Equilibrium class 9 | conditions of equilibrium class 9 | 9th class physics | atifahmedofficial

Equilibrium class 9 | conditions of equilibrium class 9 | 9th class physics | atifahmedofficial

4.8 EQUILIBRIUM
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. Consider a log of
wood of weight w supported by ropes as shown in
figure 4.26. Here the weight w is balanced by the forces F1
and F pulling the log upward. In case of objects moving with 2
uniform velocity, the resultant force acting on them is zero. A
car moving with uniform velocity on a levelled road and an
aeroplane flying in the air with uniform velocity are the
examples of bodies in equilibrium.
A body is said to be in equilibrium if no net
force acts on it.
A body in equilibrium thus remains at rest or
moves with uniform velocity.
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 FOR 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 F , F , F ,
1 2 3
...........,F
n are
acting on a body such that
The symbol is a Greek letter called sigma used for
summation. Equation 4.9 is called the first condition for
The first condition for equilibrium can also be
stated in terms of x and y-components of the forces
acting on the body as:
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
(constant velocity) also satisfies first condition for
equilibrium and is thus in equilibrium.
EXAMPLE 4.5
A block of weight 10 N is hanging through a cord
as shown in figure 4.29. Find the tension in the cord.
SOLUTION
Weight of the block w = 10 N
Tension in the cord T = ?
Applying first condition for equilibrium
There is no force acting along x-axis.
Thus, the tension in the cord is 10 N.
SECOND CONDITION FOR EQUILIBRIUM
First condition for equilibrium does not ensure
that a body is in equilibrium. This is clear from the
following example. Consider a body pulled by the
forces F1 and F2 as shown in figure 4.30(a). The two
forces are equal but opposite to each other. Both are
acting along the same line, hence their resultant will be
zero. According to the first condition, the bod
equilibrium. Now shift the location of the forces as shown
in figure 4.30(b). In this situation, 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 for
equilibrium in addition to the first condition for
equilibrium. This is called second condition for
equilibrium. According to this, a body satisfies second
condition for equilibrium when the resultant torque acting
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