Chapter 06
Equilibrium
SQ3R:
 Define Equilibrium , static , static equilibrium, dynamic equilibrium, parallel forces, like
parallel force, unlike parallel forces, Axis of rotation, Torque, Centre of gravity, couple ,
Momentum arm.
 What do you understand by two like and unlike parallel forces?
 What is couple? Calculate the momentum of the couple .
 Define equilibrium. How many types of equilibrium? Give one example of each.
 Explain the two conditions of equilibrium and relate the formula.
 Explain three states of equilibrium.
 Define center of gravity. How would you locate the center of gravity of an irregular piece of
a metal?
 Prove that moment of the couple is equal to the product of one of the forces and Arm of the
couple.
 Define torque. Write down its unit and formula.
 A body of 20 kg is moving with a speed of 15m/s. Find it Momentum?
 Find the tension in each cord if the weight of the suspended body is 980N.
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BASIC TERMINOLOGIES:
Parallel force
Parallel Forces that act in the same or opposite directions at different points on an object. The
moment arm or lever arm is the perpendicular distance between the line of action of the force and
the center of moments. .
Like parallel force:
If two parallel force are acting in same direction they are known as like parallel force.
Resultant of two like parallel forces :
Consider two like parallel force F1 and F2 acting on a body at A and B, as shown in figure. Suppose
R is the resultant force of F1 and F2 , then
R= F1+ F2
It’s mean that the resultant of two like parallel forces is a force whose magnitude is equal to the sum
of the magnitudes of the two force and the direction is the same as either of the forces.
Unlike parallel force:
If two parallel forces are acting in opposite directions they are known as unlike parallel forces.
Resultant of two unlike parallel forces:
Consider two unlike parallel forces F1 and F2 acting on a body at A and B, as shown. Suppose R is the
resultant force of F1 and F2. Here F1 is greater than F2.
Thus
R= F1 – F2
It means that the resultant of two unlike parallel forces is also a force whose magnitude is equal to
the difference of the magnitudes of the two forces and the direction is the same as that of the
greater force .
Axis of rotation
The straight line through all fixed points of a rotating rigid body around which all other points of the
body move in circles.
Torque
Torque is the measure of the force that can cause an object to rotate about an axis.
Moment arm
The moment arm or lever arm is the perpendicular distance between the line of action of the force
and the center of moments.
Couple
Couple, in mechanics, pair of equal and unlike parallel forces having different lines of action. The
only effect of a couple is to produce or prevent the turning of a body.
Explanation
Consider two equal , unlike parallel forces, each of magnitude F, acting at A and B.
Fig 6.9
The torque or moments of two forces given by
The moment of the forces F at A = F × OA
The moment of the forces F at B = F × OB
Both these moments have the same direction i.e counter clockwise, so the total momentum of the
two forces is equal to the sum of the two moments.
Moment of the couple = F× OA + F × OB
= F( OA + OB)
= F × AB
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Moment of the couple is equal to the product of one of the forces and the perpendicular distance
between the lines of action of two forces . This perpendicular distance between the two forces is
called the arm of the couple.
Centre of gravity
Centre of gravity, in physics, an imaginary point in a body of matter where, for convenience in
certain calculations, the total weight of the body may be thought to be concentrated.
Position of centre of gravity
From book pg 89
Centre of gravity of an irregular shaped body:
We can find the centre of gravity of an irregular shaped bodies. By simple method .this method is as
under:
Drill three small holes near the edge of the plate whose center of gravity is to be located. Suspend
the plate from a nail fired horizontally in a wall using one of the wholes, say A. when the plate is at
rest , suspend a plumb line from the nail . Draw a line Aa on the plate along the plumb line. The
center of gravity lies somewhere on the line Aa.
Repeat the above procedure with hall B on the nail. Again the centre of gravity must lie some
where on the line Bb. The only point common to the lines Aa and Bb is G , therefore this point must
be the centre of gravity if the plate is suspended using third hole C, the line Cc will also pass through
the point G.
Add figure Pg no 90
Equilibrium
Equilibrium is defined as a state of balance or a stable situation where opposing forces cancel each
other out and where no changes are occurring.
