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A cube has a density of 1800 kg/m3 while at rest in the laboratory. What is the cube's density as measured by an experimenter in the laboratory as the cube moves through the laboratory at 84.0 % of the speed of light in a direction perpendicular to one of its faces? You may want to review

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Answer:

3317.44401 kg/m³

Explanation:

[tex]\rho'[/tex] = Actual density of cube = 1800 kg/m³

[tex]\rho[/tex] = Density change due to motion

v = Velocity of cube = 0.84c

c = Speed of light = [tex]3\times 10^8\ m/s[/tex]

Relativistic density is given by

[tex]\rho=\dfrac{\rho'}{\sqrt{1-\dfrac{v^2}{c^2}}}\\\Rightarrow \rho=\dfrac{1800}{\sqrt{1-\dfrac{0.84^2c^2}{c^2}}}\\\Rightarrow \rho=\dfrac{1800}{\sqrt{1-0.84^2}}\\\Rightarrow \rho=3317.44401\ kg/m^3[/tex]

The cube's density as measured by an experimenter in the laboratory is 3317.44401 kg/m³

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