Centripetal Motion and Masses at the Fair

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    Centripetal Motion
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SUMMARY

The discussion centers on the principles of centripetal motion as observed in amusement park rides, specifically a ride where chairs rotate in a circle. It is established that the angle at which the chairs rise is determined by the ratio of centripetal force to gravitational weight, both of which are proportional to mass, resulting in mass cancellation. Consequently, all chairs, regardless of the mass of the occupants, rise to the same angle when the chains are of equal length and the angular speed is constant. The application of Newton's 2nd law is essential for calculating the height each chair rises.

PREREQUISITES
  • Understanding of centripetal force and its relationship to mass
  • Familiarity with Newton's 2nd law of motion
  • Basic knowledge of angular velocity and its effects on motion
  • Concept of tension in a chain or rope
NEXT STEPS
  • Study the principles of centripetal acceleration in detail
  • Learn how to apply Newton's 2nd law to rotational systems
  • Explore the mathematical relationship between tension and angle in circular motion
  • Investigate different amusement park rides and their physics
USEFUL FOR

Physics students, mechanical engineers, amusement ride designers, and anyone interested in the dynamics of circular motion.

catenn
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Hi, I was told about Centripetal Motion and learned some about rides at the fairs. There is one ride with chairs hanging by a chain in a circle that simply rotates at a certain speed without turning at any angle. Does anyone understand why all of the chairs move up at the same angle even though each person will have a different mass, and even the empty chairs move the same. How can all of the masses cancel? Thanks.
 
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It turns out that the angle a chair rises depends on the ratio of the centripetal force (which is proportional to mass) to the weight (which is also proportional to mass). So the mass does cancel. As long as the chains are the same length, the seats will rise to the same angle for a given angular speed regardless of the mass of the person.
 
Thank you very much!
 
What procedure do you exactly follow to determine the height each chair is going to rise?
 
Apply Newton's 2nd law. The chairs are centripetally accelerated, so there is a net force in the horizontal direction. Realizing that the tension in the chain acts along its length allows you to calculate the angle the chain makes with the vertical.
 

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