lecture 1 introduction to statics

LECTURE 1

Introduction to Statics

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

WHAT AND WHY STUDY STATICS ??

Mechanics can be divided into 3 branches:- Rigid-body Mechanics

- Deformable-body Mechanics- Fluid Mechanics

Rigid-body Mechanics deals with

- Statics - Dynamics

Statics is actually the application of mathematics and basic physics (Newton’s laws) to study forces in materials, machines and structures. Forces are of interest to engineers for two reasons:

1. they cause materials to deform and break, and2. they cause things to move.

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

� Statics is used to calculate forces in systems that don’t move, or move at constant velocity. The application of physics to study motion is known as dynamics.

Structural engineers – Design buildings and structures,Mechanical engineers – Design machinery, which may range from engines to micro electro-mechanical systems.Biomedical engineers – Design artificial organs and implants.

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

Fundamental 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 anotherMeasure of resistance of matter to a change in velocity

Time – Conceive as succession of events

Force – “push” or “pull” exerted by one body on another– Occur due to direct contact between bodies e.g. – Person pushing against the wall– Occur through a distance without direct contact e.g. – Gravitational, electrical and magnetic forces

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

Fundamental concepts

Idealizations

� Particles – Consider mass but neglect size

E.g.: Size of Earth insignificant compared to its size of orbit

� Rigid Body – Combination of large number of particles

– Neglect material properties

E.g.: Deformations in structures, machines and mechanism

� 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

E.g.: Contact force between wheel and ground

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

Newton’s Three Laws of Motion

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

“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”

Newton’s First Law

Newton’s 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”

maF =

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

“The mutual forces of action and reaction between two particles are equal

and, opposite and collinear”

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

Newton’s Third Law

Newton’s Law of Gravitational Attraction

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

221

r

mmGF =

Weight,

Letting yields

2r

mMGW e=

2/ rGMg e= mgW =

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

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°

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

Units of Measurement

Name Length Time Mass Force

International Systems of Units (SI)

Meter (m)

Second (s)

Kilogram (kg)

Newton (N)

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

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

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

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN

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

E.g.: 4,000,000 N = 4000 kN (kilo-newton)

= 4 MN (mega- newton)

0.005m = 5 mm (mili-meter)

Exponential Form

Prefix SI Symbol

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

PROF. DR. SHAHRUDDIN BIN MAHZAN@MOHD ZIN