How Does a Rotating Space Station Simulate Gravity for Astronauts?

[MiniOreo1998]

Homework Statement

To simulate gravity, a circular space station with a radius of 150 m is rotated so that astronauts standing on the inner surface move at 30 m/s. If the 75 kg astronaut stands on a bathroom scale, what reading will it give? (Assume that the scale is calibrated in Newtons)

I'm confident with my answer, however, am not quite sure how to "word it". The area I lack confidence in is my ability to properly express myself through mathematics. Any tips that could help me build intuition on proper "writing" conventions would be truly appreciated.

Homework Equations

Fc = m v² / r

The Attempt at a Solution

[/B]
Fc = m v² / r

Fc = (75) (30)² / 150

Fc = 450 N

The scale would read 450 N

 

[Satvik Pandey]

Homework Statement

To simulate gravity, a circular space station with a radius of 150 m is rotated so that astronauts standing on the inner surface move at 30 m/s. If the 75 kg astronaut stands on a bathroom scale, what reading will it give? (Assume that the scale is calibrated in Newtons)

I'm confident with my answer, however, am not quite sure how to "word it". The area I lack confidence in is my ability to properly express myself through mathematics. Any tips that could help me build intuition on proper "writing" conventions would be truly appreciated.

Homework Equations

Fc = m v² / r

The Attempt at a Solution

[/B]
Fc = m v² / r

Fc = (75) (30)² / 150

Fc = 450 N

The scale would read 450 N

The answer is correct.
Draw the Free body diagram.

Here the only force acting on the Astronaut is the normal reaction. This Normal reaction provides the centripetal force required to move astronaut in a circular motion. So ##N=\frac{mv^{2}}{R}##. Also the weight is nothing but the reactionary force acting on the body from a ground.
So its weight is equal to ##N## which is equal to ##\frac{mv^{2}}{R}##.