The document discusses engineering mechanics and introduces concepts of units, SI units, and resultants and components of forces. It provides an overview of the history and development of mechanics from classical Newtonian mechanics to modern theories. It also defines key concepts like base and derived units in the SI system and how to calculate the resultant force and decompose a force into components.

1. CENG- 131
Lecture 1: Units; introduction to SI units;
resultants and components

2. Introduction to Engineering Mechanics
• The state of rest and state of motion of the bodies under the
action of different forces has engaged the attention of
philosophers, mathematicians and scientists for many centuries.
The branch of physical science that deals with the state of rest
or the state of motion is termed as Mechanics.
• Starting from the analysis of rigid bodies under gravitational
force and applied forces the mechanics has grown to the
analysis of robotics, aircraft, spacecraft under dynamic forces,
atmospheric forces, temperature forces, etc

3. • Sir Issac Newton, the principal architect of mechanics, consolidated
the philosophy and experimental findings developed around the state
of rest and state of motion of the bodies and put forth them in the
form of three laws of motion as well as the law of gravitation. The
mechanics based on these laws is called Classical mechanics or
Newtonian mechanics.
• Albert Einstein proved that Newtonian mechanics fails to explain the
behavior of highspeed (speed of light) bodies. He put forth the theory
of Relativistic Mechanics.
• Schrödinger (1887–1961) and Broglie (1892–1965) showed that
Newtonian mechanics fails to explain the behavior of particles when
atomic distances are concerned. They put forth the theory of
Quantum Mechanics.
• Engineers are keen to use the laws of mechanics to actual field
problems. Application of laws of mechanics to field problems is
termed as Engineering Mechanics.

4. Units
• Units can be defined as the standard amount of a quantity for
measuring physical quantities. Since there are many types of
measurable
• Probably the earliest known forms of units of measurement are
dated back in the 4th Or 3rd millennium BC. These forms of units of
measurements were famous among the Mesopotamian civilisation,
Egyptian civilisation and Indus Valley civilisation. During these early
days the units were used for denoting shape, size of clothes,
bartering items and food , etc.
• The unit of measurements were made for any quantity of a thing with
physical properties to be measured.
• quantities there are many types of units too.

5. Base units and derived units.
• A base unit or a fundamental unit is the unit used for the
measurement of base quantities. Base quantities are those
quantities which can be conventionally chosen as a subset of
some physical quantities.
• Derived units can be defined as those units of measurement
which are formed due to the multiplication and division of the
base units without and fixed numerical factors.

6. Types of units of measurement list
• CGS system units. (The form of this is the centimetre-gram-
second system of units.)
• FPS system units. (The full form of this is the foot-pound-
second system of units)
• MKS system units. (The full form of this system is meter,
kilogram and second.)
• SI units.

7. Introduction to SI units
• SI unit is an international system of
measurements that are used universally in
technical and scientific research to avoid the
confusion with the units. Having a standard
unit system is important because it helps the
entire world to understand the measurements in
one set of unit systems.
• There are several SI units used in physics that
are used to express the different quantities.
The quantities can be classified into two
groups i.e. base units and derived units.

8. Sl. No. Name of the
Quantity
SI Unit SI Unit Symbol
1. Length (l) Meter m
2. Mass (M) Kilogram kg
3. Time (T) Second s
4. Electric current
(I)
Ampere A
5. Thermodynamic
temperature (Θ)
Kelvin K
6. Amount of
substance (N)
Mole mol
7. Luminous
intensity (J)
Candela cd

9. SI Base Units
• These are the fundamental units and are considered
as the building blocks of the system. All the
other units are derived from the SI Base units.
One of the examples is that the SI unit of mass
is kilogram. This is often confused with grams.
• There are 7 SI base units. The seven units along
with their SI unit and symbol are given below:
1.Unit of length, meter (m): Meter is the SI unit of
length and is defined by taking the fixed value of
the speed of light in vacuum. It is expressed as
m.s-1.
2.Unit of mass, kilogram (kg): Kilogram is the SI
unit of mass and is defined by taking the fixed
value of the Planck constant. It is expressed as
2 -1

