Variably Solving for Minimum Tangential Speed

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SUMMARY

The discussion focuses on calculating the minimum tangential speed required for a rider to remain adhered to the side of a carnival ride when it rotates about a vertical axis. Key variables include the radius of the circle (R), the coefficient of static friction (u), and gravitational acceleration (g). The relevant equations are F = ma, F = un, and Ca = v^2/r. The solution involves determining the relationship between these variables to derive the minimum speed formula, V = sqrt(Ca * r), ensuring the rider does not fall due to insufficient frictional force.

PREREQUISITES
  • Understanding of Newton's laws of motion (F = ma)
  • Knowledge of circular motion dynamics (Ca = v^2/r)
  • Familiarity with static friction concepts (F = un)
  • Basic grasp of gravitational effects on objects
NEXT STEPS
  • Research the derivation of centripetal force in circular motion
  • Study the relationship between static friction and normal force
  • Explore real-world applications of friction in rotational systems
  • Learn about the effects of varying radius on tangential speed requirements
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of rotational motion and frictional forces in practical applications.

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Homework Statement


A ride at a carnival rotates about a vertical axis. When spinning fast enough the bottom is dropped and the rider sticks to the side. Find the minimum tangential speed so that the rider does not fall. R=radius of circle, u= coefficient of static friction and g represents gravity. The answer must be in these terms.


Homework Equations


F = ma
F = un
Ca = v^2/r

The Attempt at a Solution


V = sqrt (Ca*r)

I think I am missing something here, as it is not with respect to the right variables. Any hints on what to do next, or if I am heading down the wrong path?
 
Physics news on Phys.org
What is the normal reaction of the surface?
In which direction the frictional force acts?
What should the condition so that rider does not fall?
 

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