Rolling in a cone, normal force

In summary, the conversation discusses a problem with a cone exerting a normal force and the confusion over how to calculate its vertical component. The person realizes their mistake and decides not to delete the thread.
  • #1
KEVmathematics
5
0
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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  • #2
Suddenly, I get it. Never mind! I can't find how to delete this thread.
 
  • #3
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.
 
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  • #4
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?
 

1. What is rolling in a cone?

Rolling in a cone refers to the movement of a round object, such as a ball or wheel, along the surface of a cone-shaped object. This type of movement is characterized by the rolling object maintaining contact with the cone at all times, resulting in a circular path.

2. How does normal force affect rolling in a cone?

Normal force is the force exerted by a surface on an object in contact with it, perpendicular to the surface. In the case of rolling in a cone, the normal force is what allows the circular motion to occur. As the rolling object moves along the cone, the normal force changes direction, keeping the object on its circular path.

3. What factors affect the normal force in rolling in a cone?

The normal force in rolling in a cone is affected by the weight of the rolling object, the angle of the cone, and the friction between the rolling object and the cone. A heavier object will have a greater normal force, while a steeper cone or higher friction will result in a greater normal force.

4. Can the normal force be greater than the weight of the rolling object in rolling in a cone?

Yes, it is possible for the normal force to be greater than the weight of the rolling object in rolling in a cone. This can occur when the angle of the cone is steep enough or when there is a high amount of friction between the rolling object and the cone.

5. How is rolling in a cone different from rolling on a flat surface?

Rolling in a cone is different from rolling on a flat surface in that it involves circular motion instead of linear motion. Additionally, the normal force in rolling in a cone is constantly changing direction, whereas the normal force in rolling on a flat surface remains constant.

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