DEFINITION
AND
CLASSIFICATION
OF FORCES
As defined before, force is the
action of one body on another. It is
a vector quantity since its effect
depends on the direction as well as
on the magnitude of the action.
The effect of the force applied

to the bracket depends on P ,
the angle q and the location of

the point of application of P .

P
q
Changing any one of these three specifications
will alter the effect on the bracket such as
the internal force generated in the wall or
deformation of the bracket material at any
point. Thus, the complete specification of the
action of a force must include its magnitude,
direction and point of application.

P
q
We can separate the action
of a force on a body into two
effects as external and
internal.

P
q

For the bracket, the effects of P
external to the bracket are the reactive
forces (not shown) exerted on the
bracket by the wall. Forces external to a
body can be either applied or reactive
forces.

P
q

The effect of P internal to the
bracket is the resulting internal
forces and deformations
distributed throughout the
material of the bracket.

P
q
Forces are classified as either
contact or body forces.
A contact force is produced by direct
physical contact; an example is the
force exerted on a body by a
supporting surface.
A body force is generated when a
body is located within a force field
such as a gravitational, electric or
magnetic field. An example of a
body force is your weight.
Forces may be further classified as
concentrated or distributed.
Every contact force is actually applied
over a finite area and is therefore a
distributed force. However, when the
dimensions of the area are very small
compared with the other dimensions of
the body, the force may be considered
concentrated at a point.
Force can be distributed over an
area, as in the case of mechanical
contact, over a volume when a
body force such as weight is
acting or over a line, as in the case
of the weight of a suspended
cable.
Concentrated Force
concrete
Distributed Force
The weight of a body is the force
of gravitational attraction
distributed over its volume and
may be taken as a concentrated
force acting through the center
of gravity.
Action and Reaction
According to Newton’s third law,
the action of a force is always
accompanied by an equal and
opposite reaction. It is essential to
distinguish between the action and
the reaction in a pair of forces.
To do so, we first isolate the body in
question and then identify the force
exerted on that body (not the force
exerted by the body).
It is very easy to mistakenly use the
wrong force of the pair unless we
distinguish carefully between action and
reaction.
CLASSIFICATION OF
FORCES ACCORDING TO
THEIR WAYS OF
APPLICATION:
Concurrent forces
Coplanar forces
Parallel forces
Collinear forces
A
B
SOME COMMON TYPES
OF FORCES
CONTACT AND FRICTION
FORCE
Let’s consider two bodies which are in contact. The
 
force acting on body 1 from body 2 is F. F can be
divided into two components as a normal force N ,
drawn perpendicular to the tangent line at the

point of contact and force F f , drawn parallel to
the tangent line.
tangent

N is named as the normal component of the contact

force and F f is named as the friction component of
the contact force. If the contacting surfaces are


smooth, then F f can be neglected ( F f = 0); but if the
contacting surfaces are rough it has to be taken into
consideration.
tangent


The relationship between N and F f is given by
Ff = mN
where m is a dimensionless coefficient of
friction varying between 0 and 1.
tangent
tangent
tangent
FORCES IN STRINGS,
CABLES, WIRES,
ROPES, CHAINS AND
BELTS
Forces in strings, cables, etc. are always taken
along the string, cable, etc. and their direction
always points away from the body in
consideration. They exert force only when they are
tight. When loose they exert no force. Hence, they
always work in tension. Usually their weights are
neglected compared to the forces they carry or
support.

T
FORCES IN
PULLEY – BELT SYSTEMS
Pulleys are wheels with grooves that are used to
change the directions of belts or ropes and
generate a higher output load with a much smaller
input force.
T1 = T2
Unless stated otherwise, or apparent from the problem,
the tension forces at both sides of a belt are taken as
equal. They are equal as long as the belt does not slide
on the pulley, and the pulley rotates freely with a
constant velocity.
T1 = T2
FORCES IN
SPRINGS
Spring force is always directed along the spring and
is in the direction as if to return the spring into its
undeformed length.
Fspring=kx (Spring force)
(k: spring constant, x: deformation of the spring)
Fspring
THREE DIMENSIONAL
DESCRIPTION OF
FORCE
* When the direction angles of a force is given;
The angles, the line of action of a force makes with the x, y and z
axes are named as direction angles. The cosines of these angles
are called direction cosines; they specify the line of action of a
vector with respect to coordinate axes.
In this case, direction angles are qx, qy and qz.
Direction cosines are cos qx, cos qy and cos qz.
cos qx = l
cos qy = m
cos qz = n
* When coordinates of two points along the line of action of a
force is given;
* When two angles describing the line of action of a
force is given;
z
Fz
F
Fy
f
Fx
x
y
q
Fxy