Rolling in a cone, normal force

[KEVmathematics]

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?

 

[KEVmathematics]

Suddenly, I get it. Never mind! I can't find how to delete this thread.

 

[PWiz]

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.

 

[PWiz]

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?