What would happen if you travelled at 3/5 c

[stunner5000pt]

using Relativistic mechanics
Gamma = 1 / (Root (1/ v^2/c^2))
The target area in a lab in a straight line tube of 400 m long. 1 million radioactive particles are shot in this tube at (3/5) c . Half of them will arrive at the other end without decaying. To the observer moving with the particle:

a) how long is the tube measured to be?
shorter than 400m, i would think it's 400 / gamma = 400 / 1.25 = 320m

b) what is the half life of the particles?
is this as easy i think it is? t = D/ v = 400 / (3/5)c = 2.22 x 10^-6 s and thus half life is 1.11 x 10^-6 s

c) What is the speed the tube is measured to move?
in the opposite direction at (3/5)c?

 

[Doc Al]

a) how long is the tube measured to be?
shorter than 400m, i would think it's 400 / gamma = 400 / 1.25 = 320m

Right.

b) what is the half life of the particles?
is this as easy i think it is? t = D/ v = 400 / (3/5)c = 2.22 x 10^-6 s and thus half life is 1.11 x 10^-6 s

Half-life should be measured in the rest frame of the particles. (You measured the travel time according to the lab frame.)

c) What is the speed the tube is measured to move?
in the opposite direction at (3/5)c?

Right.

 

[stunner5000pt]

For the B Part is the following correct??

since the distnace traveled in the lab fram is 400 m, and velocity is 3/5c then the time is 2.22 e -6 s

furthermore, the half life is given by 2.22e-6 / gamma = 1.776 e -6s


Is this correct or am i still off?? please help!

 

[Doc Al]

You got it. You figured the travel time according to the lab frame. Then accounted for time dilation. (If you think of the particles as moving clocks, they must exhibit time dilation.)

Another way to do it is to figure the travel time directly from the lab frame. In the lab frame, you found the distance "traveled" to be 320m (from part A). Figure the travel time t = D/v. That's the half-life.