JJ205 ENGINEERING MECHANICS

```JJ205
ENGINEERING MECHANICS
COURSE LEARNING OUTCOMES :
Upon completion of this course, students should be able to:
CLO 1. apply the principles of statics and dynamics to solve engineering
problems (C3)
CLO 2. sketch related diagram to be used in problem solving (C3)
CLO 3. study the theory of engineering mechanics to solve related
engineering problems in group (A3)
BASIC CONCEPTS ON STATICS

CLO 1. apply the principles of statics and
dynamics to solve engineering problems (C3)

CLO 3. study the theory of engineering
mechanics to solve related engineering
problems in group (A3)
INTODUCTION (CLO 1)

MECHANICS - Body of Knowledge which
Deals with the Study and Prediction of the
State of Rest or Motion of Particles and Bodies
under the action of Forces.

STATICS - Statics Deals With the Equilibrium
of Bodies, That Is Those That Are Either at
Rest or Move With a Constant Velocity.

DYNAMICS - Dynamics Is Concerned With
the Accelerated Motion of Bodies
BASIC CONCEPTS BUT VITAL TO THE
STATICS (CLO 1)
SPACE
 The geometric region in which study of body is involved is called
space. At point in the space may be referred with respect to a
predetermined point by a set of linear and angular
measurements. The reference point is called the origin and set of
measurements as ‘coordinates’.
 If coordinates involve only in mutually perpendicular directions
they are known as Cartesian coordinates. If the coordinates
involve angle and distances, it is termed as polar coordinate
system.

FORCE – Force is considered as a ‘push’ or ‘pull’ exerted by
one body on another. This interaction can occur when there is
direct contact between the bodies, such as a person pushing on
a wall, or it can occur through a distance when the bodies are
physically separated.
MASS


The quantity of the matter possessed by a body is called
mass. The mass of a body will not change unless the
body is damaged and part of it is physically separated.
When a body is taken out in a space craft, the mass will
not change but its weight may change due to change in
gravitational force. Even the body may become
weightless when gravitational force vanishes but the
mass remain the same.
Continue…

TIME – Time is conceived as a succession of
events. Although the principles of statics are
time independent, this quantity does play an
important role in the study of dynamics.

LENGTH – Length is needed to locate the
position of a point in space and thereby
describe the size of a physical system. Once a
standard unit of length is defined, one can then
quantitatively define distances and geometric
properties of a body as multiples of the unit
length.
BASIC CONCEPTS BUT VITAL TO THE
STATICS (CLO 1)

PARTICLES – A particle has a mass, but a size that can be
neglected. For example, the size of the earth is insignificant
compared to the size of its orbits, and therefore the earth
can be modeled as a particle when studying its orbital
motion. When a body is idealized as a particle, the principles
of mechanics reduces to a rather simplified form since the
geometry of the body will not be involved in the analysis of
the problem

RIGID BODY – A rigid body can be considered as a
combination of a large number of particles in which all the
particles remain at a fixed distance from one another both
before and after applying a load.

Concentrated force –
assumed to act at a point on a body.
◦ We can represent a load by a concentrated
force, provided the area over which the load
is applied is very small compared to the
overall size of the body.
◦ Example: contact force between a wheel and
the ground.
SCALARS AND VECTORS (CLO 1)
SCALARS – A quantity characterized by a
positive or negative number is called
scalar. For example; mass, volume and
length.
 VECTOR – A vector is quantity that has
both a magnitude and the direction. For
example; weight, force and moment.

VECTORS (CLO 1)

FREE VECTORS – One whose action is not
confined to or associated with a unique line
in space. For example, if a body moves
without rotation, then the movement or
displacement of any point in the body maybe
taken as a vector, and this vector will be
describe equally well the direction and
magnitude of the displacement of every
point in the body. Hence , we may represent
the displacement of such a body by a free
vector.
VECTORS

SLIDING VECTORS – Is one for which a
unique line in space must be maintained
along which the quantity acts. When we
deal with the external action of a force on
a rigid body, the force may be applied at
any point along its line of action without
changing its effect on the body as a whole
and hence may be considered a sliding
vector.
VECTORS

FIXED VECTORS – is one for which a
unique point of application is specified, and
therefore the vector occupies a particular
position in space. The action of a force on a
deformable or non rigid body must be
specified by a fixed vector at the point of
application of the force. In this problem the
forces and deformations internal to the body
will be dependent on the point of application
of the force, as well as its magnitude and line
of action.
NEWTON’S LAWS OF MOTION
(CLO 1)

FIRST LAW – A particle originally at rest, or moving in a
straight line with constant velocity, will remain in this state
provided the particle is not subjected to an unbalanced
force.

SECOND LAW – A particle acted upon by an unbalanced
force ‘F’ experiences an acceleration ‘a’ that has the same
direction as the force and a magnitude that is directly
proportional to the force. If ‘F’ is applied to a particle of mass
‘m’, this law maybe expressed mathematically as ; F = ma.

THIRD LAW – The mutual forces of action and reaction
between two particles are equal, opposite, and collinear.
SI SYSTEM AND UNIT (CLO 3)

Mechanics deals with four fundamental
quantities; length, mass, force, and time.
SI UNITS
QUANTITY
DIMENSIONAL
SYMBOL
UNIT
SYMBOL
MASS
M
Kilogram
kg
LENGTH
L
Meter
m
TIME
T
second
s
FORCE
F
newton
N
* The unit of force, called a newton (N), is derived from F=ma.
1 newton is equal to a force required to give 1 kg of mass an acceleration of 1 m/s2.
(N = kg. m/s2)
PREFIXES (CLO 3)

When a numerical quantity is either very
large or very small, the units used to
define its size maybe modified by using
prefix. For example;
Exponential form
prefix
SI symbol
1 000000000
109
giga
G
1000
103
kilo
k
0.001
10-3
mili
m
0.000001
10-6
micro
µ
0.000000001
10-9
nano
n
Example (CLO 3) :

Evaluate each of the following and express
with SI units having an appropriate prefix:
a) (50 mN)(6 GN)
b) (400 mm)(0.6 MN)2
c) 45 MN3/900 Gg
Continue…

First, convert each number to base units, perform
the indicated operations, then, choose an
appropriate prefix.
a)
Note carefully the convention kN2 = (kN)2 = 106 N2
Continue…
b)
We can also write:
Continue…
Exercises:
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