Easy Statics Problem: Solving Tension in a Continuous Wire with Eccentric COG

[lidstrompl]

I have (what is seems to me) and easy statics problem to solve. I simply need to work out the tension in a single continuous wire connected to the load (with eccentric COG) on two ends - as shown, and passing through a frictionless pulley on top.

I know that the tension in the wire must be the same, however I could not visualise it entirely, because to me it seems that it would be possible for the load to rotate around the centre of gravity (in the current configuration). The reason I am saying that is that if the tension is the same in the wires (does not matter what the weight is) then the balance of moments about COG (after drawing my FBD) does not balance out...

Any help with this one would be greatly appreciated.

Thank you

 

[PhanthomJay]

I have (what is seems to me) and easy statics problem to solve. I simply need to work out the tension in a single continuous wire connected to the load (with eccentric COG) on two ends - as shown, and passing through a frictionless pulley on top.

I know that the tension in the wire must be the same, however I could not visualise it entirely, because to me it seems that it would be possible for the load to rotate around the centre of gravity (in the current configuration). The reason I am saying that is that if the tension is the same in the wires (does not matter what the weight is) then the balance of moments about COG (after drawing my FBD) does not balance out...

Any help with this one would be u appreciated.

Thank you

you are quite correct, the system cannot be in equilibrium in the position shown because there is no way to balance the horizontal force at the pulley as caused by the unequal horizontal components of the equal tensions. Thus, the system must translate and rotate until the bisector of the new line angle of the rope at the pulley lines up with the vertical line of action of the CG weight force. Note that the CG does not move horizontally.