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Chapter 1
Introduction to Basic Mechanics,
Resolution of Vectors
Mechanics?
• Mechanics is a branch of the physical sciences
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.
Division of Mechanics
• Mechanics of fluids, a phase of 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 bodied or bodies considered to be
rigid, and of the effects of these forces on the
motions of bodies.
Analytic mechanics
Analytic mechanics includes the study of:
• Statics, deals with the equilibrium of bodies,
that is, those that are either at rest or move
with a constant velocity
• Dynamicsis, which deals with the accelerated
motion of bodies.
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.
Base of Analytical Mechanics
Application of Newton’s Laws
• Law I define the condition of equilibrium and
from it develop the first part of the workStatics.
• Law III applies to both Statics and Dynamics.
• The study of Dynamics is developed from Law
II.
Analytic Mechanics: Dealing 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 equilibrium.
• Force is a vector quantity. The characteristics
of a force vector are that has (1) magnitude (2)
sense or direction and (3) line of action.
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 of Analytic
Mechanics 3rd Edition, Virgil Moring Faires)
Laws of cosine
• R2 = F12 + F22 – 2F1F2 cos(180 - α)
• or, R2 = F12 + F22 + 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)
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 = F12 + F22 or, R = (F12 + F22)1/2 ………….. (3)
• Components of a resultant that are at 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.
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 block with a 1 ft x 4 ft. rectangular section is 20 ft long and
weighs W= 9000 lb. If a 2000 lb force acts 8 ft from the base,
what is the magnitude of the resultant R of these two forces
and where does the line of action of R intersect the base of the
block?
• 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?
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.
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.
 Welcome to Basic Mechanics 
• 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.
Closure
• The composition of forces as presented in this chapter may be
carried 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.
 !!Assignments!! 
From the Book:
• No. 16 (Similar to the previous problem)
• No. 22
 !!Assignments!! 
 !!Assignments!! 
 !!Assignments!! 
Hints: You have to use Sine Law to solve the problems. Search Google If you
don’t know the Sine Law.
THANK YOU 