Static Equilibrium

Static Equilibrium refers to the physical state of an object when it is at rest and no external force or torque is applied to it. In Static Equilibrium, the word ‘static’ refers to the body being at rest and the word ‘equilibrium’ refers to the state where all opposing forces cancel out each other and the net force on the object becomes zero.

In this article, we will discuss more about Static Equilibrium, the classification of static equilibrium, its examples, and the difference between Static and Dynamic Equilibrium.

What is an Equilibrium?

Equilibrium refers to a state of balance or stability in a system, where opposing forces or factors are evenly matched and cancel out each other. However, the state of equilibrium does not necessarily mean that everything is at rest; it can also refer to a dynamic balance where certain quantities or conditions remain constant over time despite ongoing processes.

The concept of Equilibrium is applied in various fields like physics and chemistry, a few of its aspects are given below:

• Mechanical Equilibrium: An object is in mechanical equilibrium when the sum of the forces acting on it is zero. This implies that the object is either at rest or moving at a constant velocity.

• Thermal Equilibrium: In thermodynamics, two systems are in thermal equilibrium when they are at the same temperature and no heat flows between them.

• Chemical Equilibrium: In a chemical reaction, equilibrium is reached when the rates of the forward and reverse reactions become equal, and the concentrations of reactants and products remain constant over time.

Apart from all these equilibrium, one such equilibrium is Static Equilibrium, which is discussed in this article in detail.

Read More, Equilibrium

What is Static Equilibrium?

Static equilibrium is a state where the sum of all the exerting torques and forces on the body is null. In other words, the object is not accelerating in any direction, and there is no change in its linear or angular velocity. The essential condition for static equilibrium is that a body is not encountering any form of movement be it rotational or translational.

This state of equilibrium is a fundamental concept in classical mechanics and is applicable to various situations, particularly in the context of physics and engineering. It is a kind of equilibrium where all parts of an object are in a state of rest. If two forces are exerted on a body that is in the state of static equilibrium, then the total sum of forces is always zero.

If the magnitude and direction of one of the forces are available, an equation can be derived to find the direction and magnitude of the unknown force. It is a crucial concept in the design of many rigid and compact structures, from roofs of buildings to huge suspension platforms. This is mainly because these systems must stay in static equilibrium under every predicted loading state.

Static Equilibrium Definition

Static Equilibrium refers to the physical state in which a system is at rest and the net force acting on it is null. It is a state in which all the forces acting on an object are balanced out and the object is not found to be in motion to the relative plane.

Examples of Static Equilibrium

Static Equilibrium is found in various objects, few of the examples of static equilibrium are discussed below:

• Book on a Table: The force of gravity pulls the book downward, and the normal force exerted by the table upward balances the gravitational force. As long as the book is not accelerating vertically, it is in static equilibrium.

• Balanced Seesaw: A seesaw in a playground is in static equilibrium when two people of equal weight sit on opposite ends. The torques produced are balanced, and the seesaw remains level.

• Satellite in Orbit: A satellite in a stable orbit around a planet is in static equilibrium. The gravitational force pulling the satellite toward the planet is balanced by the centripetal force required to keep it in orbit.

• Simple Pendulum: A pendulum hanging from a string is another example of static equilibrium. The force of gravity acting on the pendulum‘s mass is balanced by the tension in the string. The pendulum remains motionless when the forces are in equilibrium.

Conditions for Static Equilibrium

For an object to be in Static Equilibrium, two conditions has to be fulfilled i.e. Translational Equilibrium and Rotational Equilibrium. These conditions make sure that the object is not experiencing any linear or angular acceleration, meaning it is at rest or moving with a constant velocity. .

Translational Equilibrium

The vector sum of all external forces acting on the object must be zero and mathematically, it is expressed as: ∑ F_k = 0. This equation states that the net force acting on the object (the sum of all individual forces) is zero.

Rotational Equilibrium

The sum of all external torques acting on the object must be zero and mathematically, it is expressed as: ∑ ͳ_k = 0.This equation states that the net torque acting on the object (the sum of all individual torques) is zero.

For an object to be in static equilibrium then above conditions must met simultaneously so that object must be in static equilibrium. If either condition is not satisfied, then object will experience translational or rotational acceleration, indicating a dynamic state.

