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A 56 kg astronaut stands on a bathroom scale inside a rotating circular space station. The radius of the space station is 250 m. The bathroom scale reads 42 kg. At what speed does the space station floor rotate?

Respuesta :

Answer:

The speed of space station floor is 49.49 m/s.

Explanation:

Given that,

Mass of astronaut = 56 kg

Radius = 250 m

We need to calculate the speed of space station floor

Using centripetal force and newton's second law

[tex]F=mg[/tex]

[tex]\dfrac{mv^2}{r}=mg[/tex]

[tex]\dfrac{v^2}{r}=g[/tex]

[tex]v=\sqrt{rg}[/tex]

Where, v = speed of space station floor

r = radius

g = acceleration due to gravity

Put the value into the formula

[tex]v=\sqrt{250\times9.8}[/tex]

[tex]v=49.49\ m/s[/tex]

Hence, The speed of space station floor is 49.49 m/s.

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