Rotational dynamics of a block in a cone

  • #1
1. Homework Statement [/b]

A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T. The walls of the cone make an angle v with the vertical. The coefficient of static friction is between the block and cone is "u". If the block is to remain at a constant height above the apex of the cone, what are the minimum and maximum values of T?

Homework Equations



F=ma

The Attempt at a Solution



Hello guys and gals, really am at a loss here.
In order for the block to remain stationary the static friction force (F) must be larger in magnitude than the forces that try to pull it down or push it up, right?
And F is the Normal force multiplied with the coefficient u.
The force required to keep the block stationary in the x-axis is m*4*pi*r/T^2.
To get the radius i take r=h*tanv.
However identifying all this basic stuff is as far i get. I cant get any farther than this.
I cant seem to identify which forces oppose which forces in the x and y axes.
Badly drawn sketch attached.

Any help appreciated.
 

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Answers and Replies

  • #2
First, friction force cannot be larger than the force that try to move it up or down, it can only be equal or less. You can think what would happen otherwise. The block isn't stationary in x direction - it's always moving. And i think you forget gravity. Just draw forces on the block - gravity, normal and centrifugal. Then you might get idea why there is minimum and maximum values of T.
 
  • #3
First, friction force cannot be larger than the force that try to move it up or down, it can only be equal or less. You can think what would happen otherwise. The block isn't stationary in x direction - it's always moving. And i think you forget gravity. Just draw forces on the block - gravity, normal and centrifugal. Then you might get idea why there is minimum and maximum values of T.

Ok thanks ill give it another try.
 

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