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# What is equilibrium?

“A body is said to be in equilibrium if no net force acts on it.”Newton’s first law of motion tells us that a body continues its state of rest or of uniform motion in a straight line if no resultant or net force acts on it.For example,a book lying on a table or a picture hanging on a wall,are at rest.The weight of the book acting downward is balanced by the upward reaction of the table.

In case of objects moving with uniform velocity,the resultant force acting on a leveled road and an aeroplane flying in the air with uniform velocity are the examples of bodies in equilibrium.

## Conditions for equilibrium:

In the above examples,we see that a body at rest or in uniform motion is in equilibrium if the resultant force  acting on it is zero.For a body in equilibrium,it must satisfy certain conditions.There are two conditions for a body to be in equilibrium.

### First condition of equilibrium:

A body is said to satisfy first condition for equilibrium if the resultant of all the forces acting on it is zero.Let n number of forces  F1,F2,F3,……,Fn  are acting on a body such that:

F1 +F2+F3+……+Fn =0

or ∑ F =0 ……(1)

The symbol ∑ is a Greek letter called sigma used for summation.Equation (1) is called the first condition of equilibrium.

The first condition for equilibrium can also be stated in terms of X and Y components of the forces acting  on the body as:

F1x +F2x+F3x+……+Fnx =0

And

F1y+F2y+F3y+……+Fny=0

or

∑ Fx =0

∑ Fy=0

A book lying on a table or a picture hanging on a wall,are at rest and thus satisfy first condition for equilibrium.A paratrooper coming down with terminal velocity also satisfies first condition for equilibrium and is thus in equilibrium.

### Second condition of equilibrium:

If the body is not in equilibrium although the first condition for equilibrium is still satisfied.It is because the body has the tendency to rotate.This situation demands another condition in addition to the first condition for equilibrium.According to this ,a body satisfies second condition for equilibrium when the resultant torque acting on it is zero.Mathematically:

∑ τ =0

## States of equilibrium:

There are three states of equilibrium.

• Stable equilibrium
• Unstable equilibrium
• Neutral equilibrium

### Stable equilibrium:

“A body is said to be in stable equilibrium if after a slight tilt it returns to its previous position.”

Consider a book lying on the table.Tilt the book slightly about its one edge by lifting it from the opposite side.It returns to its previous position when sets free.Such a state of the body is called stable equilibrium.

When a body is in stable equilibrium,its centre of gravity is at the lowest position.When it is tilted ,its centre of gravity rises.It returns to its stable equilibrium as long as the centre of gravity acts through the base of the body.

### Why base of vehicle is kept low,wide,and heavy?

A vehicle is made heavy at its bottom to keep its centre of gravity as low as possible.A lower centre of gravity keeps it stable.Moreover,the base of a vehicle is made wide so that the vertical line passing through its centre of gravity should not get out of its base during a turn.

### Unstable equilibrium:

“If a body does not returns to its previous position when sets free after a slightest tilt is said to be in unstable equilibrium.”

Take a pencil and try to keep it in the vertical position on its tip.Whenever you leave it,the pencil topples over about its tip and falls down.This is called the unstable equilibrium.In unstable equilibrium,a body may be made to stay only for a moment.Thus a body is unstable equilibrium.

The centre of gravity of the body is at its highest position in the state of unstable equilibrium.As the body topples over about its base (tip),its centre of gravity moves towards its lower position and does not return to its previous position.

### Neutral equilibrium:

“If a body remains in its new position when disturbed from its previous position,it is said to be in a state of neutral equilibrium.”

Take a ball and place it on a horizontal surface.Roll the ball over the surface and leave it after displacing from its previous position.It remains in its new position and does not return to  its previous position.This is called neutral equilibrium.

In neutral equilibrium,all the new states in which a body is moved,are the stable states and the body,remains in its new state.In neutral equilibrium,height,irrespective to its new position.There are various objects which have neutral equilibrium such as a ball,a sphere,a roller,a pencil lying horizontally,an egg lying horizontally on a flat surface etc.

## Examples of equilibrium:

In applying the conditions for equilibrium (zero resultant force and zero resultant torque about any point),we can clarify and simplify the procedure as follows:

First,we draw an imaginary boundary around the system under consideration.This helps us to see clearly just what body or system of bodies to which we are applying the laws of equilibrium.This process is called isolating the system.

Second,we draw vectors representing the magnitude,direction,and point of application of all external forces.An external force is one that acts from outside the boundary that was drawn earlier.Examples of external forces often encountered are gravitational forces and forces exerted by strings,wires,rods,and beams that cross the boundary.Note that only external forces acting on the system need be considered;all internal forces cancel one another in pairs.

There are some cases in which the direction of a force may not be obvious.To determine the direction of a certain force,make an imaginary cut through the member exerting the force at the point where it crosses the boundary.If the ends of this cut tend to pull apart,the force acts outward.If you are in doubt,choose the direction arbitrarily.A negative value for a force in the solution means that the forces acts in the direction opposite to that assumed.

Third,we choose a convenient coordinate system along whose axes we resolve the external forces before applying the first condition of equilibrium.The goal here is to simplify the calculations.The preferable coordinate system is usually one that minimizes the number of forces that must be resolved into components.

Fourth,we choose a convenient coordinate system along whose axes we resolve the external torques before applying the second condition of equilibrium.The goal again is to simplify calculations,and and we may use different coordinate systems in applying the two conditions for static equilibrium if this proves to be convenient.Foe example,calculating torques about a point through which  several forces act eliminates those forces from the torque equation.

The torque components resulting from all external forces must be zero about any axis for equilibrium. Internal torques will cancel in pairs and need not be considered.