VECTORS- CHAPTER 1
The force system may be classified as
(1) coplanar or non-coplanar, (2) collinear and non collinear (3) concurrent or non-concurrent, (4) parallel or non-parallel.
Law of Sine
In any triangle, any two sides are proportional to the sides of the opposite angles.
Law of Cosine
In any triangle, the square of any sides is equal to the sum of the squares of the other sides minus twice their product times the cosine of their included angle.
ruler and protractor.
The length of the arrow representing the resultant vector and the angles representing directions is measured using
GRAPHICAL ADDITION AND SUBTRACTION OF VECTORS
To add vectors graphically, lay the first one on set axes with its tail at the origin. Place the next vector with its tail at the previous vector's head. When there are no more vectors, draw a straight line from the origin to the head of the last vector. This serves as the resultant vector.
ANALYTICAL ADDITION OF 2 VECTORS
To solve for the resultant vector of a right triangle use the Pythagorean Theorem and its angle is determine using trigonometric functions.For an oblique triangle, use law of cosine to solve for resultant vector and law of sines to determine its angle.
Graphical Subtraction of Two Vectors
To subtract vectors graphically, reverse the direction of B, thus forming -B . Then add A and -B. R = A + (-B).
Component Method
a more convenient way to add vectors
vector's magnitude
arrow's length indicates
Scalar Examples
length, area, distance, time, energy, work, power and speed
Scalar Quantity
represented by their magnitude with appropriate units
Vector Quantities
require both magnitude and direction for their complete specification
point of application We can also use a single letter with an arrow above it or simply a bold letter without need of arrow, R = R. For my class, vector is represented by a boldface type.
tail represents
system of forces
A group or set of forces is called
Equilibrant Force
An equilibrant force is a force which brings a body into mechanical equilibrium. Therefore, an equilibrant force is equal in magnitude and opposite in direction to the resultant of all the other forces acting on a body.
Coplanar Force
Coplanar force system refers to the number of forces which remain in same plane. It is also stated as the number of forces in a system which remains in single plane. This force system can be collinear, concurrent, parallel and non concurrent - nonparallel.
Concurrent force system
Current force system is a set of two or more forces whose lines of action intersect at a point at the same time. Concurrent forces may or may not be coplanar.
Pythagorean Theorem Formula
F^2 = FX^2 + Fy^2
balanced: the forces are in equilibrium
If a body has two or more forces acting on it and it does not move (accelerate) then the forces are
Parallel force system
If the line of action of forces forming the system are parallel.These parallel forces can either be in the same direction or in opposite directions.
Non-parallel force system
It is a particular case of non concurrent force system where the line of action does not form a parallel system.
For the concurrent and non coplanar force system, Resultant force can be determined by:
R = EF= sqrt. ( (EFx)^2 + (EFy)^2 + (EFz)^2)
direction of the vector
The arrowhead (tip) indicates
Non-concurrent force system
The forces that do not meet at one point of intersection while acting on the same object. Since they do not intersect at one point, they are not parallel, and the resultant cannot equal zero.
Collinear force system
The forces which are acting along a straight line are called as collinear forces
Non collinear force system
The forces which are not acting along a straight line
Component Method
The sum of three or more vectors is determined using
component method
The sum of two or more vectors can be determined using
resultant
The sum of two or more vectors is represented by single vector called
(a) Trigonometric Functions and Pythagorean Theorem for right triangle and (b) the Law of Sine and Law of Cosine for oblique triangle.
The sum of two vectors is determined usin
Graphical method and analytical method through the use of Pythagorean theorem and trigonometric functionsfor right triangle and Law of Sines and Law of Cosines for oblique triangle, or the component methodfor three or more vectors.
This vector may be found by using
vector addition is commutative and associative
Vectors can be taken in any order of succession like A + B = B + A = R,
Vector Examples
force, velocity, displacement, acceleration, and momentum.
Non coplanar forces
forces that act at different planes. At any case, forces will not be acting in a single plane for a non coplanar force system. This system of force may be concurrent, parallel and non concurrent-non parallel.
