Forces during the motion of an object in a vertical circle

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Discussion Overview

The discussion revolves around the forces acting on an object moving in a vertical circle, particularly at the point where the normal force (R) is considered to be zero. Participants explore the implications of this assumption and its relation to centripetal force and motion dynamics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question the assumption that the normal force R can be zero at point D, seeking clarification on the basis for this assumption.
  • It is noted that normal forces are contact forces that must act perpendicular to the tangent of the curve, and if R is less than zero, contact is lost, implying R must be greater than zero.
  • Participants discuss the scenario where R equals zero, questioning whether the object can still maintain circular motion under these conditions.
  • One participant suggests that at R=0, gravity provides the necessary centripetal force, allowing the object to remain in circular motion without contact, likening it to a satellite in orbit.
  • There is a mention that if the object's speed is less than a certain threshold, continuous circular motion cannot be maintained.

Areas of Agreement / Disagreement

Participants express differing views on the implications of R being zero, with some supporting the idea that circular motion can still occur without contact, while others emphasize the necessity of a non-zero normal force for maintaining contact and circular motion.

Contextual Notes

The discussion includes assumptions about the nature of forces and motion in a vertical circle, particularly regarding the conditions under which contact is maintained or lost, and the specific speed required for circular motion.

influx
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At D, by resolving and equating to centripetal force we know that R + W = mv^2/r, however, why do we assume R=0? Based on what?

I know my post is short and usually a longer solution is required but I do not have a problem with the maths in the attached, it's just the concept of letting R=0 that I need clarified.

Thanks
 
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influx said:
View attachment 81979View attachment 81980

At D, by resolving and equating to centripetal force we know that R + W = mv^2/r, however, why do we assume R=0? Based on what?

I know my post is short and usually a longer solution is required but I do not have a problem with the maths in the attached, it's just the concept of letting R=0 that I need clarified.

Thanks
Based on the fact that normal forces are contact forces perpendicular to the tangent of the curve that in this instance must push on the object. If it is less than 0, contact is lost. So it must push with a value greater than 0. Problem is looking for minimums.
 
PhanthomJay said:
Based on the fact that normal forces are contact forces perpendicular to the tangent of the curve that in this instance must push on the object. If it is less than 0, contact is lost. So it must push with a value greater than 0. Problem is looking for minimums.

What happens at exactly R=0? It remains in a circular motion?
 
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influx said:
What happens at exactly R=0? It remains in a circular motion?
Yes, gravity only supplies the centripetal force without contact at that point D. The pellet remains at a distance 2 feet from the center of the circle without 'dropping', even though contact is momentarily lost, and with a speed of [itex]\sqrt{rg}[/itex]. It behaves like a satellite in orbit at that specific point, no contact necessary at that point. If the speed was less than that, then continuous circular motion could no be maintained.
 
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