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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 magnitude P, the angle q and the location of the point of application of (point A). P
P
q
A
Changing any one of these three specifications will alter the effect of 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
P
A
We can separate the action of a force on a body into two effects as external andinternal.
P
q
A
For the bracket, the effects of external to the bracket are the reactive forces (N, V, M) exerted on the bracket by the wall. Forces external to a body can be either applied or reactive forces.
P
P
qN
VM
A
The effect of internal to the bracket is the resulting internal forces and deformations distributed throughout the material of the bracket.
P
P
q
A
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.
concrete
Concentrated Force
Distributed Force
W
w
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
1F 2F
3F
4F
1F
2F
3F
4F
APlane1F
2F
3F
Parallel forces
1F
2F
3F
4F
5F
1F
2F
3F
4F
5F
Collinear forces
A B
F
F
T T
T
T
C C
C
C
T: TensionC: Compression
SOME COMMON TYPES
OF FORCES
CONTACT AND FRICTION FORCES
Let’s consider two disks A and B which are in contact.
The force acting on disk B from disk A is . can be
divided into two components as a normal force ,
drawn perpendicular to the tangent line at the point
of contact and force , drawn parallel to the
tangent line.
F
fF
NF
tangent drawn at point of contact
F fF
N
direction of normal force passes through the center
is named as the normal component of the contact
force and is named as the friction component of
the contact force. If the contacting surfaces are
smooth, then can be neglected ( = 0); but if the
contacting surfaces are rough it has to be taken into
consideration.
fF
N
fF
fF
F
fF
N
The relationship between and is given by
Ff = mN
where m is a dimensionless coefficient of
friction varying between 0 and 1.
N
fF
F
fF
N
tangent
tangent
F
fF
N
If one of the contacting surfaces is flat then
the tangent will be parallel to the surface.
FORCES IN STRINGS, CABLES, WIRES,
ROPES, CHAINS AND BELTS
T
Forces in strings,
cables, etc. are always
taken along the string,
cable, etc. and their
direction always
points away from the
body in consideration.
1T
2T
3T
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.
1T
2T
3T
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
1T
2T
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
1T
2T
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
Fspring
Fspring
equilibrium
stretched
compressed
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.
z
y
x
F
xF yF
zF
yq
xq
zq
In this case, direction angles are qx, qy and qz.
Direction cosines arecos qx, cos qy and cos qz.
cos qx = l
cos qy = m
cos qz = n
1,1
coscoscos
coscoscos
coscoscos
cos,cos,cos
222
nmln
knjmilkjin
kjiFF
nFF
kFjFiFF
FFFFFF
kFjFiFF
zyx
zyx
zyx
zzyyxx
zyx
qqq
qqq
qqq
qqq
z
y
xi xF
yF
zF
yq
xq
zq
k
j
* When coordinates of two points along the line of action of a force is given;
ABr /
Fn
AAA zyxA ,,
BBB zyxB ,,
z
y
x
F
222
/
/
coscoscos
ABABAB
ABABAB
zyx
AB
ABF
zzyyxx
kzzjyyixxFF
kjiFF
r
rFnFF
qqq
* When two angles describing the line of action of a force is given;
sincossin
coscoscos
sin,cos
FFF
FFF
FFF
FFFF
xyy
xyx
zxy
zxy
x
y
z
q
F
zF
yF
xF
xyF
kjin
nFF
kjiFF
kFjFiFF
kFjFiFF
F
F
zyx
sinsincoscoscos
sinsincoscoscos
sinsincoscoscos