Astronomy Chapter 5

The acceleration of gravity on Earth is approximately 10 m/s2 (more precisely, 9.8 m/s2). If you drop a rock from a tall building, about how fast will it be falling after 3 seconds?

30 m/s (not m/s^2)

Newton showed that Kepler's laws are ________.

natural consequences of the law of universal gravitation

As a gas cloud in space shrinks, it

spins faster

When you are standing on a scale in an elevator, what exactly does the scale measure?

the force you exert on the scale 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.

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.

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.

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.

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.

Consider the elliptical orbit of a comet around the Sun. Where in its orbit does it have the largest amount of total orbital energy?

It always has the same total orbital energy.

Suppose you are in an elevator that is traveling upward at constant speed. How does your weight compare to your normal weight on the ground?

It is the same

If the Sun instantaneously turned into a black hole of one solar mass, what would happen to the Earth?

It would continue to orbit the black hole.

The fact that Voyager 1 continues to speed out of the solar system, even though its rockets have no fuel, is an example of

Newton's first law of motion.

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 (as well as Newton's) theory.

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?

The elevator moves downward while slowing in speed. 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.

If the Earth rotated once every 48 hours, and everything else was the same, which of the following statements would NOT be true?

The length of the year would be longer.

Imagine a spaceship in orbit around a planet. Its engine suffers a severe malfunction, and explodes. What is the most physically realistic depiction of this event?

The spacecraft breaks apart, and the pieces continue to orbit the planet.

Suppose you are in an elevator car when the elevator cable breaks. Which of the following correctly describes what happens and why.

You float weightlessly within the elevator car because you and the elevator both begin to accelerate downward at the same rate. 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!

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.

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: 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.