Solve for r in Circular Motion Problem - Urgent Help Needed

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To determine the radius (r) for astronauts to weigh half of their Earth weight in a rotating space station moving at 42.7 m/s, the concept of artificial gravity through centripetal acceleration must be applied. The formula for centripetal acceleration is a = V^2/r, where V is the tangential velocity. To achieve half of Earth's gravity, the required centripetal acceleration should equal 0.5g (where g is the acceleration due to gravity on Earth). The correct approach involves setting the centripetal acceleration equal to 0.5g and solving for r, leading to the equation r = V^2/(0.5g). The initial solution was incorrect due to misunderstanding the nature of artificial gravity versus real gravity.
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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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