1. This chapter introduces the fundamental concepts of engineering mechanics including basic quantities like length, mass, time and force. It describes Newton's laws of motion and gravitation. 2. The chapter outlines the standard procedures for applying the International System of Units (SI) and performing numerical calculations in mechanics. It emphasizes dimensional homogeneity and significant figures. 3. A general problem-solving procedure is presented, involving defining the problem, making assumptions, establishing a theoretical model, solving the governing equations, and interpreting the results.

1. Chapter 1
General Principles
Engineering Mechanics: Statics

2. Chapter Objectives
To provide an introduction to the basic quantities and
idealizations of mechanics.
To give a statement of Newton’s Laws of Motion and
Gravitation.
To review the principles for applying the SI system of
units.
To examine the standard procedures for performing
numerical calculations.
To present a general guide for solving problems.

3. Chapter Outline
Mechanics
Fundamental Concepts
Units of Measurement
The International System of Units
Numerical Calculations
General Procedure for Analysis

4. 1.1 Mechanics
Mechanics can be divided into 3
branches:
- Rigid-body Mechanics
- Deformable-body Mechanics
- Fluid Mechanics
Rigid-body Mechanics deals with
- Statics
- Dynamics

5. 1.1 Mechanics
Statics – Equilibrium of bodies
At rest
Move with constant velocity
Dynamics – Accelerated motion of
bodies

6. 1.2 Fundamentals Concepts
Basic Quantities
Length
– Locate position and describe size of physical
system
– Define distance and geometric properties of a
body
Mass
– Comparison of action of one body against
another
– Measure of resistance of matter to a change in
velocity

7. 1.2 Fundamentals Concepts
Basic Quantities
Time
– Conceive as succession of events
Force
– “push” or “pull” exerted by one body on
another
– Occur due to direct contact between bodies
Eg: Person pushing against the wall
– Occur through a distance without direct
contact Eg: Gravitational, electrical and magnetic
forces

8. 1.2 Fundamentals Concepts
Idealizations
Particles
– Consider mass but neglect size
Eg: Size of Earth insignificant compared to its
size of orbit
Rigid Body
– Combination of large number of particles
– Neglect material properties
Eg: Deformations in structures, machines and
mechanism

9. 1.2 Fundamentals Concepts
Idealizations
Concentrated Force
– Effect of loading, assumed to act at a
point on a body
– Represented by a concentrated force,
provided loading area is small compared to
overall size
Eg: Contact force between wheel and ground

10. 1.2 Fundamentals Concepts
Newton’s Three Laws of Motion
First Law
“A particle originally at rest, or moving in a
straight line with constant velocity, will
remain in this state provided that the particle
is not subjected to an unbalanced
force”

11. 1.2 Fundamentals Concepts
Newton’s Three Laws of Motion
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”
F = ma

12. 1.2 Fundamentals Concepts
Newton’s Three Laws of Motion
Third Law
“The mutual forces of action and reaction
between two particles are equal and,
opposite and collinear”

13. 1.2 Fundamentals Concepts
Newton’s Law of Gravitational Attraction
m1 m 2
F =G 2
r
F = force of gravitation between two particles
G = universal constant of gravitation
m1,m2 = mass of each of the two particles
r = distance between the two particles

14. 1.2 Fundamentals Concepts
mM e
Weight, W =G 2
r
Letting g = GM e / r 2 yields
W = mg

15. 1.2 Fundamentals Concepts
Comparing F = mg with F = ma
g is the acceleration due to gravity
Since g is dependent on r, weight of a body is
not an absolute quantity
Magnitude is determined from where the
measurement is taken
For most engineering calculations, g is
determined at sea level and at a latitude of 45°

16. 1.3 Units of Measurement
SI Units
Système International d’Unités
F = ma is maintained only if
– Three of the units, called base units, are
arbitrarily defined
– Fourth unit is derived from the equation
SI system specifies length in meters (m), time in
seconds (s) and mass in kilograms (kg)
Unit of force, called Newton (N) is derived from F
= ma