10. 1.Unit of time, second (s): Second is the SI unit of time and
is defined by taking the fixed value of Cesium frequency. It
is expressed as s1.
2.Unit of electric current, ampere (A): Ampere is the SI unit
of electric current and is defined by taking the fixed value
of the elementary charge.
3.Unit of thermodynamic temperature, Kelvin (K): Kelvin is
the SI unit of thermodynamic temperature and is defined by
taking the fixed value of Boltzmann constant k =
1.380649×10-23.
4.Unit of the amount of substance, mole (mol): Mole is the SI
unit of the amount of substance and is defined by the fixed
value of Avogadro constant NA. One mole contains
6.02214076×1023 elementary entities and is expressed as mol-
1.
5.Unit of luminous intensity, candela (cd): Candela is the SI
unit of luminous intensity and is defined by the fixed value
of the luminous efficacy.

11. SI Derived Units
Sl. No Unit(s)
Name
SI Unit SI Unit
Symbol
Expresse
d in SI
Base Unit
Expresse
d in other
SI units
1. Force,
Weight
Newton N kg⋅m⋅s
-2
–
2. Frequenc
y
Hertz Hz s
-1
–
3. Electric
charge
Coulomb C s⋅A –
4. Electric
potential
(Voltage)
Volt V kg.m
2
.s
-
3
.A
-1
W/A
5. Inductanc
e
Henry H kg.m
2
.s
-
2
.A
-2
Wb/A
6. Capacitan
ce
Farad F kg
−1
.m
−2
.s
4
.A
2
C/V
7. Resistanc
e,
Impedanc
e,
Reactanc
e
Ohm Ω kg.m
2
.s
−3
.
A
−2
V/A

12. 8. Electrical
conducta
nce
Siemens S kg
−1
.m
−2
.s
3
.A
2
Ω−1
9. Magnetic
flux
Weber Wb kg.m
2
.s
−2
.
A
−1
V⋅s
10. Magnetic
flux
density
Tesla T kg.s
−2
.A
−1
Wb/m
2
11. Energy,
Work,
Heat
Joule J kg.m
2
.s
−2
N⋅m =
Pa⋅m
3
12. Power,
Radiant
flux
Watt W kg.m
2
.s
−3
J/s
13. Angle Radian rad m.m
−1
–
14. Radioactiv
ity
Becquerel Bq s
-1
–
15. Luminous
flux
Lumen lm cd cd⋅sr

13. Resultant force
• The resultant force is described as the total
amount of force acting on the object or body
along with the direction of the body. The
resultant force is zero when the object is at
rest or it is traveling with the same velocity
as the object. The resultant force should be
equal for all the force since all the force is
acting in the same direction.

14. Formula of Resultant Force
• If one force is acting perpendicular to
another, the resultant force is determined by
using the Pythagorean theorem. The Resultant
force formula is given by,
• FR = F1 + F2 +
F3
• Where
• F1, F2, F3 are the three forces acting in the
same direction on an object.

15. Determine the FR when three forces such as 80 N, 100 N,
and 30 N are acting on an object simultaneously and 30 N
force is opposite to the other two forces.
• Given:
• F1 = 80 N
• F2 = 100 N
• F3 = -30 N
• F3 is a negative value because it is acting
opposite to the other two force
• The formula for resultant force is
• FR = F1+F2+F3
• FR = 80 + 100 – 30
• FR = 150 N

16. Component of a force
• Forces acting at some angle from the the coordinate axes can be
resolved into mutually perpendicular forces called components.
The component of a force parallel to the x-axis is called the x-
component, parallel to y-axis the y-component, and so on.

17. Components of a Force in XY Plane
Given the slope of the line of action of the force as v/h