What is the Equilibrium of a Uniform Rod with Unknown Weight?

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SUMMARY

The discussion focuses on determining the equilibrium of a uniform rod weighing 263 N and measuring 2.20 m, with an additional 225 N weight at one end and an unknown weight W positioned 55.6 cm from the left end. The system achieves horizontal balance with the fulcrum located 83.2 cm from the right end. Participants emphasize the application of torque equations and Newton's laws to solve for the unknown weight W by ensuring the sum of all torques equals zero.

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  • Understanding of torque equations and their application in static equilibrium.
  • Familiarity with Newton's laws of motion.
  • Knowledge of the concept of moments and their calculation.
  • Ability to analyze forces acting on a lever system.
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  • Study the principles of static equilibrium in physics.
  • Learn how to calculate torques about a fulcrum in various scenarios.
  • Explore examples of lever systems and their applications in real-world problems.
  • Investigate the relationship between forces, distances, and moments in equilibrium situations.
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Students studying physics, particularly those focusing on mechanics and static equilibrium, as well as educators seeking to enhance their understanding of torque and lever systems.

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Homework Statement



A uniform, 263-N rod that is 2.20m long carries a 225-N weight at its right end and an unknown weight W toward the left end (see attached figure). When W is placed 55.6-cm from the left end of the rod, the system just balances horizontally when the fulcrum is located 83.2-cm from the right end.


Homework Equations



Basic Torque equations + Newton's laws.

The Attempt at a Solution



I don't exactly know where to start. I know the sum of all torques has to be 0, but I'm not sure what numbers to use or where the mass of the rod comes into play. Can anybody help?
 

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If the length of the rod is 2.2 m, then its weight will act at the center of this rod. So it acts at what distance?

The sum of all moments (torques) about any point = 0 for equilibrium means that wherever you take moments, all should add up to zero. So consider taking moments about the fulcrum. What are the forces acting and their respective distances from the fulcrum?
 

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