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

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Homework Help Overview

The problem involves calculating the radius of a hill that allows a person to feel weightless while traveling at 42 mph. The context is centered around circular motion and the forces acting on an object in a vertical circle.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between feeling weightless and the forces acting on a person, particularly the normal reaction and gravitational force. There are inquiries about the assumptions regarding the hill's shape and the forces involved in circular motion.

Discussion Status

The discussion is actively exploring the implications of feeling weightless in terms of the forces at play. Some participants have provided insights into the relationship between weight and normal force, while others are questioning the assumptions made about the forces involved in circular motion.

Contextual Notes

There is an assumption that the hill is circular, and participants are considering the implications of this assumption on the forces acting on the person. The specific numerical answer of 35.6 m is mentioned, but it is not being treated as a solution within the discussion.

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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 vertical circle would gravity be force acting on me?
 
Hafsaaa said:
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?
 
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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