Question

Consider an event with space-time coordinates (t=2.00s,x=2.50×108m) in an inertial frame of reference s. let s' be a second inertial frame of reference moving, in the positive x direction, with speed 2.70×108m/s relative to frame s. find the value of γ that will be needed to transform coordinates between frames s and s'. use c=3.00×108m/s for the speed of light in vacuum.

Answer 1

The value of γ needed for transformation between the two frames is 2.2942.

To transform the position, time, mass from one coordinate frame to another frame which moves with a speed v relative to the first, we need to calculate the Lorentz constant γ .

This is given by,

$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$

Substitute $2.70*10^8 m/s$ for v and $3.00*10^8 m/s$ for c.

$\gamma =\frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \\ =\frac{1}{\sqrt{1-\frac{(2.70*10^8 m/s)^2}{(3.00*10^8 m/s)^2}}} \\ =\frac{1}{\sqrt{0.19}} \\ =2.2942$

The Lorentz factor needed for transforming the position and time coordinates from the given frame to the frame moving with a speed v relative to it is 2.2942