Question

Suppose that we are able to cause a meter stick to move with a speed of 0.9457c. What would be its length (in meters) in our frame of reference?

Answer 1

Here, we have to find the length of the stick in our reference. Let say our reference of the frame is "S"

And the frame in which the stick is moving is S'

Given-

Length of the stick (L') = 1m

Speed of stick (s')= 0.9457c , Where c = speed of light in vacuum

To find the length of the stick in S frame

We have to use LENGTH CONTRACTION EQUATION

L=L'/ ....................(1) Where L = Length of the stick in S frame and = Lorentz Factor

Now, First, we have to find the value of Lorentz Factor ( ) using Lorentz Factor Equation-

=1/sqrt(1-(s'^2/c^2))...................(2)

Inserting values in eq (2)

=1/sqrt(1-(0.9457c^2/c^2))

=3.04

Putting the value of in eq (1)

L=L'/

L=1meter/3.04

L=0.33 m

Hence, the length of the stick in our reference is 0.33m