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

[Hafsaaa]

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.

 

[rock.freak667]

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?

 

[Hafsaaa]

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 vertical circle would gravity be force acting on me?

 

[rock.freak667]

Well since I'm moving in a vertical 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?

 

[Hafsaaa]

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?

 

[rock.freak667]

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.