17. 1.3 Units of Measurement
Name Length Time Mass Force
Internationa Meter Second Kilogram Newton
l Systems of (m) (s) (kg) (N)
Units (SI)
 kg .m 
 2 
 s 

18. 1.3 Units of Measurement
At the standard location,
g = 9.806 65 m/s2
For calculations, we use
g = 9.81 m/s2
Thus,
W = mg (g = 9.81m/s2)
Hence, a body of mass 1 kg has a weight
of 9.81 N, a 2 kg body weighs 19.62 N

19. 1.4 The International System of
Units
Prefixes
For a very large or very small numerical
quantity, the units can be modified by
using a prefix
Each represent a multiple or sub-multiple
of a unit
Eg: 4,000,000 N = 4000 kN (kilo-newton)
= 4 MN (mega- newton)
0.005m = 5 mm (milli-meter)

20. 1.4 The International System of
Units
Exponential Prefix SI Symbol
Form
Multiple
1 000 000 000 109 Giga G
1 000 000 106 Mega M
1 000 103 Kilo k
Sub-Multiple
0.001 10-3 Milli m
0.000 001 10-6 Micro µ
0.000 000 001 10-9 nano n

21. 1.4 The International System of
Units
Rules for Use
Never write a symbol with a plural “s”.
Easily confused with second (s)
Symbols are always written in
lowercase letters, except the 2 largest
prefixes, mega (M) and giga (G)
Symbols named after an individual are
capitalized Eg: newton (N)

22. 1.4 The International System of
Units
Rules for Use
Quantities defined by several units
which are multiples, are separated by a
dot
Eg: N = kg.m/s2 = kg.m.s-2
The exponential power represented for
a unit having a prefix refer to both the
unit and its prefix
Eg: µN2 = (µN)2 = µN. µN

23. 1.4 The International System of
Units
Rules for Use
Physical constants with several digits on
either side should be written with a space
between 3 digits rather than a comma
Eg: 73 569.213 427
In calculations, represent numbers in
terms of their base or derived units by
converting all prefixes to powers of 10

24. 1.4 The International System of
Units
Rules for Use
Eg: (50kN)(60nm) = [50(103)N][60(10-9)m]
= 3000(10-6)N.m
= 3(10-3)N.m
= 3 mN.m
The final result should be expressed using
a single prefix

25. 1.4 The International System of
Units
Rules for Use
Compound prefix should not be used
Eg: kµs (kilo-micro-second) should be expressed as
ms (milli-second) since
1 kµs = 1 (103)(10-6) s = 1 (10-3) s = 1ms
With exception of base unit kilogram, avoid use
of prefix in the denominator of composite units
Eg: Do not write N/mm but rather kN/m
Also, m/mg should be expressed as Mm/kg

26. 1.4 The International System of
Units
Rules for Use
Although not expressed in terms of
multiples of 10, the minute, hour etc are
retained for practical purposes as multiples
of second.
Plane angular measurements are made
using radians. In this class, degrees would
be often used where 180° = π rad

27. 1.5 Numerical Calculations
Dimensional Homogeneity
- Each term must be expressed in the
same units
Eg: s = vt + ½ at2 where s is position
in meters (m), t is time in seconds (s),
v is velocity in m/s and a is acceleration
in m/s2
- Regardless of how the equation is
evaluated, it maintains its dimensional
homogeneity

28. 1.5 Numerical Calculations
Dimensional Homogeneity
- All the terms of an equation can be
replaced by a consistent set of units,
that can be used as a partial check for
algebraic manipulations of an equation

29. 1.5 Numerical Calculations
Significant Figures
- The accuracy of a number is specified by
the number of significant figures it contains
- A significant figure is any digit including
zero, provided it is not used to specify the
location of the decimal point for the number
Eg: 5604 and 34.52 have four significant
numbers

