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

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In summary, the problem involves finding the tension in a single wire connected to a load with an eccentric center of gravity and passing through a frictionless pulley. The tension must be the same on both ends, but the system cannot be in equilibrium due to unequal horizontal components of the tensions. The system must translate and rotate until the rope lines up with the vertical line of action of the center of gravity.
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lidstrompl
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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

problem.png
 
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  • #2
lidstrompl said:
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

problem.png
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.
 

1. What is statics and why is it important?

Statics is the branch of mechanics that deals with the study of objects at rest or in a state of constant motion. It is important because it helps us understand how forces act on objects and how they are balanced, which is essential in designing structures and machines that can withstand different loads and forces.

2. What is tension and how is it related to statics?

Tension is a force that acts along a string, rope, or wire when it is pulled tight by forces acting on both ends. In statics, tension is important because it helps us calculate the amount of force required to keep an object in equilibrium when it is suspended or connected to other objects.

3. What is an eccentric COG and how does it affect tension in a continuous wire?

An eccentric COG (center of gravity) refers to the point where the weight of an object is evenly distributed in all directions. In a continuous wire, an eccentric COG can cause an uneven distribution of weight, resulting in varying levels of tension along the wire. This can impact the stability and balance of the wire and the objects it is supporting.

4. How do you solve for tension in a continuous wire with an eccentric COG?

To solve for tension in a continuous wire with an eccentric COG, you will need to use the principles of statics and apply them to the specific scenario. This will involve calculating the forces acting on the wire and finding the point at which they are balanced. You can then use this information to determine the tension in the wire at different points.

5. How can understanding tension in a continuous wire with an eccentric COG be applied in real-life situations?

Understanding tension in a continuous wire with an eccentric COG can be applied in various real-life situations, such as designing bridges, cranes, or other structures that involve the use of wires or cables. It can also be useful in determining the appropriate tension for supporting objects or loads in different scenarios, such as in elevators or suspension systems.

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