Question

The Stanford Linear Accelerator (SLAC) accelerates electrons to $v=0.99999997c$in a $3.2km$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?

Short answer

$1.92\times {10}^{-3}m$is the tube in the electrons’ reference frame.

Step-by-step solution

Given Information 

We have found to how long is the tube in the electrons’ reference frame.

Simplify

The length of the electron is given as

$l=l_0\times \gamma =32\times \frac{1}{\sqrt{1-{\left({\displaystyle \frac{0.99999997C}{C}}\right)}^2}}=32\times 5.99999991\times {10}^{-8}=1.92\times {10}^{-6}km$

Hence the distance seen by the electron will be$1.92\times {10}^{-6}km=1.92\times {10}^{-3}m$.