Answer to Question #266246 in Mechanics | Relativity for Dinesh priyananda

Question

A non-flat screen, older style television display (see figure) works by accelerating electrons over a short distance to relativistic speed, and then using electromagnetic fields to control where the electron beam strikes a fluorescent layer at the front of the tube. Suppose the electrons travel at 6.00 × 107 m/s through a distance of 0.200 m from the start of the beam to the screen.  

(a) What is the time of travel of an electron in the rest frame of the television set?  

(b) What is the electron’s time of travel in its own rest frame?

Answer 1

(a) The time is

$$t_a=\frac{d/v}{\sqrt{1-v^2/c^2}}=3.4\text{ ns}.$$

(b) The time is

$$t_b=\frac{d}{v}=3.3\text{ ns}.$$