Bennick exam

Hunter College of the City University of New York

Science 101 - Foundations of Science, Fall 2000

Study and Exam Questions on Theme 1 - Heliocentricity

Chapter in And Yet it Moves! by Alfred Bennick

I

1. Describe one method for determining the length of a year.
2. Any given method for determining the length of a year has some uncertainty in the result. How can we, while using the same method, reduce this uncertainty and thus obtain a more accurate measure of the length of a year? Why does this work?
3. Describe a major advantage, and a major disadvantage, of the Mayan and Julian Day calendar system.
4. Define a solar calendar, and state a major problem with constructing one. Describe Sosigenes' solution to this problem.

II

5. What is the: celestial pole, celestial equator, ecliptic, vernal equinox?
6. Describe the daily and yearly motion of the sun relative to our horizon and the celestial sphere.
7. Describe the motion of the planets relative to the celestial sphere, pointing out ways in which the motion of Mars, Jupiter, and Saturn is similar to that of Mercury and Venus and ways in which their motion differs.
8. The Babylonians made very accurate observations of the behavior of celestial bodies, but never developed explanations. How did this limit the power of their descriptions?

III

9. What are models of phenomena and why are they developed?
10. What did the Pythagoreans say the laws of the universe were based on? Although they were ultimately unsuccessful, why was their approach nevertheless important?
11. What were Plato's basic assumptions about the motion of heavenly objects, and why did he make these assumptions?
12. What model did Plato use to explain the motions of the planets? In what major way did the motions his model predicted differ from what is observed?
13. What major problem in Plato's model did Eudoxus attempt to address, and what additions to Plato's model did he make to address it?

IV

14. Explain Aristotle's view of the connection between laws governing motions in the heavens and laws governing motions on earth. Why was this view important?
15. What, in Aristotle's view, is forced motion? What causes it to occur? How is this a problem in projectile motion?
16. Explain verbally the relationship Aristotle found among force, resistance, weight, and velocity.
17. Describe how Aristotle reached his conclusions about how objects fall.

V

18. Why and how did Aristotle modify Eudoxus' model of the universe?
19. How did Aristotle's model of the universe explain the great diversity of matter on the earth?
20. State briefly four of Aristotle's arguments for believing that the earth is a sphere and explain clearly the reasoning he used in one of these arguments.
21. Explain the relationship between Aristotle's "natural" motion and his placement of the earth at the center of the universe?

VI

22. In what way did Heracleides propose to modify Aristotle's model of the universe? How did his proposal simplify the model?
23. How did Aristarchus arrive at his conclusions about the relative sizes of the sun and the moon?
24. Why did Aristarchus conclude that the sun was at the center of the universe?
25. State three arguments against a moving earth used by the Greeks before 200 AD. Were these arguments reasonable in the context of the time?

VII

26. What observations did Eratosthenes use to calculate the size of the earth?
27. In air, a necklace weighs 30 grams, while in water it weighs 28 grams. What is the specific gravity of the necklace?
28. The specific gravity of a metal bar is found to be 6.4. The bar is then cut in half and the specific gravity of each piece measured. What specific gravity will be found?
29. Are the results of a given measurement "exact?" If not, why not, and how can you determine the "best," i.e., most probable, value of that measurement?

VIII

30. Ptolemy's model of the planetary system featured epicycles, eccentrics, and equants. Describe two of these.
31. Explain how a major epicycle can account for retrograde motion.
32. Describe "precession of the equinoxes." What information did Hipparchus make use of in discovering this effect?
33. How is Ptolemy's use of equants inconsistent with the basic assumptions Aristotle used in modelling the universe?

IX

34. How did astronomers of the Middle Ages calculate the size of the universe? Why did different astronomers get differing answers for this calculation?
35. How did the scholasticism of Thomas Acquinas so powerfully combine Aristotle's quintessence into a religious view of the universe?
36. What were two experiments proposed by Buridan of Paris to show that there were flaws in Aristotle's description of projectile motion?
37. Describe one of the arguments used by Nicholas of Oresme to demonstrate that Aristotle had not proved some of the statements he made to support the idea that the earth was stationary rather than in motion.

X

38. Describe the solar system according to Copernicus.
39. What did the Copernican system predict about the apparent motion of the stars? Was this observed by his contemporaries?
40. We never see Mercury or Venus very far from the sun. Why, according to Copernicus?
41. How does the Copernican model account for retrograde motion?

XI

42. Tycho never observed any effect of parallax on the apparent position of stars. Explain the hybrid model of the universe he developed and show why it predicts no parallax.
43. Explain the effects of the development of printing on the dissemination and functioning of science.
44. How did the nova and comet seen during Tycho's time cast further doubt on the astronomical system of Aristotle and Ptolemy?
45. Describe the astronomical work of Tycho which contributed most to the discarding of the Ptolemaic system.

XII

46. What led Kepler to conclude that the equant was a better model for the earth's motion around the sun than the eccentric?
47. What led Kepler to conclude that the planets orbited in ellipses rather than circles?
48. How did the first two laws of Kepler conflict with the basic assumptions of Aristotle?
49. What feature of Kepler's third law pleased him so?

