A particle is on equilibrium state when the forces acting on it are balanced, means that there is no net force or change in motion. A particle needs all forces acting on it to be added up to zero for equilibrium.Equilibrium can be two type:
Static Equilibrium:- When all the forces acting on a particle are balanced and the particle is at rest, this state is known as static equilibrium. Not a single thing is moving in any direction.
Dynamic Equilibrium:- It is used to describe a particle that is moving at a constant speed, when the forces acting on it are balanced.
Conditions for Equilibrium:-
Two main conditions must be satisfied:
1.Translational Equilibrium: In this, makes sure that particle isn’t moving faster in any direction. Newton’s First Law of Motion states that the vector total of all the forces acting on an object must be zero to remain in its state of rest or uniform motion. This can be expressed mathematically as follow: F = 0
This means the forces acting along the x, y, and z directions should individually sum total of zero: Fx = 0, Fy = 0, Fz = 0
These equations ensure that the particle is not accelerating along any of the axes
2. Rotational Equilibrium: All torques, acting on a particle should add up to zero if the particle or object has the ability to rotate. We shall be confident that the object won’t rotate at the same angle. In terms of mathematics:
τ=0
Where τ represents torque. Torque is the rotational equivalent of force, and its magnitude depends on the force applied and distance from the pivot point.
Free-Body Diagram (FBD)
In a case, a particle is hung by two strings, for example, the FBD must display the tension in each string, the particle’s weight as a result of gravity, and any additional forces (such as a reaction force). When every force has been taken into consideration, the equilibrium requirements can be used.
Types of Equilibrium
1.Stable Equilibrium: A particle is hung by two strings, for example, Free-Body Diagram (FBD) must display the tension in each string, particle’s weight as a result of gravity, and any additional forces (such as a reaction force). When every force has been taken into consideration, the equilibrium requirements can be used.
2. Unstable Equilibrium: Particle will deviate from its equilibrium position at the slightest interference. Potential energy is at its highest point. Consider a ball balanced on the edge of an upside-down bowl. The ball will roll off the bowl and not come back to its initial place if there is even a slight disruption.
3. Neutral Equilibrium: When a particle is disturbed and without trying to travel farther or return to its original place, it is said to be in neutral equilibrium.
Real-Life Examples
Hanging Bridge: A hanging bridge’s cables are in balance because the weight of the bridge and the tension in the cables are equal.
Book on a Table: A book on a table is in static equilibrium when the upward normal force applied by the table balances the downward gravity pull.
Walking: Every pace a person takes when walking generates a dynamic equilibrium where factors like gravity, friction, and the force from their legs balance each other out as the body advances.
Lami’s Theorem:- If three concurrent forces (forces acting at same point) P, Q, and R are acting on a particle, to keep the particle in equilibrium, then Lami’s theorem states:-
P / Sin alpha = Q / Sin bita = R / Sin gama
Alpha is angle opposite to force P
Bita is angle opposite to force Q
Gama is angle opposite to force R
Importance of Equilibrium in Physics
Equilibrium is essential to understand how rigid bodies and particles behave. Engineers and physicists may construct stable structures and understand forces in complex systems by using it to tackle statics and dynamics challenges. Equilibrium concepts are used in mechanics to analyse forces acting on cars, bridges, and other structures.
Note:
A particle’s equilibrium is primary to physics since it clarifies how forces combine to produce stability or continuous motion. A particle can either stay at rest or move at a constant speed if necessities the both translational and rotational equilibrium are met. It is essential to understand this idea in order to solve mechanics problems and to apply it to engineering, architecture, and daily life.
When all of the forces working on a particle are balanced and there is no net force, the particle is said to be in equilibrium. It is guarantees that the particle either stays at rest or travels at a steady speed.
The two types of equilibrium are:
Static Equilibrium: The particle is at rest, with no motion.
Dynamic Equilibrium: The particle is in motion with constant velocity, with balanced forces.
Vector sum of all forces acting on the particle must be zero for translational equilibrium to occur. This can be expressed as follows:
F = 0
It ensures that particle is not accelerating.
For rotational equilibrium, the sum of all torques (moments of forces) acting on the particle must be zero:
Τ = 0
It ensures that the particle is not rotating or rotates at a constant angular velocity.
A Free-Body Diagram (FBD) is a diagram that shows every force that is applied to a particle. It is essential for examining a particle’s equilibrium because its make possible the application and visualisation of equilibrium conditions, which eases problem-solving.
A particle is said to be in stable equilibrium when it tends to return to its initial position following a small perturbation. When the system reaches its minimum potential energy, this usually occurs.
It is possible for a particle in motion to be in dynamic equilibrium if it is traveling at a constant speed and there are no net forces acting on it.
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