Question

Prove that the volume of a cube that moves with a velocity vin

the parallel direction to one of the edges is:
, being V0 the volume of the cubemeasured from a
reference frame in which the cube doesn'tmove.

Answer 1

Proof is given below

Step-by-step explanation:

The length contraction is given by Δx = Δx' *√(1 - v² / c²)

where Δx' is the proper length and is measured in the frame where the object is at rest

Since the y' and z' axes are perpendicular to the direction of motion there is no contraction

So if you let V0 = Δy' * Δz' *Δx'

and V = Δy * Δz * Δx = Δy'* Δz' * Δx

Then

V = V0 * √(1 - v² / c²)