Chapter: Introduction to Forces Acting on Particle and Rigid Body ll Applied Mechanics ll Class 11 ll Part 2 of 3

Characteristics of a force:

To determine the effects of a force, acting on a body, we must know the following characteristics of a force:

1. The magnitude of the force (i.e., 100 N, 50 N, 20 kN, 5 kN, etc.)
2. The direction of the line, along which the force acts (i.e., along OX, OY, at 30° North of East etc.). It is also known as the line of action of the force.
3. Nature of the force (i.e., whether the force is a push or pull). This is denoted by placing an arrowhead on the line of action of the force.
4. The point at which (or through which) the force acts on the body.

Force System:

When several forces of different magnitudes and direction act upon a body, they constitute a system of forces. The main types of force systems are as follows:

1) Coplanar Force System:

Lines of action of all the
forces lie in the same plane in this system as shown
in Fig. (A).

2) Collinear Force System:

Lines of action of all the
forces lie in the same straight line in this system as
shown in Fig. (B).

3) Concurrent Force System:

Lines of action of all the
forces meet at a point in this system. The concurrent
forces may not be collinear or coplanar as shown in
Fig. C

4) Parallel Force System:

Lines of action of all the
forces are in parallel as shown in Fig. D

5) Non-Coplanar Force System:

Lines of action of all
the forces do not lie in the same plane as shown in
Fig. (E)

6) Non- Concurrent Force System:

Lines of action of
all the forces do not meet at a point in this system as
shown in Fig. (E & F).

7) Non-Parallel Force System:

The lines of action of all
the forces are not in parallel as shown in Fig. (H)

8) Coplanar Concurrent Force System:

Lines of action of all the forces lie in
the same plane and meet at a point shown in Fig. (G)

9) Coplanar Non-Concurrent Force System:

Lines of action of all the forces lie
in the same plane but do not meet at a point as shown in Fig. (A) above.
They may be in parallel.

10) Coplanar parallel Force System:

Lines of action of all the forces are in
parallel in the same plane shown in Fig. (D)

11) Coplanar, non-concurrent, non-parallel Force System:

The lines of action
of all the forces are not in parallel, they do not meet at a point but they are in
the same plane as shown in Fig. (A)

12) Non- Coplanar, non-concurrent Force System:

The lines of action of all the
forces do not lie in the same plane and do not meet at a point as shown in Fig.
(E).

Fundamental Laws of Mechanics

1. Newton’s First Law
2. Newton’s Second Law
3. Newton’s Third Law
4. Newton’s Law of gravitation
5. Law of transmissibility of Force
6. Parallelogram law of Forces

1. Newton’s First Law:

It states that every body continues in its state of rest or of
uniform motion in a straight line unless it is compelled by an external agency acting on
it.

Newton’s First Law for rotation:

Newton’s laws of motion of rotation state
that, “Every body continues in its state of rest or of uniform motion of rotation
about an axis unless it is acted upon by some external torque”

2) Newton’s Second Law:

It states that the rate of change of momentum of a body is
directly proportional to the impressed force and it takes place in the direction of the
force acting on it.
Force α rate of change of momentum But, Momentum = Mass x velocity 

As mass does not change, 

Force α Mass x rate of change velocity 

Force α Mass x acceleration 

F α ma

F = ma

3) Newton’s Third Law: rolling papers

It states that for every action there is an equal and opposite
reaction

4) Newton’s Law of gravitation:

Everybody attracts the other body. The force of
attraction between any two bodies is directly proportional to their masses and inversely
proportional to the square of the distance between them. 

F= G 𝑚1 𝑚2/ 𝑑 2

Where G is the constant of proportionality, it is known as the constant of gravitation.
Experimentally, it is proved that the value of G = 6.673 x 10-11 Nm2 /kg2.

5) Law of transmissibility of Force:

Statement: “The point of application of force may be
transmitted along its line of action without changing its effect on the rigid body to which
the force is applied”.
Explanation: A force is acting at point A along line of action AB on a rigid body as shown in
Fig. (a). Two equal and opposite forces of magnitude ‘P’ are added at point ‘B’ along the line of
action AB according to the law of superposition as shown in Fig (b).

Two equal and opposite forces of the magnitude ‘P’ at points A and B can be
subtracted without changing the action of the original force P according to the law of
superposition as shown in Fig (c).

Thus the point of application of force P is transmitted along its line of action from A to
B

6) Varignon’s Theorem of Moments/Principle of Moments:

Statement: “The algebraic sum of the moments of all the forces about any point is equal to
the moment of their resultant about the same point”.
i.e. ∑M = ∑ (Moments of forces) = Moment of R

Proof:

In the above Figure, AB and AC represent forces P and Q resp. and ‘O’ is the point about which the moment is taken. ABCD represents a parallelogram. A diagonal AD represents the resultant of
forces P and Q. Now extend CD up to the point ‘O’ which is the line of CD. Join OA and OB.

Now, we know that

Moment of force = 2(Area of the triangle)

Moment of force P = 2 x Area of Triangle AOB

Moment of force Q = 2 x Area of Triangle AOC

The algebraic sum of Moments of forces P and Q = ∑ M = 2 x (Area of ∆ADB + Area of ∆AOC) 

Now,

Area of ∆ AOB = Area of ∆ADB = Area of ∆ACD

Since AB = CD (base is same) and height is same

∑ M = 2 x (Area of ∆ ACD + Area of ∆ AOD) = 2 x (Area of ∆ AOD)

∑ M = Moment of Resultant Force ‘R’.

Application of Varignon’s Theorem of Moments / Principle of Moments:

1) It is generally used to locate the point of application of the resultant.

2) In the case of a coplanar non-concurrent system of forces, this concept is
used to locate the line of action of the resultant.

TO BE CONTINUED.....

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