OR
A body is said to be in equilibrium if the net process acting on it is zero
Static equilibrium
Static equilibrium is a state when body is at rest .
Example
Consider a spherical ball of weight 5 N suspended from the string the ball is in static equilibrium.
There are the two forces acting on the ball Its weight vertically downward. Tension in the string
vertically upward. So the net force acting on the body is said to be in equilibrium.
Dynamic equilibrium
Dynamic equilibrium states that when body is moving at a constant velocity.
Example
When a paratrooper jumps from an aero plane, it moves down with an acceleration due to gravity.
The force of gravity on the paratrooper acts downward. Thereafter, The parachute opens and an
upward force due to reaction of air on parachute acts on it. Now the force of gravity acting vertically
downward is balanced by the air reaction acting vertically upward, the paratrooper falls down with
uniform velocity. We see that for a body to remain in dynamic equilibrium the upward force must be
balanced by the down ward force.
Conditions of Equilibrium:
For a body to remain of n Equilibrium, it must satisfy two conditions, known as
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First condition of Equilibrium:
The first condition of equilibrium states that if a body is in equilibrium, then the vector sum of all the
forces acting on the body must be equal to zero.
From book pg 94
Thus the (sigma ) represents the summation of all the forces F1, F2, F3, .....( Arrow on F1,f2,F3)
acting on the body. It follows from the above statement that the linear acceleration of a body in
equilibrium is zero. In two dimensions the first condition of equilibrium let’s two the following
Book pag 94
If a body is in equilibrium, then the summation of the x- components and the y- components all the
forces must be equal to zero.
Use of first condition of Equilibrium
In Physics the first condition of equilibrium is used to determine the magnitude and direction of an
unknown forces acting on a body if all the other forces are known .
Second condition of equilibrium
From book pg no 96
Use of second condition of equilibrium
Second condition of equilibrium is also used to calculate the unknown force acting on bodies in
equilibrium.
States of Equilibrium
There are three states of Equilibrium of a body. They are
1. Stable equilibrium
A body is said to be in stable equilibrium if it comes back to its original position when it is slightly
displaced.
For example
A cone standing on its base. The center of gravity of the cone is nearer the base. When this cone is
displaced its center of gravity is raised. A cone in stable equilibrium should have its center of gravity
as low as possible.
2.Unstable equilibrium
A body is said to be in unstable equilibrium if it does not come back to its original position when it is
slightly displaced.
Example
A cone balanced on its apex is in
Unstable equilibrium. When this come is disturbed it’s centre or gravity is lowered.
3.Neutral equilibrium
A body is said to be in neural equilibrium if on being slightly displaced it does not come back to its
original position but occupies a new position similar to its original position.
Example
A cone resting on its side is in neutral equilibrium. If the cone is pushed slightly its center of gravity is
neither rest nor lowered but Is remains at the same height.
Key points:
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Like parallel forces :
Like parallel forces which act in the same direction are called like parallel force.
Unlike parallel forces:
Parallel forces which act in opposite directions are called unlike parallel forces.
Torque:
The capability of a force to rotate a body about a point is called torque. It is vector quantity and its
magnitude equal to the product of force and momentum.
Centre of Gravity:
It is a point inside or outside the body at which the whole weight of the body is acting.
Couple:
Two equal but opposite parallel forces which act at point on the body make together a couple.
Equilibrium:
A body at rest or moving with uniform velocity is in a state of Equilibrium. The net force on such
body is zero and its acceleration is also zero.
Condition of Equilibrium
For a body to be in a state of equilibrium two conditions are to be fulfilled.
(i)
The resultant of all forces acting on the body should be zero.
(ii)
The resultant of all the torque acting on the body should be zero.
States of Equilibrium:
(i)
Stable equilibrium:
Such a state in which on disturbing a body slightly, then come back to its original position. The body
is said to be in stable equilibrium.
(ii)
Unstable equilibrium:
Such a state in which on disturbing the body slightly, the body does not come to its original position.
The body is said to be in unstable equilibrium
(iii)
Neutral equilibrium:
A state in which on disturbing the body slightly, the centre of gravity does not shift. The body is said
to be in the state of neutral equilibrium.
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