VECTORS- CHAPTER 1

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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.


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