Inertial Reference Frames Video Lessons

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# Problem: 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? Answer in m.

###### FREE Expert Solution

The length of the tube in the electron's reference frame is:

$\overline{){\mathbf{L}}{\mathbf{=}}{{\mathbf{L}}}_{{\mathbf{0}}}\sqrt{\mathbf{1}\mathbf{-}\frac{{\mathbf{v}}^{\mathbf{2}}}{{\mathbf{c}}^{\mathbf{2}}}}}$, where L0 is the total length of the tube, v is the velocity of the electron, and c is the speed of light in a vacuum.

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###### Problem Details

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? Answer in m.