Equilibrium - A rod influenced by multiple rope tensions

AI Thread Summary
The discussion focuses on a smooth, identical rod in equilibrium, influenced by multiple rope tensions from weights X and Y, both equal to P. The user calculates the torque and determines that when X equals P, the rod remains balanced. However, the textbook suggests that X can also be 6P, indicating that if X increases beyond a certain point, the rod will rotate. The analysis includes considerations of how varying weights of X affect the rod's stability and direction of rotation. Ultimately, the equilibrium condition is contingent on the relationship between the weights and the rod's center of gravity.
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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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