Question

How much work must be done to increase the speed of an electron from (a) 0.14c to 0.16c and (b) from 0.92c to 0.94c? Note that the speed increase is 0.02c in both cases.

Answer 1

Here , for the work done

A) from 0.14c to 0.16c

work done = change in kinetic energy

work done = (total energy1 - rest energy) - (total energy2 - rest energy)

work done = total energy1 - total energy2

work done = 9.11 *10^-31 * (3 *10^8)^2/sqrt(1 - 0.16^2) - 9.11 *10^-31 * (3 *10^8)^2/sqrt(1 - 0.14^2)

work done = 2.54 *10^-16 J

the work needed is 2.54 *10^-16 J

B)

from 0.92 m to 0.94m

work done = change in kinetic energy

work done = (total energy1 - rest energy) - (total energy2 - rest energy)

work done = total energy1 - total energy2

work done = 9.11 *10^-31 * (3 *10^8)^2/sqrt(1 - 0.94^2) - 9.11 *10^-31 * (3 *10^8)^2/sqrt(1 - 0.92^2)

work done = 3.11 *10^-14 J

the work needed is 3.11 *10^-14 J