Answer: Which runs slower, a clock at the top of the

Problem 1E What is different about the reference frames that apply to special relativity and to general relativity?

What is the principal difference between the theory of special relativity and the theory of general relativity?

Problem 2RQ In a spaceship accelerating at g, far from Earth’s gravity, how does the motion of a dropped ball compare with the motion of a ball dropped at Earth’s surface?

Problem 3E Provide a classical explanation for an astronaut in an orbiting spacecraft experiencing no net force (as measured by a weighing scale), even though the astronaut is in the grips of Earth gravity.

Problem 3RQ Exactly what is equivalent in the principle of equivalence?

Problem 4E An astronaut is provided a “gravity” when the spaceship’s engines are activated to accelerate the ship. This requires the use of fuel. Is there a way to accelerate and provide “gravity” without the sustained use of fuel? Explain, perhaps using ideas from Chapter 8.

Problem 4RQ Compare the bending of the paths of baseballs and photons by a gravitational field.

Problem 5E In a spaceship far from the reaches of gravity, under what conditions could you feel as if the spaceship were stationary on Earth’s surface?

Why must the Sun be eclipsed to measure the deflection of starlight passing near the Sun?

Problem 6E In his famous novel Journey to the Moon, Jules Verne stated that occupants in a spaceship would shift their orientation from up to down when the ship crossed the point where the Moon’s gravitation became greater than Earth’s. Is this correct? Defend your answer.

Problem 6RQ What is the effect of strong gravitation on measurements of time?

Problem 7E What happens to the separation distance between two people if they both walk north at the same rate from two locations on Earth’s equator? And just for fun, where in the world is a step in every direction a step south?

Problem 7RQ Which runs slower, a clock at the top of the tallest skyscraper in Chicago or a clock on the shore of Lake Michigan?

Problem 8E We readily note the bending of light by reflection and refraction, but why are we not aware of the bending of light by gravity?

Problem 8RQ How does the frequency of a particular spectral line observed in sunlight compare with the frequency of that line observed from a source on Earth?

Light does bend in a gravitational field. Why is this bending not taken into consideration by surveyors who use laser beams as straight lines?

Problem 9RQ If we view events occurring on a star that is collapsing to become a black hole, do we see time speeded up or slowed down?

Problem 10E Why do we say that light travels in straight lines? Is it strictly accurate to say that a laser beam provides a perfectly straight line for purposes of surveying? Explain.

Problem 10RQ Of all the planets, why is Mercury the best candidate for finding evidence of the relationship between gravitation and space?

Your friend says that light passing the Sun is bent whether or not Earth experiences a solar eclipse. Do you agree or disagree, and why?

Problem 11RQ In what kind of gravitational field are Newton’s laws valid?

Problem 12E In 2004, when Mercury passed between the Sun and Earth, sunlight was not appreciably bent as it passed Mercury. Why?

Problem 12RQ A measuring stick placed along the circumference of a rotating disk will appear contracted, but if it is oriented along a radius, it will not. Explain.

Problem 13E A setting Sun is seen as distorted on Earth, but not by astronauts on the Moon. What causes this distortion?

Problem 13RQ The ratio of circumference to diameter for measured circles on a disk equals ? when the disk is at rest, but not when the disk is rotating. Explain.

Problem 14E At the end of 1 s, a horizontally fired bullet drops a vertical distance of 4.9 m from its otherwise straight-line path in a gravitational field of 1 g. By what distance would a beam of light drop from its otherwise straight-line path if it traveled in a uniform field of 1 g for 1 s? For 2 s?

Problem 14RQ What effect does mass have on spacetime?

Problem 15E Light changes its energy when it “falls” in a gravitational field. This change in energy is not evidenced by a change in speed, however. What is the evidence for this change in energy?

What occurs in the surrounding space when a massive object undergoes a change in its motion?

Problem 16E Would we notice a slowing down or speeding up of a clock if we carried it to the bottom of a very deep well?

Problem 19E Why will the gravitational field intensity increase on the surface of a shrinking star?

Problem 19RQ Is Newtonian physics adequate to get a rocket to the Moon?

Problem 20E Will a clock at the equator run slightly faster or slightly slower than an identical clock at one of Earth’s poles?

Problem 20RQ How does Newtonian physics link with quantum theory and relativity theory?

Problem 23E Which would run slower, a clock at the center of a rotating space habitat or one at the edge? Or would there be no difference?

Problem 25E Splitting hairs, if you shine a beam of colored light to a friend above in a high tower, will the color of light your friend receives be the same color you send? Explain.

Problem 26E Is light emitted from the surface of a massive star red-shifted or blue-shifted by gravity?

Problem 28E Would an astronaut falling into a black hole see the outside universe red-shifted or blue-shifted?

Problem 29E How can we “observe” a black hole if neither matter nor radiation can escape from it?

Problem 40E Make up a multiple-choice question to check a classmate’s understanding of the effect of gravity on time.