30. 1.5 Numerical Calculations
Significant Figures
- When numbers begin or end with zero, we make
use of prefixes to clarify the number of significant
figures
Eg: 400 as one significant figure would be 0.4(103)
2500 as three significant figures would be
2.50(103)

31. 1.5 Numerical Calculations
Computers are often used in engineering for
advanced design and analysis

32. 1.5 Numerical Calculations
Rounding Off Numbers
- For numerical calculations, the accuracy
obtained from the solution of a problem
would never be better than the accuracy of
the problem data
- Often handheld calculators or computers
involve more figures in the answer than the
number of significant figures in the data

33. 1.5 Numerical Calculations
Rounding Off Numbers
- Calculated results should always be
“rounded off” to an appropriate number of
significant figures

34. 1.5 Numerical Calculations
Rules for Rounding to n significant
figures
- If the n+1 digit is less than 5, the n+1 digit and
others following it are dropped
Eg: 2.326 and 0.451 rounded off to n = 2
significance figures would be 2.3 and 0.45
- If the n+1 digit is equal to 5 with zero following it,
then round nth digit to an even number
Eg: 1.245(103) and 0.8655 rounded off to n = 3
significant figures become 1.24(103) and 0.866

35. 1.5 Numerical Calculations
Rules for Rounding to n significant
figures
- If the n+1 digit is greater than 5 or equal
to 5 with non-zero digits following it,
increase the nth digit by 1 and drop the
n+1digit and the others following it
Eg: 0.723 87 and 565.5003 rounded off to
n = 3 significance figures become 0.724
and 566

36. 1.5 Numerical Calculations
Calculations
- To ensure the accuracy of the final
results, always retain a greater number of
digits than the problem data
- If possible, try work out computations so
that numbers that are approximately equal
are not subtracted
-In engineering, we generally round off
final answers to three significant figures

37. 1.5 Numerical Calculations
Example 1.1
Evaluate each of the following and express with
SI units having an approximate prefix: (a) (50
mN)(6 GN), (b) (400 mm)(0.6 MN)2, (c) 45
MN3/900 Gg
Solution
First convert to base units, perform indicated
operations and choose an appropriate prefix

38. 1.5 Numerical Calculations
(a) (50mN )(6GN )
[ ( ) ][ ( ) ]
= 50 10 −3 N 6 109 N
= 300(10 )N
6 2
= 300(10 )N 
6  1kN  1kN 
2
3  3

10 N 10 N  
= 300kN 2

39. 1.5 Numerical Calculations
(b) (400mm )(0.6MN )2
[ ( )m][0.6(10 )N ]
= 400 10 −3 6 2
= [400(10 )m][0.36(10 )N ]
−3 12 2
= 144(10 )m.N
9 2
= 144Gm.kN 2

40. 1.5 Numerical Calculations
(c) 3
45MN / 900Gg
=
(
45 10 N 6
)
3
( )
900 106 kg
= 0.05(10 )N / kg12 3
= 0.05(10 )N 
 1kN  1
12 3
 3
 10 N  kg
= 0.05(10 )kN / kg
3 3
= 50kN 3 / kg

41. 1.6 General Procedure for
Analysis
Most efficient way of learning is to solve
problems
To be successful at this, it is important to
present work in a logical and orderly way as
suggested:
1) Read problem carefully and try correlate
actual physical situation with theory
2) Draw any necessary diagrams and
tabulate the problem data

42. 1.6 General Procedure for
Analysis
3) Apply relevant principles, generally in
mathematics forms
4) Solve the necessary equations
algebraically as far as practical, making sure
that they are dimensionally homogenous,
using a consistent set of units and complete
the solution numerically
5) Report the answer with no more
significance figures than accuracy of the
given data

43. 1.6 General Procedure for
Analysis
6) Study the answer with technical judgment and
common sense to determine whether or not it
seems reasonable

44. 1.6 General Procedure for
Analysis
When solving the problems, do the work as
neatly as possible. Being neat generally
stimulates clear and orderly thinking and vice
versa.