Question

A box at rest has the shape of a cube 3.5 m on a side. This box is loaded onto the flat floor of a spaceship and the spaceship then flies past us with a horizontal speed of 0.80 c. What is the volume of the box as we observe it? Express your answer to two significant figures and include the appropriate units.

Answer 1

Answer:

$V_o=25.725\ m^3$

Explanation:

Given:

sides of the cube, $a=3.5\ m$

speed of the cube with respect to the observer, $v=0.8c$

Since the relative velocity of the object is relativistic, so there will be a length contraction according to the observer:

$a_o=a\div\frac{1}{\sqrt{1-\frac{v^2}{c^2} } }$

where:

$a_o=$ observed length of the side along the direction of velocity

$a_o=3.5\div\frac{1}{\sqrt{1-\frac{(0.8c)^2}{c^2} } }$

$a_o=2.1\ m$ is the observed length of the cube edge only in the direction of the velocity due to relativistic effect of length contraction.

So the observed volume will be:

$V_o=a\times a\times a_o$

$V_o=3.5\times 3.5\times 2.1$

$V_o=25.725\ m^3$