# Stuck on special relativity

1. Oct 30, 2009

### jdub99

1. The problem statement, all variables and given/known data

An unstable high-energy particle is created in the laboratory, and it moves at a speed of 0.978c. Relative to a stationary reference frame fixed to the laboratory, the particle travels a distance of 1.38x10-3 m before disintegrating.

(a) What is the proper distance traveled?
(b) What is the distance measured by a hypothetical person traveling with the particle?
(c) What is the proper lifetime?
(d) What is the dilated lifetime?

2. Relevant equations

L0/(gamma)=L

(gamma)=1/sqrt(1-(v/c)2)

3. The attempt at a solution

Stuck on part A:
V=.978c
L= 1.38x10-3m
L0=?

(gamma)=1/sqrt(1-(v/c)2)= 1/sqrt(1-(.978)2)= 4.79

L0=L x (gamma)= (1.38x10-3m)(4.79)= .00662m

2. Oct 30, 2009

### Staff: Mentor

According to the particle frame, is the distance traveled shorter or longer than seen in the lab frame?

3. Oct 30, 2009

### jdub99

Distance should be greater for L0 because (gamma) is going to always be greater than 1. Right? It should be shorter in the lab frame compared to particle frame.

Last edited: Oct 30, 2009
4. Oct 30, 2009

### Staff: Mentor

Realize that the distance is measured at rest in the lab frame, so I suppose that's the distance they want as the "proper distance". From the view of the particle frame, that distance is moving. What happens to moving lengths? (That's really part b, not part a. Oops!)

5. Oct 30, 2009

### jdub99

Lengths contract when moving. so the particle should be the shorter distance. So part a is the given part of the question. Ok parts a and b make

Last edited: Oct 30, 2009