Arts and Science 2D06 - 2008/09
Suggested Chapter Problems

It helps to study physics by doing as many sample problems as possible. Here are recommended problems taken from each chapter of the text relevant to our curriculum. Most are the odd-numbered ones, so you can check your answer in the back of the book.

Notice the chapter problems come in two types: conceptual Questions that usually involve descriptive reasoning; and quantitative Problems that involve calculations. The Questions are just as important as the Problems at probing your understanding of the key concepts in the chapter ... do both types. And do as many as you have time for. The suggested lists below may look quite long -- but that's just to give you a lot to choose from; a quick reading of each problem may tell you right away whether it will tell you something new or not. Enjoy!

If you get stuck with finding the right method or setting up the problems -- please don't hesitate to get help from either me or your TA. We're available!

More problems will be added as we get farther into the term. Do not bother to work too far ahead of lectures -- it may be counterproductive.

• Chapter 2:
  Questions 1, 2, 7, 10, 11, 14, 15, 17
  Problems 9, 15, 18, 23, 31, 33, 37, 45, 47, 55, 61, 83, 89


• Chapter 3:
  Questions 2, 6, 13, 16, 24, 25
  Problems 7, 11, 15, 18, 19, 23, 27, 29, 33, 37, 45, 51, 83


• Chapter 4:
  Questions 5, 6, 11, 14, 19
  Problems 5, 7, 13, 19, 35, 41, 47, 61, 67, 73


• Chapter 5:
  Questions 6, 7, 12, 15
  Problems 5, 7, 11, 16, 17, 27, 37, 43, 45, 47, 69, 79


• Chapter 7:
  Questions 5, 6, 8, 12, 14
  Problems 3, 5, 15, 17, 21, 31, 37, 45, 47, 49, 67, 69, 71


• Chapter 8:
  Questions 5, 9, 13, 14, 21
  Problems 1, 3, 9, 11, 13, 17, 21(a-d), 27, 31, 72, 79


• Chapter 6:
  Questions 1, 13, 20
  Problems 1, 3, 5, 21


• Chapter 10:
  Questions 3, 13, 21, 22, 23
  Problems 3, 5, 7, 69, 71, 87, 107a


• Chapter 9:
  Questions 3, 4, 9, 10, 14
  Problems 2, 9, 11, 13, 23, 32, 35, 46, 51, 85


• Chapter 37:
  Study sections 1 - 11 (that is, the shorter versions of them covered in lectures -- no need to study the derivations).
  
  Questions: 1, 3, 5, 8, 11, 13, 18
  Problems: 1, 3, 5, 6 (answer: v/c=0.943), 7, 9, 13, 15, 25, 29, 33, 35, 37, 61, 67
  
  Extra relativity problems on Lorentz transformation:
  
  (1) Reference frames (xy) and (x'y') coincide at t = t' = 0, and (x'y') is moving to the right at v = 0.8 c. At t' = 0.01 sec and x' = 400 km, a light goes on. Where and when did this event occur in the "lab" frame (xy)?
  (answer: x = 4667 km, t = 0.018 sec)
  
  (2) A light goes on at (x=0, t=0), and a bit later on a second light goes on at (x = 90 km, t = 0.00016 sec). Now suppose that a second reference frame (x'y') travels to the right at speed v. What is the necessary speed v for which these two events are simultaneous as seen from (x'y')?
  (answer: v = 0.53 c)
  
  (3) A spaceship travelling at v = 0.9 c fires a light beam straight ahead, directly towards a mirror that is 300,000 km away (as seen from the "outside" laboratory frame). The light beam reflects off the mirror and goes straight back towards the ship. Where does the beam meet up with the ship (as measured from its original position), and how long does it take?
  (answer: x = 285,000 km, t = 1.05 sec)
  As measured from within the ship, where and when does the beam meet up with it?
  (answer: x' = 0, t' = 0.45 sec)


• Chapter 13:
  Questions 2, 4, 8, 9, 13, 21
  Problems 3, 5, 7, 13, 21, 23a, 27, 29, 31, 33, 45, 50, 51, 52, 55


• Chapter 14:
  Questions 3, 6, 8, 12, 13
  Problems 1, 3, 5, 7, 13, 15, 19, 27, 41, 43, 45 (Hint: At what time t is it at theta = 5 degrees? At what time is it at theta = -5 degrees? So then what is the time interval between those two positions?)


• Chapter 15:
  Questions 2, 15, 17
  Problems 1, 12, 21, 23, 25, 35, 37, 41, 61


• Chapter 35:
  Questions 6, 9
  Problems 3, 5, 9 (NB: in problem 9, it asks what wavelength of visible light would have a minimum at the same location. Visible light is between 400 and 800 nm.)
  
  Supplementary problem: Light of wavelength 627 nm illuminates a pair of slits 1000 nm apart. What is the smallest angle (theta) at which the light intensity of the fringe pattern is 1/4 of the central maximum? (ans: 0.211 radian)


• Chapter 36:
  Questions 5, 11
  Problems 2, 3, 13


• Chapter 38:
  Questions 14, 16, 17, 18, 23, 25, 29
  Problems 5, 9, 11, 31, 37, 42 [ans: (a)], 43, 49, 85


• Chapter 39:
  Questions 2, 4, 8, 11 (NB: what question 11 means is that the wave function is zero at some points in the box, where the nodes are. Can the particle travel "through" a node?)
  Problems 1, 3, 7, 9(a,b), 16, 17, 19, 21, 25, 41, 45


• Review questions for General Relativity:
  1) It seems paradoxical to say that free-fall is equivalent to no gravity, because isn't free-fall caused by the action of gravity? What does Einstein mean by this? State the equivalence principle in your own words.
  
  (2) How does your body feel in free fall? How would it feel in a region of space far away from the Earth where there are no nearby masses and no gravity?
  
  (3) Einstein's principle says that if a beam of light goes across the room, it actually falls in the gravitational field, just like a projectile. Why don't we see this happening, or what makes it difficult to actually measure?
  
  (4) Contrast the Newtonian and Einsteinian views of what gravity is. Describe.
  
  (5) In what ways can we actually see the effects of curved space on light (or other objects) travelling through it?
  
  (6) What's an 'escape velocity'?
  
  (7) Calculate the mass of a black hole that has a radius (= Schwarzschild radius, or equivalently the radius of the event horizon) equal to 1 km. How massive is that compared with the mass of the Earth?
  
  (8) Suppose you are standing at the edge of a cliff, holding a ball. At time t = 0, you jump off the cliff and simultaneously toss the ball straight upward. Draw a graph of y'(t) where y' is the distance of the ball above you; that is, y' is the location of the ball relative to you. What has happened to the acceleration due to gravity, in this graph? (First it might help to draw a graph of y1(t) and y2(t), where y is your position relative to the top of the cliff and y2 is the position of the ball relative to the top of the cliff.)