Static Equilibrium of a Rigid Body

Static equilibrium of a rigid body refers to the state in which the entire object is stationary and not accelerating. Static equilibrium of a rigid body is possible only when the body posses both translational equilibrium and rotational equilibrium. This means that the sum of all forces acting on the body is zero, and the sum of all torques acting on the body is also zero.

These conditions make sure that the rigid body is at rest only and not rotating at all.

Static Equilibrium Formula

The Formula of Static Equilibrium can be represented as ∑ F_k = 0 and ∑ ͳ_k = 0, which simply means the total force and torque acting on an object is zero.

Difference Between Static and Dynamic Equilibrium

The basic difference between Static and Dynamic Equilibrium is given below:

Static Equilibrium vs Dynamic Equilibrium
Static Equilibrium	Dynamic Equilibrium
It is irreversible in nature.	It is reversible in nature.
The forward and backward reaction rates are zero.	The forward and the backward reaction rates are equal.
It can occur in both open and closed systems.	It can only occur in closed systems.
This implies that no chemical reaction going in the system.	This equilibrium implies that the reactants and the products are still participating in chemical reactions.
Static Equilibrium is mainly applied for mechanical concept rather than a chemical concept	Dynamic Equilibrium is more often applied with a chemical concept.
Examples: Conversion of diamond to graphite Book on a Table Balanced Seesaw, etc.	Example:  NO2(g) + CO(g) ⇌  NO(g) + CO2(g) The above reaction is in dynamic equilibrium.

Importance of Static Equilibrium

Static equilibrium is a fundamental concept in physics and engineering, and has various applications in real-world scenarios and some of the applications are:

• Statics Equilibrium in Physics: Static equilibrium is an important concept in physics while analyzing forces and torques. Problems related tp objects at rest often require the application of static equilibrium principles.

• Aviation: Aircraft design involves the use of static equilibrium to ensure the stability of the aircraft during flight and when parked on the ground.

• Construction and Civil Engineering: For the of Construction of a tall building or a tower, it is crucial to consider static equilibrium to prevent collapse. This involves the analyzing of the forces acting on each part of the structure and ensuring that they balance out.

• Mechanical Engineering: Static Equilibrium plays an important role in designing of machines and mechanical components. For example, when designing a lever or a pulley system, engineers must ensure that the forces and torques are balanced for the system to function properly.

• Electrical Engineering (Transmission Towers): The static equilibrium of transmission towers is considered in their design to ensure stability under the forces of wind and the weight of power lines.

The above examples highlight the broad range of applications for static equilibrium across various engineering and scientific disciplines, emphasizing its importance in ensuring stability and safety in diverse systems and structures.

Read More,

• Equilibrium of Bodies
• Lami’s Theorem
• Pascal’s Law

Static Equilibrium: Frequently Asked Questions

Define Static Equilibrium.

Static equilibrium refers to a state where an object is at rest and experiences no net force or net torque. In other words, the sum of all forces acting on the object is zero, and the sum of all torques (rotational forces) is also zero.

What 2 Conditions defines Static Equilibrium?

Static equilibrium requires two conditions: no net force (sum of all forces is zero) and no net torque (sum of all torques is zero).

What is the Difference between Static and Dynamic Equilibirium in Chemistry?

• Static Equilibrium: No observable change, reactants and products remain constant over time.
• Dynamic Equilibrium: Reactants and products change, but at equal rates, maintaining constant concentrations.

What are the Laws for Static Equilibrium?

Two Laws has to be satisfied for any object to be in Static Equilibrium.

• The vector sum of all external forces acting on the object must be zero.
• The sum of all torques (rotational forces) acting on the object must be zero.

How is Static Equilibrium different from Dynamic Equilibrium?

Static equilibrium deals with objects at rest, while dynamic equilibrium involves objects moving at a constant velocity with zero acceleration. In static equilibrium, the net force and net torque are zero, whereas in dynamic equilibrium, the net force is still zero, but there may be a constant non-zero velocity.

What is Formula of Static Equilibrium?

The Formula of Static Equilibrium can be represented as ∑ F_k = 0 and ∑ ͳ_k = 0. i.e. net force and net torque of the system must be zero.

What is Mechanical Equilibrium?

Mechanical equilibrium is a state where all forces and torques acting on a system are balanced, resulting in no motion or constant velocity.