Circular Motion and speed of mass

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SUMMARY

The discussion focuses on determining the speed of a mass m moving in a horizontal circle of radius r within a frictionless cone with an angle of 2t. The key equations derived include the normal force equation N = m*v^2/r, where N is the normal force directed towards the center of the circle. The analysis emphasizes that gravity is the only vertical force acting on the mass, and the normal force acts perpendicular to the cone's surface. Understanding the relationship between these forces is crucial for solving the problem.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with free body diagrams
  • Knowledge of circular motion dynamics
  • Basic trigonometry related to angles in physics
NEXT STEPS
  • Study the derivation of centripetal acceleration in circular motion
  • Learn about the role of normal force in inclined planes
  • Explore applications of Newton's second law in circular motion
  • Investigate the effects of varying angles on forces in conical motion
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Physics students, educators, and anyone interested in understanding the dynamics of circular motion and forces acting on objects in a conical setup.

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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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