Question

The control panel on a spaceship contains a light that blinks every 1.81 s as observed by an astronaut in the ship. If the spaceship is moving past Earth with a speed of 0.793c, determine the proper time interval between blinks and the time interval between blinks as observed by a person on Earth.

(a)

the proper time interval (in s) between blinks

s

(b) the time interval (in s) between blinks as observed by a person on Earth

s

(c) An electron has a momentum with magnitude six times the magnitude of its classical momentum. Find the speed of the electron.
c

Answer 1

Let the spaceship be moving at a speed v = 0.793 c , relative to the earth.

As the astronaut is inside the spaceship , he will be at rest relative to the spaceship.

So his velocity relative to spaceship is zero.

A) Time interval between the blinks of light t = 1.81 s

A time interval that is measured in a frame of reference that occurs at the same position by a clock at rest relative to that frame is called proper time interval.

Here clock will be at rest relative to the astronaut and spaceship.

Then the proper time interval t = t = 1.81 s

B) An observer on the earth will observe a time interval more than that observed by the astronaut.This longer time interval is called dilated time interval.

It is given by t' =  t / { 1 - ( v / c )² }

= 1.8 / { 1 - ( 0.793 c / c )² }

= 1.81 / ( 1 - 0.793² )

= 1.81 / ( 1 - 0.628849 )

= 1.81 / 0.371151

= 1.81 / 0.60922

= 2.971 s

So time interval between the blinks as observed by the person on the earth is t' = 3.389 s or 2.97 s

c)Mv = P = mv/sqrt(1 - (v/c)^2) = p/L(v/c) = 6p

1/L(v/c)^2 = 36 and

1/36 = 1 - (v/c)^2

(v/c)^2 = 35/36 ==> v/c = 0.97222

so v = .9722c ==>0.97222*3*10^8=291666666.66 m/s