INTRODUCTION
STATICS OF RIGID BODIES (CE0001)
This module will be covering the basic terms and
concepts applicable in static analysis of rigid
bodies including discussions on units,
measurement, rounding numbers, and significant
figures.
branch of physics that considers the action of forces on solid bodies and fluids
branch of mechanics that applies the principles of mechanics to engineering design
branch of Engineering Mechanics concerned with rigid bodies at rest and forces in equilibrium
The purpose of mechanics is
to explain and predict
physical phenomena and
thus to lay the foundations
for engineering applications.
DIMENSION
refers to the type of measurement (i.e mass, velocity, length)
UNIT
standard of measurement for dimensions (i.e kg, ft/sec, miles)
SPACE
geometric region occupied by bodies whose positions are described by linear and angular measurements
relative to a coordinate system
MASS
quantity of a matter in a body
measure of the inertia of a body (resistance to a change of velocity)
FORCE
the mechanical interaction between bodies that causes a tendency of equilibrium or motion
FOUR(4) CHARACTERISTICS OF A FORCE
Line of Action
FORCE
the mechanical interaction between bodies that causes a tendency of equilibrium or motion
TWO(2) CATEGORIES OF A FORCE
developed when two
bodies touch
acts through spaces or bodies
also called as BODY force
Normal-Direction
Tangential-Direction (Friction)
Weight of an object
Gravitational attraction
FORCE
the mechanical interaction between bodies that causes a tendency of equilibrium or motion
SOME COMMON TYPES OF FORCES
Applied
Tension
Frictional
Spring
FORCE
the mechanical interaction between bodies that causes a tendency of equilibrium or motion
FORCE TYPES According to POINT of Application
𝑪𝒐𝒏𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝑭𝒐𝒓𝒄𝒆𝒔
𝑵𝒐𝒏 − 𝑪𝒐𝒏𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝑭𝒐𝒓𝒄𝒆𝒔
𝑷𝒂𝒓𝒂𝒍𝒍𝒆𝒍
𝑵𝒐𝒏 − 𝑷𝒂𝒓𝒂𝒍𝒍𝒆𝒍
FORCE
the mechanical interaction between bodies that causes a tendency of equilibrium or motion
FORCE TYPES According to PLANE of Application
𝑪𝒐𝒑𝒍𝒂𝒏𝒂𝒓 𝑭𝒐𝒓𝒄𝒆𝒔
𝑵𝒐𝒏 − 𝑪𝒐𝒑𝒍𝒂𝒏𝒂𝒓 𝑭𝒐𝒓𝒄𝒆𝒔
used in mechanics in order to simplify the application of the theory and to represent physical phenomena
into mathematical representations (assumptions)
1
2
3
PARTICLE. The principles of mechanics reduce bodies to a rather
simplified form or particles since its geometry will not be involved
in the analysis of the problem. In short, size is neglected.
RIGID BODY. This is an assumption that the particles of any body
shall remain fixed despite the application of a force. It neglects the
reality of deformation.
CONCENTRATED FORCE. This represents the effect of a loading
or a force applied which is assumed to act at a point on a body.
The area of contact is neglected.
the study of elementary mechanics rests on these principles which are based on experimental evidence
1
PARALLELOGRAM LAW FOR THE
ADDITION OF FORCES
This states that two forces acting on a particle may be
replaced by a single force, called their resultant, obtained
by drawing the diagonal of the parallelogram which has
sides equal to the given forces.
the study of elementary mechanics rests on these principles which are based on experimental evidence
2
PRINCIPLE OF TRANSMISSIBILITY
This states that the conditions of equilibrium or of motion of
a rigid body will remain unchanged if a force acting at a
given point of the rigid body is replaced by a force of the
same magnitude and same direction, but acting at a
different point, provided that the two forces have the same
line of action .
the study of elementary mechanics rests on these principles which are based on experimental evidence
3
NEWTON’S FIRST LAW OF MOTION
If the resultant force acting on a particle is zero, the particle
will remain at rest (if originally at rest) or will move with
constant speed in a straight line (if originally in motion).
the study of elementary mechanics rests on these principles which are based on experimental evidence
4
NEWTON’S SECOND LAW OF MOTION
(LAW OF ACCELERATION)
If the resultant force acting on a particle is not zero, the particle
will have an acceleration proportional to the magnitude of the
resultant and in the direction of this resultant force.
