Hello. I'm from Brazil, so my English isn't very good, sorry if I make a grammar mistake. I have a question about motion in a rotating plain. Actually, I can solve the question, but I'm missing a point:

That's the question: There's a box in a cone. The cone has a friction coefficient of μ. The box's mass is M. The angle that the cone does with the ground is θ. The gravity field is g. The cone is spinning with a constant angular velocity. The problem asks to find the maximum speed V that the box can move (in this case, it's a circular motion) without go up, using only μ, M, θ and g.

 

 

 

 

In the figure, I represented the force diagram by the perspective of a inertial referential. "N" is the normal force, "F" is the friction force and "W" is the weight. I found the speed V by equaling the components of the force parallel to the ground with the formula for the centripetal force. But than I thought: "What force can move the box up?". I couldn't find any component of any force that is parallel to the cone and points up. Please, help me =D

Edited October 13, 200817 yr by Branos

Wow... uberly strange question.

 

I've never been good at the practical work. I mean, i was always fine working out my own wee problems in lecture class, but this question you have, i wouldn't know how the hell to answer it. I've never seen anything like it before.

 

Sorry.

I think if you add the fictional force, the central petal force, you will then be more clear about what you need to do.

 

You might have to work it out in cylindrical polar coordinates although that might be over complicating the problem...

Using a fictional force, I can solve the problem. The fictional force has a components that's parallel to the cone and points up. But that's the point: I want do solve it in a inertial referential! According to Newton's Law of motion, any problem that can be solved in a non-inertial referential can also be solved in a inertial referential. Why doesn't this apply to this question?

(Off topic: I can be any lepton I want? Like a positron, for example? =D)

Because it's an accelerating frame you can't have an inertial frame... I think... (the spinning is an acceleration) so you will always have psydoforces...