# What is gamma for an object with speed B = 0.1?

1. Feb 6, 2005

### dranger35

Hey I was given 3 problems for homework, I just need help on some and the others I want to make sure i did it right.

Problem 1: What is gamma for an object with speed B = 0.1?

Problem 2: You are at rest, and see me as moving with a speed of
B = 0.05. I see a car moving with a speed of B = 0.05. How fast do
you measure the car to be moving? In particular, how much
different is the car's speed from B = 0.1?

Problem 3: Assume that you can measure the phase difference to 1 degree.
What is the minimum w(omega) that you can measure? Assume light with
a wave length of 1000 nm, and a 0.1 m2 coil with 1000 loops.

for 1 I know gamma=1/sq. root(1-B^2). Now is that all you do, because it just seems to easy.

for 2 I 'm not sure how to start it

for 3 I know difference in phase= 8(pi)(Area)(3 of loops)(omega) /c(wavelength) , but how do i find the area?

2. Feb 6, 2005

### cepheid

Staff Emeritus
Problem 1: Dead simple. Just look at the definitions of gamma and beta. The object's velocity is 0.1c, or one-tenth the speed of light. How do I know? Because $\beta$ is defined as the ratio of an object's speed to the speed of light: v/c = 0.1c/c = 0.1. Now tell me? What is the factor gamma, and why is it important? (This is an integral part of special relativity here. If you can't do this problem right away without even thinking about it, then I'd recommend reviewing the def'ns of gamma and beta). *EDIT* Oh...you did do the problem without thinking about it too much. Good! Well then, to answer your question, yes, the problem really is that easy...a matter of simple substitution. But I want to re-emphasize that you make sure you know what these factors mean.

Problem 2: Start like this. You're "at rest". (Why did I put this in quotes? ) Call your inertial frame of reference S. You see me moving at beta = 0.05. So, call my inertial frame of reference S'. I (and my frame) am therefore moving at v' = 0.05c relative to you. Now you see another car, also moving at 0.05c (call this velocity: u). So u relative to you is 0.05c. What is u' (relative to me?) i.e, if the velocity u is 0.05c in the S frame, how do I calculate this velocity as measured in the S' frame? (u').

Problem 3 seems to be worded too vaguely for me, at least, to figure out what's going on.