Calculating Centripetal Force: Diagramming and Solving for X and Y Forces

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Discussion Overview

The discussion revolves around the calculation and understanding of centripetal force, specifically the expression F = (mv^2)/r. Participants explore how to diagram and solve for the forces acting in the x and y directions, and the implications for work done in circular motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant asks how to prove the centripetal force formula by diagramming and solving for forces in the x and y directions.
  • Another participant provides a link to a Wikipedia article on centripetal force, suggesting it as a resource for understanding the topic.
  • A later reply discusses the concept of work in the context of centripetal force, stating that work done in circular motion at constant speed is zero due to the perpendicular nature of force and displacement vectors.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the method of proving the centripetal force formula or the implications for work done, as different aspects of the topic are being explored without resolution.

Contextual Notes

The discussion includes assumptions about the nature of forces in circular motion and the definition of work, which may depend on specific conditions not fully articulated by participants.

kdburns
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How would you go about proving that centripetal F=(mv^2)/r by diagramming and solving for the magnitude of the forces in the x and y direction?

For example, suppose I wanted to calculate the work done in the radial direction by centripetal force.
 
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Thanks so much! Really helpful
 
Work is the product of the applied force magnitude x the magnitude of the displacement (D) in the same direction as the applied force. As a result, this is sometimes expressed as W = F x Dcosθ where θ is the angle between the two vectors (F and D). Since the F and D vectors are always perpendicular for circular motion of a mass at a constant speed, the angle between the two vectors is always 90°. So, the work done in circular motion at constant speed is 0 since cos90° is 0.
 

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