Special theory of relativity – problems and solutions

Special theory of relativity – problems and solutions

1. An object whose length is 60 m moves at a speed of 0.6 c (c = the speed of light). According to a stationary observer, what is the length of the object?

Known :

The proper length (L_o) = 60 meters

Object’s speed (v) = 0.6 c

Wanted : The length contraction (L)

c = the speed of light

L_o = the proper length

L = the length contraction

The length contraction (L) :

2. An event observed by a stationary observer for 12 seconds. What is the time interval

Known :

The time interval of the event according to a stationary observer (t_s) = 12 seconds

The speed of observer (v) = 0.8 c

Wanted: The time interval of the event according to an observer who moving at a speed of 0.8 c (t_m)

Solution :

The equation of the time dilation :

t_s = the time interval according to a stationary observer

t_m = the time interval according to a moving observer

The time interval according to a moving observer (t_m) :