Calculating the Radius of a Hill for Weightless Sensation at 42 mph

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To determine the radius of a hill that creates a weightless sensation at 42 mph, one must assume the hill is circular. When feeling weightless, the normal force acting on the person is zero, meaning gravity provides the necessary centripetal force. By equating the gravitational force to the centripetal force, the radius can be calculated. The solution indicates that the radius of the hill is approximately 35.6 meters. This approach effectively combines principles of circular motion and gravitational forces.
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Homework Statement



It is found (through and error) that you will "feel" weightless when you travela round at 42 mph over a smoothy rounded hill. What is the radius of the hill?


Homework Equations



I'm not sure what equation to use with this problem

The Attempt at a Solution


the only thing I know is the answer, which is 35.6 m.
Could someone help walk through this problem? It would be much appreciated.
 
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Hafsaaa said:

The Attempt at a Solution


the only thing I know is the answer, which is 35.6 m.
Could someone help walk through this problem? It would be much appreciated.

You'll need to assume the hill is circular, so if you feel weightless, how does this relate to your actual weight with respect to the normal reaction. For circular motion what sort of force would keep you moving in a circle?
 
rock.freak667 said:
You'll need to assume the hill is circular, so if you feel weightless, how does this relate to your actual weight with respect to the normal reaction. For circular motion what sort of force would keep you moving in a circle?

Well since I'm moving in a verticle circle would gravity be force acting on me?
 
Hafsaaa said:
Well since I'm moving in a verticle circle would gravity be force acting on me?

There would be the normal reaction and your weight. If you are weightless then what is the normal reaction equal to?
 
rock.freak667 said:
There would be the normal reaction and your weight. If you are weightless then what is the normal reaction equal to?

it would be zero correct?
 
Hafsaaa said:
it would be zero correct?

Right, so that means only the weight is providing the centripetal force. So equate the two and solve for r.
 

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