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Phy 3031 Modern physics, Spring 2007
Homework set #4. Due at the start of class on Wednesday, January 31, 2007.
For numerical answers give two significant digits. The first should be correct, the second can
be approximate.
1. Bob rides a train past the station platform with a speed v, while Alice sits on the
platform. They both notice a bird flying in the same direction as the train moves.
Alice measures the speed of the bird to be u0 .
(a) What speed u does Bob measure for the bird, if v = 3c/4 and u0 = 3c/4 ?
(b) What is c − u when v = 0.9999 c and u0 = 0.9999 c?
2. The relativistic velocity addition formula is
u =
u0 + v
.
1 + vu0 /c2
Solve this equation for u0 in terms of u, v and c.
3. An automobile of length ` = 11 ft moves at a speed v = 0.6 c toward a garage of width
w = 10 ft. Two auto mechanics are stationed at doors at the ends of the garage.
(a) How many feet long do the mechanics measure the automobile to be?
(b) Are the mechanics able to close the doors of the garage simultaneously (as determined in their frame of reference) thereby closing the automobile inside?
(c) How many feet long does the driver measure his automobile to be?
(d) From the driver’s point of view are the mechanics able to close the doors of the
garage simultaneously thereby closing the driver inside?
(e) How many feet wide does the driver measure the garage to be?
4. In a high energy physics particle-accelerator experiment, about 1024 muons are created
with a speed v = 0.995 c, and the muons then travel down a tube whose length is 4.2 km
before striking a target.
Muons have a half-life of about 1.4×10−6 s. This means that, with a bunch of muons at
rest, every 1.4 × 10−6 s about half of the muons decay into electrons and other things.
q
(a) What is 1 − v 2 /c2 for the muons? Give an answer which is correct to one
significant figure.
(b) In a physicist’s frame of reference, how long does it take for a muon to travel
down the tube?
(c) In a muon’s frame of reference, how long is the tube?
(d) In a muon’s frame of reference, how long does it take for a muon to travel down
the tube?
(e) How many muons are expected to hit the target, before decaying?