hour.

A. going around a circular track at a steady 100 miles per hour.

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 __________. A. greater than your normal weight at rest. B. equal to your normal weight at rest. C. less than your normal weight at rest.

A. 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.

If Earth were twice as far from the Sun, the force of gravity attracting Earth to the Sun would be ____. A. one-quarter as strong. B. one-third as strong. C. half as strong. D. twice as strong.

A. one-quarter as strong. (because 2 would be 1 over 2 squared, as the inverse square law suggests).

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 __________. A. the Moon has a larger acceleration than Earth, because it has a smaller mass. B. Earth has a larger acceleration than the Moon, because it has a larger mass. C. the Moon and Earth both have equal accelerations, because the forces are equal.

A. 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.

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. A. The two balls take different amounts of time to reach the ground. B. Both balls fall to the ground in the same amount of time. C. The less massive ball takes longer to reach the ground. D. The more massive ball takes longer to reach the ground.

B. Both balls fall to the ground in the same amount of time. 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.

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? A. Earth would slowly spiral into the black hole. B. Earth's orbit would not change. C. Earth would slowly fall into the black hole. D. Earth would be quickly sucked into the black hole.

B. Earth's orbit would not change.

To make a rocket turn left, you need to: ____. A. fire an engine that shoots out gas to the left. B. fire an engine that shoots out gas to the right. C. spin the rocket clockwise.

B. fire an engine that shoots out gas to the right.

If you are standing on a scale in an elevator, what exactly does the scale measure? A. your mass. B. the force you exert on the scale. C. the gravitational force exerted on you by Earth.

B. the force you exert on the scale. Correct. 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.

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? A. Because gravity has a greater effect on the larger ball. B. Because air resistance has a greater effect on the smaller ball. C. Because air resistance has a greater effect on the larger ball. D. Because gravity has a greater effect on the smaller ball.

C. 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. ------------------------ Newton's theory of gravity has been tested extensively, and while it passed many tests, it did not pass all of them. For example, its prediction for how Mercury's orbit changes with time disagrees slightly with observations. Einstein's general theory of relativity improves on Newton's theory: In most cases the two theories of gravity predict the same results, but in the situations where they differ, Einstein's theory works better than Newton's.

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 __________. A. greater than your normal weight at rest. B. equal to your normal weight at rest. C. less than your normal weight at rest.

C. 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, 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.

Compared to their values on Earth, on another planet your ____. A. weight would be the same but your mass would be different. B. mass and weight would both be the same. C. mass would be the same but your weight would be different.

C. mass would be the same but your weight would be different.

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? A. The elevator moves upward with constant velocity. B. The elevator moves downward with constant velocity. C. The elevator moves upward while slowing in speed. D. The elevator moves downward while slowing in speed. E. The elevator moves downward while increasing in speed.

D. The elevator moves downward while slowing in speed. Correct. 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.

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. Asteroid: hydrogen atom. Asteroid: Asteroid. Asteroid: Moon. Asteroid: Earth. Asteroid: Sun.

Largest Acceleration. 1. Asteroid: Sun. 2. Asteroid: Earth. 3. Asteroid: Moon. 4. Asteroid: Asteroid. 5. Asteroid: hydrogen atom. Smallest Acceleration. 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.

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.

Pictures closer to Earth exhibit a stronger force. Pictures farther from Earth exhibit a weaker force. Correct. 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.

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.

Pictures closer to Moon exhibit a stronger force. Pictures farther from Moon exhibit a weaker force. Correct. 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.

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: hydrogen atom. Asteroid: Asteroid. Asteroid: Moon. Asteroid: Earth. Asteroid: Sun.

Strongest Force. 1. Asteroid: Sun. 2. Asteroid: Earth. 3. Asteroid: Moon. 4. Asteroid: Asteroid. 5. Asteroid: hydrogen atom. Weakest Force. 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.

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. Asteroid: hydrogen atom. Asteroid: Asteroid. Asteroid: Moon. Asteroid: Earth. Asteroid: Sun.

Strongest Force. 1. Asteroid: Sun. 2. Asteroid: Earth. 3. Asteroid: Moon. 4. Asteroid: Asteroid. 5. Asteroid: hydrogen atom. Weakest Force. 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.