Mechanical Equilibrium

The universe is a constant interaction of forces, and all phenomena that we observe are a result of these forces. Without forces, there would not be anything in the universe because everything from the formation of molecules to the revolving of planets around the Sun is a direct result of the interaction between forces.

According to thermodynamics, the entropy of the universe is constantly increasing. In a situation of increasing entropy, all bodies want to be at equilibrium.

Factors affecting a body in mechanical equilibrium

A body is put into motion when its acceleration is increased. This happens due to the application of force. Along with force, inertia also decides how much a body will move and accelerate. There are a few key factors that determine mechanical equilibrium.

Force

The motion of a body is caused due to the application of force. The application of force deforms, moves, and changes an object. It can allow us to change the position of a body, make it go faster or make it go slower, change the height of the body from the ground etc. There are various types of forces that can act on a body, ranging from frictional force to gravitational force.

Forces can be classified into two types: contact and non-contact forces. Forces that can be exerted only when the applicant of the force and the body on which it is going to be applied are in contact are called contact forces. Whereas forces that do not require the applicant of the force and the body on which it is going to be applied to be in contact are called non-contact forces.

Acceleration on a body

When force is applied to a rigid body already in motion with a fixed velocity v, then the application of the external force results in a change in the velocity of the body. The measure of the change in velocity with respect to the time of a rigid body in motion due to the application of an external force is called acceleration. Let v be the velocity of a rigid body, then the acceleration of the body is given as a=dv/dt.

Inertia

According to Newton’s second law, all bodies tend to resist a change in their state. If a body is at rest, it will resist a change to a state of motion. If a body is in motion, it will resist a change to a state of rest. But the property that measures this tendency of a body to resist a change in its state is called inertia. Inertia is a measure of the amount of force that will be required to either stop a moving body and bring it to rest in unit distance or to put a body at rest into motion. Inertia is by virtue of the mass of the body and is an innate property of every object that has a mass.

The conditions for mechanical equilibrium

Let us study the two conditions required to achieve mechanical equilibrium.

In a system under observation, when the observed parameters of the system do not change with time, the system is said to be in equilibrium. Extending this definition to motion, when a rigid body is moving such that its parameters do not change with time, it is said to be in mechanical equilibrium.

When a body is moving but at constant velocity

When an external force is acting on a body, but the force is just enough to maintain a fixed velocity of the body, the body is said to be in mechanical equilibrium. The net force on the body should not produce acceleration to ensure that the body stays in mechanical equilibrium.

When a body is at rest and no force is applied

If a body is at rest and no force is causing a displacement in the position of the body, then it is said to be in mechanical equilibrium. In order to maintain mechanical equilibrium in this stage, no external force must be applied to the body. If an external force is applied, then an equal and opposite force must also be applied to keep the net force on the body at zero.

The equation for mechanical equilibrium

Mechanical equilibrium requires that the net force that is acting on the body should be equal to zero. In other words, if there are multiple forces that are applied to a body, the total sum of all these forces must be equal to zero. To find out the amount of offsetting force that will be required to maintain a mechanical equilibrium, we can add up all the forces and equate them to zero.

Let us try to understand the formula for mechanical equilibrium with an example. If there is a body of mass m, on which a force is applied F1 such that the acceleration on the body is a. In order to maintain mechanical equilibrium, the force on the body should be offset by another force, F2. Therefore, to maintain mechanical equilibrium:

F1 + F2 = 0 ⇒ F1 = -F2

Conclusion

According to thermodynamics, the entropy of the universe is constantly increasing. In a situation of increasing entropy, all bodies want to be at equilibrium. In a system under observation, when the observed parameters of the system do not change with time, then the system is said to be in equilibrium. Extending this definition to motion, when a rigid body is moving such that its parameters do not change with time, it is said to be in mechanical equilibrium.