Name _________________
Test 1
September 19, 2014
This test consists of three parts. Please note that in parts II and III, you can skip one
question of those offered.
Possibly useful formulas:


 
F  qE  qu  B
p  qRB
 
u pc

c E
f 
f0
 1  v cos  c 
x    x  vt 
t     t  vx c 2 
y  y,
z  z
1   
E     E  vpx 
px    px  vE c
py  p y
pz  pz
n
2

u x 
ux  v
1  vu x c 2
uy
u y 
 1  vu x c 2 
u z 
uz
 1  vu x c 2 
 1  n  12 n  n  1  2 
Part I: Multiple Choice [20 points]
For each question, choose the best answer (2 points each)
1. The speed of light in vacuum as viewed by some observer depends on
A) The speed of the source (only)
B) The speed of the observer (only)
C) The speed of the source AND the speed of the observer
D) Neither the speed of the source nor the speed of the observer
E) The observer’s IQ divided by the source’s shoe size
2. Under what condition can you absolutely determine which of two events A and B
occurred first; that is, when will all observers agree which came first?
A) When the separation is timelike
B) When the separation is lightlike
C) When the two events occur at the same place
D) You can always tell
E) You can never tell
3. Suppose two observers are examining the same system but one is moving relative to
the other along the x-axis. Which of the following momenta components pi or energy
E will the two agree on?
A) px but not py, pz, nor E
B) py and pz, but not px nor E
C) E, but not any component of momentum
D) E and px, but not py nor pz
E) All three components of the momentum pi, but not the energy E
4. In particle colliders, particles are forced to move in circles by _______ fields
A) Gravitational B) Scalar
C) Electric D) Magnetic E) None of these
5. If tachyons exist, with a negative mass squared, which of the following would
describe their speed?
A) It would always be slower than c
B) It would always be faster than c
C) It would always be equal to c
D) It could be at speed c or slower, but not faster
E) It could have any speed between 0 and infinity
6. The binomial approximation   1  v 2 2c 2 works pretty well for a particle moving
D) at any constant speed E) never
A) slowly
B) quickly C) at c
7. The Lorentz transformation tells you how to write primed coordinates in terms of
unprimed. If we wanted to write x in terms of the primed coordinates, which would
be the correct formula?
A) x    t   vx 
B) x    t   vx 
C) x    x  vt  
D) x    x  vt  
E) None of the above
8. In which of the following ways is time UNLIKE the other three dimensions of space?
A) Observers may disagree on space coordinates, but they agree on time
B) Observers may disagree on time coordinates, but they agree on space
C) Though the pace of time may differ for different observers, they all agree on
whether two events are simultaneous
D) Objects can move through space, but not through time
E) Time enters the distance formula with the opposite sign
9. The effective mass of two objects moving opposite directions, with velocity v each
with mass m, will be
A) 2m
B) 2m/
C) 2m
D) 0
E) None of these
10. Suppose a pole vaulter runs through a barn with a pole the same length as the barn. A
farmer briefly closes both doors at the same time, showing the pole is actually shorter
than the barn. How does the pole vaulter explain the fact that his pole fits in the
barn?
A) He is accelerating, and hence not in an inertial frame, so his perspective is wrong
B) Since he is the one that is truly moving, he actually sees his pole as short
C) He will actually see the doors of the barn hitting his pole, so it doesn’t fit
D) He will see the pole tilted at an angle, so it fits
E) He will claim that farmer didn’t close the doors simultaneously
Part II: Short answer [20 points]
Choose two of the following questions and give a short answer (1-3 sentences)
(10 points each).
11. Suppose we have two events in spacetime, with coordinates P1   x1 , y1 , z1 , t1  and
P2   x2 , y2 , z2 , t2  . Under what circumstances can we conclude that event P2 is in the
absolute future of P1? At least one formula is required.
12. You are running out of time to finish this test, so you decide to work on the test while
running around the room in circles very fast. You reason that since the room is
moving relative to you, time slows down relative to you, and this will give you extra
time to finish the test. Assuming you can run at high speeds, explain why this is or
isn’t a good idea.
13. Explain qualitatively why the equations F = ma and F = dp/dt cannot both be true in
relativity. Also, explain which of these is preferred, and why (a conservation law
should be mentioned).
Part III: Calculation: [60 points]
Choose three of the following four questions and perform the indicated calculations (20
points each)
14. Luke Skywalker is flying his X-wing starfighter (length 12.50 m) past the Millenium
Falcon, flown by Han Solo. He notices as he passes that when his watch advances
11.0 seconds, while Solo’s only advances 4.00 seconds.
(a) What is the relative speed, as a fraction of c, of the two spacecraft? Can we say
for sure which of the two is really moving, and which one is stationary?
(b) How long does the X-wing appear to Han Solo?
(c) To Luke, the Millenium Falcon appears to be the same length as his starfighter.
How long is the Millenium Falcon according to Han Solo?
15. Atomic hydrogen atoms produce
us
alien
clou
radio waves with a frequency of
1420 MHz. Suppose a cloud of hydrogen gas is moving directly away from me, as
sketched above, at a velocity of v = 1.80  108 m/s.
(a) What frequency would I observe for this cloud?
(b) An alien culture is along the line of sight to the cloud, and moving at a speed of
2.50  108 m/s compared to us. From their point of view, how fast is the cloud
moving?
(c) If the alien culture measured the frequency from the cloud, would they see a
higher or lower frequency? You do not need to perform a calculation.
16. A charged pion + at rest has mass 139.6 MeV/c2.
+

+
It decays spontaneously to a massless neutrino 
traveling to the left with energy E = 29.8 MeV, and to a muon+.
(a) What is the momentum of the neutrino in MeV/c? What is the energy and
momentum of the muon?
(b) What is the mass of the muon, in MeV/c2? What is its velocity as a fraction of c?
(c) A muon is itself unstable. In its own frame, its average lifetime is 2.197 s.
What is the average expected lifetime for this moving muon?
17. The intergalactic launcher accelerates spacecraft of mass 1950 kg from rest by
pushing them along a track that reaches from the Sun to Neptune (d = 4.501012 m)
with a force of 2.57  107 N.
(a) What is the initial and final energy of the spacecraft (in J)?
(b) What is the initial and final momentum (in kgm/s) and velocity (in m/s) of the
spacecraft?
(c) How long does it take to launch a ship this way?