Rolling in a cone, normal force

AI Thread Summary
The discussion revolves around understanding the normal force exerted by a cone and its components. The initial confusion stemmed from incorrectly calculating the vertical component of the normal force, with one participant mistakenly using N/sinθ instead of the correct N*sinθ. The clarification emphasized that when decomposing forces, the perpendicular component cannot exceed the actual force's magnitude. Participants highlighted the importance of visualizing the weight as the hypotenuse of a triangle to derive the correct expression. The thread concludes with a recognition of the resolution of the initial doubt, questioning the need to delete the discussion.
KEVmathematics
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I have a small problem with this question. In this problem, the cone exerts a normal force. This force, should be perpendicular to the inside surface of the cone. In equating the vertical forces, I need the vertical component of this normal force. I would draw this force perpendicular to the surface, and then using the angle θ, I would get a force of N/sinθ. But in the book, it says that it should be N*sinθ. What am I doing wrong here?
 

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Suddenly, I get it. Never mind! I can't find how to delete this thread.
 
You are decomposing the weight into its components which will be parallel and perpendicular to the inner surface of the cone. How can the perpendicular component have a magnitude greater than the actual force? Whenever you split a force at any angle, you get a value between 0 and the magnitude of the force depending upon the angle. Make the weight the hypotenuse of the triangle and see what expression you get.
 
Last edited:
KEVmathematics said:
Suddenly, I get it. Never mind! I can't find how to delete this thread.
As far as I'm aware, that is not possible. And why delete proof that you resolved your own doubt?
 

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