1. Introduction to Basic Mechanics,
Resolution of Vectors
Introduction to Basic Mechanics,
SI Units, Resolution of Vectors
Chapter 1
2. Mechanics?
• Mechanics is a branch of the physical science
that is concerned with the state of rest or
motion of bodies that are subjected to the
action of forces.
• It deals with the effect of forces upon material
bodies.
3. Division of Mechanics
• Mechanics of fluids, a phase of it is called
hydraulics
• Mechanics of materials, more often called
strength of materials, as subject which deals with
the internal forces or stresses in bodies
• Analytic mechanics or mechanics of
engineering, a study of external forces on bodies,
ordinarily rigid bodies or bodies considered to be
rigid, and of the effects of these forces on the
motions of bodies.
4. Analytic Mechanics
Analytic mechanics includes the study of:
• Statics, which deals with the forces acting on
bodies or structures which are at rest relative
to the earth or which are moving with a
constant velocity
• Dynamics, which deals with the accelerated
motion of bodies.
5. Our Concern: Statics
• We can consider statics as a special case of
dynamics, in which the acceleration is zero.
• However, statics deserves separate treatment in
engineering education since many objects are
designed with the intention that they remain in
equilibrium.
7. Application of Newton’s Laws
• Law 1 define the condition of equilibrium and
from it develops the first part of the work-
Statics.
• Law 3 applies to both Statics and Dynamics.
• The study of Dynamics is developed from Law
2.
8. SI Units
• The SI is founded on seven SI base units for
seven base quantities assumed to be
mutually independent, as given in Table 1.
9.
10. SI Derived Units
• Other quantities, called derived quantities, are
defined in terms of the seven base quantities
via a system of quantity equations. The SI
derived units for these derived quantities are
obtained from these equations and the seven SI
base units. Examples of such SI derived units
are given in Table 2
12. For ease of understanding and convenience,
SI derived units have been given special
names and symbols, as shown in Table 3.
13. Table 3. SI derived units with special
names and symbols
14. Analytic Mechanics: Deals with Forces
• In mechanics, a force arises out of the
interaction of two bodies and causes or tends
to cause the motion of the bodies. A body
which is at rest or is moving with a constant
velocity is said to be in equilibrium.
• Force is a vector quantity. The characteristics
of a force vector are that it has (1) magnitude
(2) sense or direction and (3) line of action.
15.
16. Vector Addition & Subtraction
• Vector quantities, such as force, acceleration,
velocity and momentum, cannot be added or
subtracted as are scalar quantities, which
posses magnitude only.
• Then How??? (See Page 3-5 [Vector Addition and
Substracting Vectors] of Analytic Mechanics 3rd
Edition, Virgil Moring Faires)
18. Resultant of Forces
The resultant of forces as presented in this chapter may be found
out either by use of the Parallelogram Law or Triangle Law.
• Parallelogram Law: If two coplanar force vectors are laid out to
scale from their point of intersection, both pointing away from
the point of intersection, and if a parallelogram is completed with
these force vectors as two sides, then the diagonal of the
parallelogram that passes through the point of intersection
represents the resultant in magnitude and direction.
• Triangle Law: If two coplanar force vectors are laid out to scale
with the tail of one at the point of other, the third side of a
triangle of which these two vectors are two sides represents the
resultant in magnitude with a sense from the tail of the first
vector to the point of the second vector.
19. Laws of Cosine
• R2 = F1
2 + F2
2 – 2F1F2 cos(180 - α)
• or, R2 = F1
2 + F2
2 + 2F1F2 cos α ……(1)
[Since, cos(180 - α) = -cosα]
• Where, α is the angle between the vectors F1 and F2.
Also from Fig. (a)
• tan θ = F2 sin α / (F1 + F2 cos α) …… (2)
20. Rectangular components
• For α = 90º, we get the special case of components
which are perpendicular to each other. Since cos 90º =
0, we have from equation (1) and also from the right
triangle AKB of Fig. (c)
• R2 = F1
2 + F2
2 or, R = (F1
2 + F2
2)1/2 ………….. (3)
• Components of a resultant that are at right angles to
each other are called rectangular components.
• Fx = F cosθ and Fy = F sinθ ..………………….(4)
• And, tanθ = Fy / Fx
• The process of finding components of a force is called
resolution.
21. Simple Math Probs.
• Find the resultant of a horizontal force of Fx = 400
lb, acting toward the right, and a vertical force of Fy
= - 300 lb, the negative sign indicating that the force
acts in the negative direction, downward.
• A force of 5000 lb. acts upward toward the right at an
angle of θ = 30 º with the horizontal. What are its
horizontal and vertical components?
22. Classification of Force System
• Based on the planes, Force System may be classified
as:
• Coplanar force system: The force vectors are all in
the same plane.
• Non-coplanar force system: The forces are not all in
the same plane.
23. Classification of Force System
• Based on Line of Action, Force system may also be classified
as:
• Collinear force systems: All the forces act along the same line
of action. A collinear system is necessarily coplanar.
• Concurrent force system: All lines of action intersect at one
point. A concurrent force system may be either coplanar or
non-coplanar provided that there are more than two forces.
• Non-concurrent force system: The lines of action of the force
vectors do not intersect at a point. A non-concurrent system
may be either coplanar or non-coplanar.
• Parallel force system: The lines of action of all force vectors
are parallel. A parallel force system may be either coplanar or
non-coplanar.
24. Welcome to Basic Mechanics
Prb 15 (Chap. 1- Faires)
In Fig, let F = 3600 lb and θ = 45º. Assume both pulleys to
have no friction so that the tension in the cable CD is 3600 lb.
Solve the problem algebraically for the force on the shaft at B
and A.
