Everything Science Grade 11

11.7 CHAPTER 11. VECTORS

The Parallelogram Method

The parallelogram method is another graphical technique of finding the resultant of two vectors.

Method: The Parallelogram Method

1. Make a rough sketchof the vector diagram.


2. Choose a scale and areference direction.


3. Choose either of thevectors to be added anddraw it as an arrow of the correct length in the
   correct direction.


4. Draw the second vector as an arrow of the correct length in the correct direction from the tailof
   the first vector.


5. Complete the parallelogram formed by thesetwo vectors.


6. The resultant is thenthe diagonal of the parallelogram. The magnitude can be determined from
   the length of its arrowusing the scale. The direction too can be determined from the scale
   diagram.

Example 4: Parallelogram Methodof Vector Addition I

QUESTION

A force of F 1 = 5N is applied to a block ina horizontal direction. Asecond force F 2 = 4N

is applied to the objectat an angle of 30◦above the horizontal.

F 1 = 5N

F^2

= 4N

30 ◦

Determine the resultantforce acting on the block using the parallelogrammethod of accurate

construction.

SOLUTION

Step 1 : Firstly make a rough sketch of the vector diagram

5N

4N

30 ◦

Step 2 : Choose a suitable scale

In this problem a scaleof 1 cm = 1 N wouldbe appropriate, since then the

vector diagram would take up a reasonable fraction of the page. Wecan now

begin the accurate scalediagram.

Step 3 : Draw the first scaled vector