XIII

50. How did what Galileo saw on the moon with his telescope undermine Aristotle's astronomy?
51. Explain why the moons of Jupiter which Galileo saw were difficult to reconcile with Aristotle's astronomy.
52. Describe how Galileo's observations of Venus subverted Ptolemy's theory of its motion.
53. Describe sunspots and three of Galileo's discoveries about them.

XIV

54. Define uniform velocity and uniform acceleration.
55. What is new about instantaneous velocity as compared to Aristotle's "change of position?"
56. Give an example of why it is not productive to define uniform acceleration as motion in which the velocity is proportional to the distance traveled.
57. Consider an object which accelerates uniformly, starting from rest, and proceeds to travel one unit of distance in one unit of time. How far will the object travel in five units of time? How long will it take to travel sixty-four units of distance?

XV

58. What led Galileo to conclude that in the absence of resistance the velocity which a falling object acquires depends only on the height it falls and not on the path through which it falls?
59. How did Galileo conclude that an object in motion on a frictionless horizontal surface will continue its motion forever?
60. What three assumptions did Galileo make in order to explain projectile motion?
61. How did Galileo's theory of resisted motion differ from that of Aristotle?

XVI

62. How did Descartes modify Galileo's law for motion in the absence of forces?
63. Describe how two straight line trips of four miles and three miles can add up to a single straight line trip of five miles.
64. What is "conservation of 'motion'?" What changes occur in the amount of "motion" in the course of a collision in which both objects are moving before the collision?

XVII

65. Define inertia. What characteristic of an object measures its inertia?
66. What observations led Newton to reject Descartes' vortices?
67. State Newton's first law of motion.
68. Describe the concept of "absolute, universal time," and name three difficulties associated with attempting to measure it.

XVIII

69. A hanging weight consisting of six paper clips is used to accelerate a glider on an air track. If a two paper clip weight is used, how will the new acceleration compare to the first acceleration? If the original six paper clip weight is used to accelerate a new glider which weighs three times as much as the old one, how will its acceleration compare to the first acceleration?
70. What is an object's weight, according to Newton?
71. Team A is in a tug-of-war with Team B. The A's are winning, as they are making the B's accelerate in the A's direction. How does the force that the A's are exerting on the B's compare to the force the B's exert on the A's? Explain.

XIX

72. Is an object traveling at a constant speed v around a horizontal circular path of radius r accelerating? If not, explain; if it is, give the magnitude and direction of the acceleration.
73. What do the falling apple and the moon have in common that may have led Newton to his law of gravity?
74. Show that inertial motion automatically predicts Kepler's second law of planetary motion.
75. Write an expression for Newton's law of gravity and explain what each symbol represents.

XX

76. What did Newton modify in Kepler's third law of planetary motion?
77. Describe two problems with Newton's gravitational theory which he did not explain.
78. Explain how Newton's law of gravity predicts that there are two high tides about every 24 hours.

XXI

79. Explain why a person walking at a uniform velocity straining to carry a heavy load does no mechanical work on that load.
80. Define energy and kinetic energy. Define and write a mathematical expression for gravitational potential energy.
81. An object at rest six feet above the floor has 24 units of gravitational potential energy. It falls freely downward. At the instant when it is two feet above the floor, what is its gravitational potential energy and its kinetic energy?

XXII

82. What is the relationship between the potential and kinetic energy of an object in a circular orbit?
83. What observational evidence convinced Lord Rumford that heat was a form of energy?
84. Two equal-weight lumps of chewing gum traveling toward each other collide, stick together, and stop. The kinetic energy they had before the collision is gone. Does this violate conservation of energy? Explain.
85. Explain how to use conservation of energy to calculate quantitatively your speed at the bottom of a roller coaster, neglecting friction.

XXIII

86. As an astronaut in a circular orbit around the earth, how can you best catch up with a satellite in the same orbit, but ahead of you, using the least amount of fuel?
87. If you are an astronaut in a circular orbit around the earth, what should you do to go into an orbit farther from the earth? A diagram may clarify your explanation. How does your speed in the larger orbit compare to your original speed?
88. If someone pushed you out of an orbiting satellite, your chances of being rescued would be better if you were pushed perpendicular to, rather than along, the direction the satellite was moving. Why?

XXIV

(This chapter will not be covered in the lecture, and none of these questions will be on any exam. You may nevertheless wish to look at them.)

1. Why can a rocket work in a vacuum where there is no air to push against?
2. In which direction, relative to the earth's motion, should a rocket headed to Mars be traveling at the "edge of the earth's gravitational field." Which gravitational field is strongest on the rocket during most of its trip? When it arrives at Mars, how does the rocket's speed compare to that of Mars?
3. How could we use Jupiter as a "slingshot" to help launch a space probe out of the solar system?
4. Explain why it is harder to reach the sun than the nearest star, although the star is over 250,000 times farther from us than the sun is.

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