Problem Set VII Assign October 23, 2006 Due November 1, 2006.
Fall 2006 Physics 200a
R. Shankar
1. The earth and sun are 8.3 lightminutes apart. Ignore their relative motion for this
problem and assume they live in a single inertial frame, the EarthSun frame. Events
A and B occur at
t
= 0 on the earth and at 2 minutes on the sun respectively. Find
the time difference between the events according to an observer moving at
u
=
.
8
c
from Earth to Sun. Repeat if observer is moving in the opposite direction at
u
=
.
8
c
.
2. Return to the EarthSun case above.
(a) What is the speed of a spacecraft that
makes the trip from the Sun to the Earth in 5 minutes according to the on board
clocks? (b) What is the trip time in the EarthSun frame? (c) Find the square of
the spacetime interval between them in lightseconds.
(You may need to come back to part (c) after I do spacetime intervals in class. Do
not just jump in and use some formula. Think in terms of events, assign as many
possible spacetime coordinates as you can to each event in any frame and use the
LT. Measure time in minutes, distance in lightminutes. Imagine a rod going from
earth to the sun, if that helps.
Note that the spatial coordinate difference between events in spacecraft frame are
not the same as distance between Earth and Sun in that frame. Even preEinstein,
if I sit in my car going at 60 mph, I leave New Haven at t=0 (Event 1) and arrive at
Boston at t= 2hrs (Event 2), the two events have the same coordinate in my frame
(i.e., where I am in the car) Δ
x
= 0 , but that is not the distance between these
towns.)
3. A muon has lifetime of 2
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 RAMAMURTISHANKAR
 Physics, Inertia, Special Relativity, Light, Frame, rest mass, R. Shankar, rest length L0, spacetime interval

Click to edit the document details