SLAC, the Stanford Linear Accelerator Center, located at Stanford University in

Question

SLAC, the Stanford Linear Accelerator Center, located at Stanford University in Palo Alto, California, accelerated electrons through a vacuum tube two miles long (it can be seen from an overpass of the Junipero Serra freeway that goes right over the accelerator). Electrons which were initially at rest were subjected to a continuous force of 2x10^-12 newton along the entire length of two miles (one mile is 1.6 kilometers) and reached speeds very near the speed of light. (a) Determine how much time was required to increase the electrons' speed from 0.958c to 0.985c. (That is, the quantity |v vector|/c increased from 0.958 to 0.985.) time = 3.23186E-10 s (b) Approximately how far did the electron go in this time? (Think about what is approximate about your result.) distance = .43867 m

Explanation / Answer

F=ma

a=F/m

m = 9.1 *10^(-31) kg

a = 2*10^(-12) / 9.1 *10^(-31)

a= 0.21978 *10^(19) m/s^2

given

u = 0.958 c

v = 0.985 c

use v^2 - u^2 = 2*a*s

s = (v^2 -u^2) / 2a

= (0.985^2 - 0.958^2 ) * c^2 / (2*0.21978 *10^(19) )

s=1.07413 x10^(-3) m

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