Question

The Stanford Linear Accelerator (SLAC) accelerates electrons to v=0.99999997c in a 3.2-km-long tube. If they travel the length of the tube at full speed (they don’t, because they are accelerating), how long is the tube in the electrons' reference frame?

Answer 1

So length of the tube in electron reference frame is 0.7348 m

Step-by-step explanation:

We have given total length of the tube
`L_V=3.2km=3200m`

Velocity of electron v = 0.99999997c ,here c is the velocity of light

We have to find the length of the tube in electron reference frame

Length of the tube in electron reference frame is given by
`L=L_V\sqrt{1-(v^2)/(c^2)}=3200* \sqrt{1-((0.99999997c)^2)/(c^2)}=1.431m`

So length of the tube in electron reference frame is 0.7348 m