Conservative Forces Homework Statement

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SUMMARY

The discussion centers on the nature of conservative forces, specifically examining whether the force F = (theta)r_hat is conservative and whether a force that depends on velocity but is always perpendicular to it can be classified as conservative. The participants analyze the conditions under which a force is considered conservative, emphasizing the importance of path independence and the existence of a potential function. The conclusion drawn is that the first force is not conservative due to its dependence on the angular coordinate, while the second force, being perpendicular to velocity, is also not conservative as it does not meet the criteria for conservative forces.

PREREQUISITES
  • Understanding of conservative forces in physics
  • Familiarity with vector calculus
  • Knowledge of potential energy concepts
  • Basic understanding of force and motion in the xy-plane
NEXT STEPS
  • Study the mathematical definition of conservative forces
  • Learn about potential energy functions and their relationship to conservative forces
  • Explore examples of non-conservative forces in physics
  • Investigate the implications of forces that are perpendicular to velocity in motion dynamics
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Students of physics, educators teaching mechanics, and anyone interested in the principles of force and motion in classical mechanics.

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Homework Statement


1. Is force F = (theta)r_hat conservative?

2. Is force which depends on velocity but is always perpendicular to velocity conservative?

Homework Equations


1. theta is from 0 to 2pi and F is limited to xy plane only

The Attempt at a Solution

 
Last edited:
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your attempt and reasoning please?
 

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