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kari74 [83]
3 years ago
10

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 t

hen 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.
Physics
1 answer:
guapka [62]3 years ago
5 0

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

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