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1.3 Scalar and vector

1.3 Scalar and Vectors

Rujukan: http://www.glenbrook.k12.il.us/gbssci/Phys/Class/vectors/u3l1a.html

> A scalar quantity is a physical quantity which has only magnitude. For example, mass, speed (laju), density, pressure, ….

 

> A vector quantity is a physical quantity which has magnitude and direction. For example, force, momentum, velocity (halaju), acceleration ….

Graphical representation of vectors

clip_image001•A vector can be represented by a straight arrow,

The length of the arrow represents the magnitude of the vector.

The vector points in the direction of the arrow.

 

Basic principle of vectors

• Two vectors P and Q are equal if:

(a) Magnitude of P = magnitude of Q        

(b) Direction of P = direction of Q

• When a vector P is multiplied by a scalar k, the product is k P and the direction remains the same as P.

The vector -P has same magnitude with P but comes in the opposite direction.

 

Sum of vectors

Method 1: Parallelogram of vectors

It two vectors clip_image003 and clip_image005 are represented in magnitude and direction by the adjacent sides OA and OB of a parallelogram OABC, then OC represents their resultant(paduan).

clip_image007

Method 2: Triangle of vectors

•Use a suitable scale to draw the first vector.

•From the end of first vector, draw a line to represent the second vector.

•Complete the triangle. The line from the beginning of the first vector to the end of the second vector represents the sum in magnitude and direction.

clip_image009

 

Example 4

A kite flies in still air is 4.0 ms-1. Find the magnitude and direction of the resultant velocity of the kite when the air flows across perpendicularly(serenjang) is 2.5 ms-1. If the distance of the kite is 30 m,

what is the time taken for the kite to fly? Calculate the height of the kite from the ground.

clip_image010

 

Vector 1- direction (yes)

            2- magnitude (c2=a2+b2)

                        c= 4.7m s-1

 

Principles of vectors

 

Relative  velocity

Let us look at two cases:            VA = 10 ms-1   VB = 3 ms-1.

 

Case one

The velocity of A relative to B = (VA – VB)

= (10- 3) ms­

= 7 ms -1 (in forward direction).

 

Case two

The velocity of B relative to A = (VB – VA)

= (3 – 10) ms­

= -7 ms -1 (in backwards direction).

 

We observe that(VB – VA) and (VA – VB) are same magnitude but different direction.

 

•Resolving(leraian) vector

A vector R can be considered as the two vectors. R refers to the resultant vectors. There are two mutually perpendicular component Rx and Ry

clip_image011

 

Example 5

The figure shows 3 forces F1, F2 and F3 acting on a point O. Calculate the resultant force and the direction of resultant.

clip_image013

 

F1

F2

F3

magnitude

3N

5N

4N

Direction

clip_image014

clip_image015

clip_image016

degree

0°

150°

240°

Resolving

X-axis

F1x=+3N

Y-axis

F1y = 0

X-axis

F2x=-4.3N

Y-axis

F2y =2.5N

 

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