Weightlessness on a Ferris Wheel

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Homework Help Overview

The problem involves determining the necessary revolutions per minute for a Ferris wheel with a diameter of 15.1 m so that passengers experience weightlessness at the topmost point. The context centers around concepts of circular motion and acceleration.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between centripetal acceleration and velocity, with some suggesting the use of free body diagrams to analyze forces at the top of the Ferris wheel. Questions arise about converting velocity to revolutions per minute and the implications of weightlessness in terms of forces acting on the passengers.

Discussion Status

The discussion includes various attempts to connect concepts of centripetal acceleration and gravitational force. Some participants have provided insights into the relationships between these forces, while others are exploring how to express velocity in terms of angular velocity and revolutions per minute. There is no explicit consensus, but several productive lines of inquiry are being pursued.

Contextual Notes

Participants are working under the assumption that the forces acting on the passengers at the top of the Ferris wheel must balance for weightlessness to occur. There may be constraints related to the specific parameters of the problem that are not fully addressed in the discussion.

Sumbhajee
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Homework Statement


How many revolutions per minute would a 15.1 m diameter Ferris wheel need to make for the passengers to feel "weightless" at the topmost point of the trip?


Homework Equations





The Attempt at a Solution


I assume this problem has something to do with finding acceleration and converting from there. I have been having a lot of trouble with this problem.
 
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What are the things you know about vertical circular motion?
 
I know that Centripetal acceleration = (velocity)^2/radius
 
If you're weightless at the top, what does that mean? Draw your free body diagram, then figure out which forces are acting where.
 
Sumbhajee said:
I know that Centripetal acceleration = (velocity)^2/radius

Can write this in terms of angular velocity?
What happens at the top of the wheel?
 
If you are weightless at the top you should have mass * gravity acting down and a centripetal force equal to gravity acting up. But how does this information help to discover revolutions per minute?
 
To set up the equation would I use the following:

9.80=V^2/7.55 and solve for velocity? But how do you convert velocity to revolutions per minute?
 
I found the answer! Thank you for all the help.
 

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