Circular Motion and speed of mass

AI Thread Summary
A mass m moves in a horizontal circle within a frictionless cone, and the goal is to determine its speed based on the radius r and cone angle 2t. The normal force acts towards the center of the circle, while gravity acts downward, creating a net force that aligns with the acceleration. The relationship between the normal force, mass, and speed is given by the equation N = m*v^2/r. The angle 2t is crucial for understanding the direction of the normal force, which is perpendicular to the cone's surface. By analyzing these forces, one can derive the speed of the mass in circular motion.
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A mass m moves in a horizontal circle of radiuss r inside a frictionless cone of angle 2t. Determine the speed of the mass.

I drew the free body diagram for the mass. Normal force points toward the center in the same direction as the acceleration. Gravity points down.

x) N = m*v^2/r

I don't know why, but gravity is the only force acting in the vertical direction. There is nothing to balance it out.

I know that I will need to use the angle 2t somehow, but I don't know what to do.
 
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The NET force will point in the same direction as the acceleration (that's from Newton's 2nd law). The normal force will point normal (perpendicular) to the surface of the cone and thus slightly upwards.
 
Yes, that's right. Remember by definition normal force is wel, NORMAL to the surface. You should be able to find it easily now. Weight leads to normal, normal leads to net.
 
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