the study of elementary mechanics rests on these principles which are based on experimental evidence
5
NEWTON’S THIRD LAW OF MOTION
(ACTION-REACTION PRINCIPLE)
The forces of action and reaction between bodies in contact
have the same magnitude, same line of action, but with
opposite sense/direction.
the study of elementary mechanics rests on these principles which are based on experimental evidence
6
NEWTON’S LAW OF GRAVITATION
This states that two particles of mass 𝑴 and 𝒎 are mutually
attracted with equal force F of magnitude given by the
formula
𝒎
where 𝒓 = distance between the two particles
𝑮 = universal constant called the constant of gravitation
𝑴
= 𝟔. 𝟔𝟕 𝒙 𝟏𝟎−𝟏𝟏 𝑵 − 𝒎𝟐 /𝒌𝒈𝟐
the study of elementary mechanics rests on these principles which are based on experimental evidence
on experimental evidence
7
PRINCIPLE OF PHYSICAL
INDEPENDENCE OF FORCE
states that if a number of forces are simultaneously acting on a
particle, then the resultant of these forces will have the same effect
as produced by all the forces
𝑭𝑹
FORCE
the mechanical interaction between bodies that causes a tendency of equilibrium or motion
RESULTANT FORCE
a force that creates the same effect to a system or body to
that of a number of forces acting at the same point (𝑭𝑹 )
COMPONENT FORCES
forces that contribute to the magnitude of the resultant (𝑭𝟏 ,
𝑭𝟐 ,and 𝑭𝟑 )
𝑭𝑹
QUANTITY
amount or number of a material gathered through measurements or computation/derivation
THREE(3) TYPES OF QUANTITIES
have of magnitude only
comprised of
magnitude with direction
comprised of
Magnitude, direction, and
axis/point of rotation
Mass
Time
Velocity
Force
Volume
Speed
Displacement
Acceleration
Area/Mass Moment of Inertia
Centroids
Centers of Mass/Gravity
FORCE
the mechanical interaction between bodies that causes a tendency of equilibrium or motion
VECTOR NOMENCLATURE
Since forces are vector quantities,
it is important to identify the
components of a vector as shown.
FREE-BODY DIAGRAMS
diagram showing all the forces acting on the object at a specific instance
EQUILIBRIUM
a state where system would remain at rest when subjected to set of forces and couples and should satisfy
the following conditions:
a system of measurement of physical quantities
TWO(2) TYPES OF UNITS
Measured in terms of some
arbitrary, but internationally
accepted units(fundamental units)
Computed in terms of or
derived with the application of
the relationship of base units
a system of measurement of physical quantities
TWO(2) SYSTEMS OF UNIT
INTERNATIONAL SYSTEM OF UNIT
1
abbreviated SI (from the French, Système International
d’Unités), is accepted in the United States and throughout
the world, and is a modern version of the metric system
(MKS).
2
U.S. CUSTOMARY UNITS
also called as British system of units or the foot-poundsecond (FPS) system has been the common system in
business and industry in English-speaking countries
Newton (derived unit)
slug (derived unit)
a system of measurement of physical quantities
a system of measurement of physical quantities
The number of significant figures contained in any number determines the accuracy of the number which
include the following rules:
1. All non-zero digits are significant numbers. (431 = 3 SF)
2. If zeros occur at the beginning of a number that is less than one, then the zeros are
not significant. (0.021 = 2 SF)
3. All trailing zeros are significant. (2.050 = 4 SF)
4. The use of scientific notation indicates the number of significant figures. (45.20 X
𝟏𝟎𝟖 = 4 SF)
Rounding off a number is necessary so that the accuracy of the result will be the same as that of the
problem data.
GENERAL RULE: When the number to be rounded is proceed by a 5 or higher, ROUND UP. Therefore,
if it is 4 below, ROUND DOWN.
Neglect special case for odd/even numbers preceded by 5.
MODULE 1
INTRODUCTION
At the end of the chapter, the learners should be able to:
Identify the basic terms and concepts used in analyzing static and rigid bodies;
Apply technical skills in handling computations involving units and measurements, and significant
units; and
Enumerate future courses that will apply concepts in this subject.