Balance conditions

Equilibrium conditions are the laws that govern statics. Statics is the science that studies the forces that are applied to a body to describe a system in equilibrium. We will say that a system is in equilibrium when the bodies that form it are at rest, that is, without movement. The forces that are applied to a body can be in three ways:
-Angular forces : Two forces are said to be angular, when they act on the same point at an angle. -Colinear forces : Two forces are collinear when the line of action is the same, although the forces can be in the same direction or in opposite directions. -Parallel forces:

Two forces are parallel when their directions are parallel, that is, the lines of action are parallel, and can also be applied in the same direction or in the opposite direction. Around us we can find numerous bodies that are in balance. The physical explanation for this to occur is due to the equilibrium conditions:

-First equilibrium condition: We will say that a body is in translational equilibrium when the resultant force of all the forces acting on it is null: ∑ F = 0.
Mathematically, in the case of coplanar forces, it must be fulfilled that the arithmetic sum of the forces or their components that are in the positive direction of the X axis is equal to the components that are in the negative direction. Similarly, the arithmetic sum of the components that are in the positive direction of the Y axis must be equal to the components that are in the negative direction:

On the other hand, from the geometric point of view, it must be observed that the forces acting on a body in equilibrium have a graph in the form of a closed polygon; since in the forces graph, the origin of each force is represented from the end of the previous force, as we can see in the following image. The fact that your graph corresponds to a closed polygon verifies that the resulting force is null, since the origin of the first force (F1) coincides with the end of the last one (F4).

-Second equilibrium condition: On the other hand, we will say that a body is in rotation equilibrium when the sum of all the forces exerted on it with respect to any point is null. Or put another way, when the sum of the torques is zero. In this case, from the mathematical point of view, and in the previous case in which the forces are coplanar; it must be fulfilled that the sum of the moments or forces associated with anti-clockwise rotations (counterclockwise), must be equal to the arithmetic sum of the moments or forces that are associated with hourly rotations ( clockwise):

A body is in translational and rotational equilibrium when the two equilibrium conditions are verified simultaneously. These equilibrium conditions become, thanks to vector algebra, a system of equations whose solution will be the solution of the equilibrium condition.

 

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