Proving Equilibrium: The Relationship Between Forces and Torque

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When three coplanar forces act on an object in equilibrium, they must either meet at a single point or be parallel. If the forces are parallel but not collinear, they create a torque that causes rotation, violating equilibrium. For equilibrium to be maintained, both the sum of forces and the sum of moments must equal zero. An example illustrates that two parallel forces of equal magnitude but opposite direction can satisfy the force condition while still producing an unbalanced torque. Understanding these principles is crucial for proving the relationship between forces and torque in equilibrium scenarios.
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When three coplanar forces act on an object, and the object is in equilibrium, then the line of action of three forces meet at one point or they are parallel. How can i prove that this is true? Thanks. I really don't know where I should start.
 
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First of all, if you're looking at the case where they are paralell, you need another condition. They need to be parallel and act along the same line, otherwise you have a moment acting on the object, and it causes rotation.
 
Is it because if three forces do not meet at a point, they will produce a torque and cause the object to rotate?
 
Yes, they will. Imagine two parallel forces, let's say at a distance d, of equal magnitude F and opposite direction. Then the equilibrium condition ΣF = 0 is satisfied, but ΣM = 0 not, because you have an unbalanced torque of magnitude F*d.
 

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