# Equilibrium of Force Systems including Torque

this is only the #3 on my homework and the only thing i didn't know here is how to calculate the tension T. please teach me how to solve the tension here because the future problems that will be given to us is related in finding the tension or compression. thank you!

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Do you know how to create a free body diagram? – ja72 Aug 25 '13 at 14:58

Since the system is in equilibrium, the torque at point A must be 0. There are three components of that torque: from the force of 200, the force of 100 and the force that comes from string at point C.

At this moment it is necessary to calculate the angle at point C.

$\tan \angle ACD={8 \over 4}=2 \implies \angle ACD \approx 1.11$

Using the definition of torque ($\vec\tau = \vec r\times\vec F$), we have

$0=2 \cdot 200+6 \cdot 100-4\cdot T\cdot \sin\angle ACD \implies T \approx 279$

Assuming the string is weightless.

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Consider the free body diagram with the tension split into components

Now follow the equilibrium conditions that sum of forces is zero and sum of moments is zero. As @QuadntumDrzewo said taking moments about point A is advantageous because you do not need to know the reaction loads at A to get to the tension. But in theory any point considered is sufficient.

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