Solve for r in Circular Motion Problem - Urgent Help Needed

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SUMMARY

The problem involves calculating the radius (r) of a rotating space station required for astronauts to experience half of their Earth weight at a tangential velocity of 42.7 m/s. The correct formula for r is derived from the relationship between centripetal acceleration and gravitational force, specifically r = GMe/V^2, where G is the gravitational constant and Me is the mass of the Earth. The initial misunderstanding stemmed from confusing artificial gravity with real gravity, emphasizing the importance of centripetal acceleration in this context.

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Urgent help needed, please! Circular motion

Suppose the surface (radius = r) of the space station is rotating at 42.7 m/s. What must be the value of r for the astronauts to weigh one-half of their Earth weight?


My soln: Let // represent square root

V = // (GMe/r)

I divided Me by 2 and made r the subject

r = GMe/V^2

but i got the anser wrong
 
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I presume the problem is talking about the artificial gravity created by a rotating space station--not real gravity. Hint: Consider centripetal acceleration.
 

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