3.6:
Categories of Equilibrium
An object's equilibrium state can be categorized based on the force systems acting on it. They are collinear, coplanar concurrent, and coplanar non-concurrent forces.
Consider two individuals exerting equal and opposite forces while pulling a rope. The two forces acting on the rope are collinear such that the net force on the rope is zero. The system is in equilibrium.
In a coplanar concurrent force system, all the forces meet at a single point on the same plane.
Here, these forces can be resolved into their horizontal and vertical components.
For a system to remain in equilibrium, the upward and downward vertical forces must balance. Similarly, the leftward and rightward horizontal forces must also be equal and oppositely directed.
In a coplanar non-concurrent force system, the forces acting on the object are parallel. Here, the moment due to F3 is clockwise and is balanced by an anticlockwise moment due to F2.
Similarly, F1 is counterbalanced by the object's weight and the net moment and the net force on the object are zero, maintaining the equilibrium.
3.6:
Categories of Equilibrium
Equilibrium is a crucial concept in physics, enabling us to understand how forces interact with bodies to produce no or constant motion. In two-dimensional equilibrium, force systems can be classified into different categories based on their characteristics.
One of the categories of equilibrium is collinear equilibrium, which involves forces acting along a straight line. This type of equilibrium requires only one force equation in the direction of the forces, as the other equations are automatically satisfied.
Another category is the coplanar concurrent equilibrium, in which all the acting forces meet at a single point in the same plane. In this category, the forces can be resolved into their horizontal and vertical components to determine equilibrium. The vertical and horizontal forces should have an equal magnitude and be directed oppositely to balance each other.
The coplanar non-concurrent equilibrium category involves forces that are parallel but not concurrent to each other. In this type of equilibrium, the moments due to the forces are balanced, resulting in zero net force on the object. For this to happen, the moments generated by the forces should be equal but opposite in direction.
Finally, general equilibrium is the most complicated category, involving any number of forces not necessarily in one plane. This type of equilibrium requires two force equations and a moment equation to obtain a solution.
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- Meriam, J.L.; Kraige, L.G., and Bolton, J.N. (2020). Engineering Mechanics ‒ Statics. Hoboken, New Jersey: John Wiley. Pp – 121-122.