Physics 264L: Assignment 4
Made available: Tuesday, September 15, 2015
Due:
Monday, September 21, 2015, by 7 pm
Problems
1. Problem 5-3 on page 160 of French.
2. Two rockets A and B leave a space station with three-dimensional velocity vectors vA and vB as
measured by the space station (which you can consider at rest). Show that the velocity vector vAB
of A relative to B generally does not equal the negative of the velocity vector vBA of B relative to A
and explain why this is the case. Discuss also under what conditions vAB does equal −vBA .
3. Problem 5-9 on page 161 of French.
4. Problem 5-10 on page 161 of French
5. Problem 5-16 on page 162 of French.
6. Problem 5-20 on page 164 of French.
7. Problem 6-1 on pages 199-200 of French.
8. Problem 6-4 on pages 200 of French.
9. Problem 6-14 on page 202 of French.
10. To the nearest integer, please give the time in hours that it took you to complete this assignment,
including reading in the text.
Also, if you got help with this assignment, please give the names of the people from whom you got
help (classmates, the TA, myself, etc).
11. Optional Challenge Problems
(a) Challenge 4.1: The manufacturer of an oscilloscope claims that the writing speed of the electron
beam (the speed with which the bright dot moves across the screen) can exceed the speed of light.
Is this possible? (Look up the acceleration voltage difference ∆V used on the oscilloscope in the
264L lab.)
1
(b) Challenge 4.2:
Assume that two inertial frames of reference S and S’ have coordinate axes
that are always parallel (so x is parallel to x′ , y is parallel to y ′ , etc), and assume that the two
coordinate origins coincide when t = 0 and t′ = 0. However, next assume that the origin of S’
moves with a general constant velocity vector v in an arbitrary direction (so v = vx̂ is the case
you already know). Show that the Lorentz transformation now becomes:
(γ − 1)
(β • x)β − γtβ,
β2
t′ = γ (t − β • x) ,
x′ = x +
where β = (1/c)v is the dimensionless normalized velocity, in terms of the speed of light.
2
(1)
(2)