Rod is toppling. Find reaction force as a function of theta

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SUMMARY

The discussion focuses on calculating the reaction force of a rod of length b and mass m as it topples from a vertical position at an angle theta. The solution involves applying principles of rigid body motion and Lagrangian mechanics to derive the reaction force f as a function of theta, specifically identifying its minimal and maximal values for theta ranging from 0 to π. The use of Lagrangian multipliers is essential for determining the constraint forces in this scenario.

PREREQUISITES
  • Understanding of rigid body motion principles
  • Familiarity with Lagrangian mechanics
  • Knowledge of constraint forces and Lagrangian multipliers
  • Basic concepts of angular motion and forces
NEXT STEPS
  • Study the derivation of equations of motion using Lagrangian mechanics
  • Learn about constraint forces and their calculation using Lagrangian multipliers
  • Explore examples of rigid body motion in mechanics
  • Investigate the effects of varying angles on reaction forces in dynamic systems
USEFUL FOR

Students in physics or engineering courses, particularly those studying mechanics, as well as educators and anyone interested in the application of Lagrangian methods to rigid body problems.

NucEngMajor
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Homework Statement


Rod of length b and mass m topples from vertical position at theta = 0. Calculate the reaction force f as a function of theta. What is the minimal and maximal values of f for theta between 0 and pi

Homework Equations


Third law?[/B]

The Attempt at a Solution


I never really worked a problem such a this in mechanics. So I was shocked to see this on my exam. I would like to know what the solution is. I had no idea how to solve. I suppose this falls under rigid body motion, but all we worked in that topic were lagrangians...
 
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can the rod slip on the ground?
 
NucEngMajor said:
I suppose this falls under rigid body motion, but all we worked in that topic were lagrangians...
In general, exam questions are related to the material that's been presented. So you wrote a Lagrangian for this constrained system and found the equation of motion. Did you also learn that the constraint forces follow from the Lagrangian multipliers ?
 

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