Equilibrium - A rod influenced by multiple rope tensions

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SUMMARY

The discussion centers on the equilibrium of a smooth, identical rod influenced by multiple rope tensions, specifically weights P, 6P, and 9P. The gravity center of the rod is located 2.5 units from both ropes X and Y. The calculations indicate that when X equals P, the rod remains in equilibrium; however, the book suggests two possible weights for X: P and 6P. As the weight of X increases, the rod will eventually rotate about one of the ropes, demonstrating the principles of torque and equilibrium in physics.

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  • Understanding of torque and equilibrium principles in physics
  • Familiarity with the concept of gravity center in rigid bodies
  • Basic knowledge of forces and their effects on objects
  • Ability to solve algebraic equations related to weight and balance
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  • Study the principles of torque in rotational dynamics
  • Learn about the conditions for static equilibrium in physics
  • Explore the concept of center of mass in rigid body mechanics
  • Investigate the effects of varying weights on equilibrium states
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Students studying physics, particularly those focusing on mechanics and equilibrium, as well as educators seeking to explain the concepts of torque and balance in real-world scenarios.

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equilibrium -- A rod influenced by multiple rope tensions

Homework Statement



Smooth and identical rod has a weight of P. The rod seems to be in equilibrium with X and Y which has a weight of P. What can be the weight of X according to the values below?(ip means rope)

P , 6P or 9P

Homework Equations


The Attempt at a Solution



I tried to find the torque. First I found the gravity center of the rod. It is 2.5 units from X and 2.5 units from Y. And found the answer as
2.5P=2.5X and X=P. But according to my book there are 2 values for X. One of them is 6P and the other is P.
 

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Think about what happens if X gets heavier and heavier. When X reaches a certain weight, the rod will begin to rotate in which direction and about which rope?

Likewise, think about what happens if X gets lighter and lighter.
 
6X=3P+P
x=2/3
 

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