How to Solve Pendulum Forces in Component Form?

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SUMMARY

The discussion focuses on solving the forces acting on a pendulum in component form, specifically addressing the application of Hooke's Law and the decomposition of forces into x and y components. Participants clarify that the gravitational force (mg) acts vertically, while the spring force (K(r-L0)) must be resolved into its respective components. The key takeaway is the necessity to split the diagonal force into x and y components to accurately analyze the pendulum's motion.

PREREQUISITES
  • Understanding of Newton's Laws of Motion
  • Familiarity with Hooke's Law
  • Knowledge of vector decomposition
  • Basic principles of pendulum dynamics
NEXT STEPS
  • Study the application of Hooke's Law in dynamic systems
  • Learn about vector decomposition techniques in physics
  • Explore the dynamics of pendulum motion and forces involved
  • Review examples of solving forces in component form
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Students studying physics, particularly those focusing on mechanics, as well as educators and tutors looking to enhance their understanding of pendulum dynamics and force analysis.

JaySean
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Homework Statement


Hi, I need help in solving question c) (a pendulum) The required data, problem and relevant equation is in the picture

The Attempt at a Solution


I am not sure how to solve it but here are my thoughts:
since mg is working at j
y(t)j= mg
does that mean K(r-L0) x(t) direction?
I am not sure how to start/think to solve this problem so any tips will be helpfull, thanks!
 

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Look at the vector attached to the second term. It is not in the i / x direction but rather in the r direction. It acts directed from the radius of the pendulum. What law describes this force?

Also, think why do we divide the r vector by its magnitude?
 
Brian T said:
Look at the vector attached to the second term. It is not in the i / x direction but rather in the r direction. It acts directed from the radius of the pendulum. What law describes this force?

Also, think why do we divide the r vector by its magnitude?
Is it Hookes law?
I assume we divide r vector by its magnitude to determine the direction of the force
 
the rope stretches along its length like a spring. all c) asks you to do is split the diagonal Force into (x,y) components.
 
Is mg=y component correct or is it wrong?
And what force is working in the x direction? Or did I misunderstand what the task is asking for?
 
mg is entirely vertical ... but most folks treat "up" as positive.
That is not the ONLY vertical Force contribution, however. The diagonal (spring) Force has x-component and y-component.
 
So K(r-L0) works both in x and y direction? Am I then supposed to split the force and find which force works in x and y direction?
 
the wording in part c) could not be more explicit.
 
r(t)=(K*r)i-K*L0j would this be correct?
 
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