How Can You Calculate the Ball's Speed Inside an Inverted Cone?

[abeltyukov]

Hi,

There is an inverted cone with height h. There is a ball rolling around inside creating a horizontal circle. The height from the tip of the inverted cone to the ball is y. a is given from the center of the cone to the outer edge.

The question asks to express the ball's speed in terms of a, h, y, and g.

I am confused as to why a is shown from the center of the cone to the edge. Is a in this case the same as acceleration?

I know a = w^2 * r as well as a = (v^2)/r
I have the forces in the y-direction: N = mg
I have the forces in the x-direction: (h-y)sin(theta) = (mv^2)/r

I believe I am screwing up on the x-direction forces. Any suggestions?


Thank you very much,
Alex

 

[Dorothy Weglend]

The normal force is perpendicular to the surface. That's not where you put it in your force equation. That will also help you fix the force equations for X.

Dorothy