# Statics

Statics is the branch of mechanics that studies the bodies in condition of balance submitted to the action of forces.

Strength is the action that one has on something, either by pulling or pushing. The most commonly used are:

• Weight: Earth attracts things and it is causes that things fall down.
• Tension: force that is exerted by a rope or wire to compensate the weight of the object.

Statics is concerned with the analysis of loads (force, torque/Momentum) on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity. When in static equilibrium, the system is either at rest, or its center of mass moves at constant velocity.

By Newton’s first law, this situation implies that the net force and net torque (also known as momentum of force) on everybody in the system is zero. From this constraint, such quantities as stress or pressure can be derived. The net forces equaling zero is known as the first condition for equilibrium, and the net torque equaling zero is known as the second condition for equilibrium.

Concurrent, coplanar and/or parallel forces: are those forces that are acting on the same body and pass through the same point. In the case that the forces do not pass through the same place they are said to be non-concurrent. If the forces are contained in the same plane they are called coplanar forces and forces which have the same direction (although they may have different sense) to a unit vector are called parallel forces.

Sum of forces- result: It is the result of adding all other forces. There are two ways to calculate the result of a system of forces:

• Graphically: it is only used when we have two forces whose resultant force is formed by the diagonal of the parallelogram.
• Analytically: the resulting is calculated mathematically.

Action-reaction forces: When you suspend a body by a thread, it stiffens by the action of the body. When a spring is compressed or stretched, there is an action that causes the phenomenon. A body placed on a table also exerts a certain action.
In all cases these actions are balanced by some other force that supply the thread, spring or table, respectively. That force is called reaction.
The reaction force is opposite to the action force which has an equal intensity but opposite direction.

FORMULA SUMMARY:

Hooke’s law (F = deforming force ; k = spring constant ; Δl = deformation produced) Bioprofe |Statics theory|01

Resultant of two recurrent forces (α = angle between F1 and F2) Bioprofe |Statics theory|02

Torque, also called momentum of force (Mo = Momentum ; F = Force ; r = displacement vector) Bioprofe |Statics theory|03

Equilibrium conditions of a solid Bioprofe |Statics theory|04

Coordinates of the gravit center of an object Bioprofe |Statics theory|05