# Mechanical balance

A body that is in mechanical equilibrium does not experience any acceleration ; consequently it remains at rest or moves at a constant speed. According to Newton's first law , the reverse also applies: Every body that does not experience any acceleration is in mechanical equilibrium. A body is in mechanical equilibrium when all the forces that act on it are in equilibrium. This is the case when it is both in equilibrium of forces and in (torsional) moment equilibrium .

• A body is in equilibrium of forces when the vector sum of all forces acting on it is zero.
• It is in equilibrium of moments with respect to a freely selectable point if the sum of all moments around this point is zero.

In addition to chemical and thermal equilibrium, mechanical equilibrium is a prerequisite for thermodynamic equilibrium .

## Mechanical equilibrium in rigid bodies

The mechanical equilibrium of rigid bodies is examined in detail in rigid body statics . If a body is in mechanical equilibrium, then it is also in moment equilibrium with respect to every point. A group of forces in which all forces are in mechanical equilibrium is called an equilibrium group. If confusion with other equilibria is impossible, the mechanical equilibrium is briefly referred to as equilibrium. As a demarcation to dynamic equilibrium also as static equilibrium . For mechanical equilibrium, the following conditions must be met (equilibrium conditions):

1. ${\ displaystyle \ sum {\ vec {F}} _ {i} = {\ vec {0}}}$ - The sum of all forces must be zero (balance of forces)
2. ${\ displaystyle \ sum {\ vec {M}} _ {i} = {\ vec {0}}}$ - The sum of all moments around any (any) point must be zero (moment equilibrium)

The total of the forces includes the applied forces and constraining forces . Applied forces are forces with certain physical causes, such as weight force or the frictional force, constraining forces are forces with certain kinematic relationships , e.g. B. rope forces and bearing forces that prevent falling or other movements of a body. In the case of a rigid body , i.e. a body that cannot deform, it is sufficient to consider the external forces , since all internal forces are always in equilibrium. In the case of deformable bodies, however, these must be taken into account.

The balance of forces and moments can be given independently of the other. If the forces that act on a body are in balance of forces, this does not mean that they are also in balance of moments. The equilibrium of moments must be fulfilled for any point, but if it is already known that a body is in equilibrium of forces as well as in equilibrium of moments with respect to any point, then it is also in equilibrium of moments with respect to every other point and thus overall in equilibrium .

## Mechanical equilibrium in fluids

If not only individual masses are considered, but a system made up of many mass points, such as a gas , then this can exert macroscopic forces in the form of pressure on another body. In order for a mechanical equilibrium to exist within such a pressure system, these forces must balance each other out so that no macroscopic subsystem does work on another subsystem. As in the mechanics of rigid bodies, only macroscopic forces are considered, not the microscopic interactions of individual fluid particles.

In the simplest case, when the potential energy of a fluid particle is the same everywhere in the system, the system is in mechanical equilibrium when the pressure is the same everywhere.

## Examples and meaning

Equilibrium situations occur in many areas of physics and technology. All buildings are generally in a good approximation in equilibrium (apart from vibrations). With the equilibrium conditions and with the deformation conditions, it is usually possible in engineering mechanics to calculate the forces that act inside components. For so-called statically determined systems, the equilibrium conditions alone are sufficient; for others, additional conditions are required such as deformations and material properties. All bodies that move at constant speed are also in static equilibrium. This is the case, for example, when driving a car (apart from local effects such as dynamic eddies or tire wear), but also with a parachutist, as soon as his speed is so high that the frictional force caused by the air friction is in balance with the weight (apart from, for example, layers of air). With hot air balloons, submarines and fish that are at a constant height or depth, the weight force is largely in equilibrium with the buoyancy force.