Parallelogram Method

Parallelogram Method


Let's say you have a box on the ground, and the box is being pulled in two directions with a certain force. You can predict the motion of the box by finding the net force acting on the box. If each force vector (where the magnitude is the tension in the rope, and the direction is the direction that the rope is "pointing") can be measured, you can add these vectors to get the net force. There are two methods for adding vectors:

Parallelogram Method

The Parallelogram MethodThis is a graphical method for adding vectors. First, a little terminology:

The tail of a vector is where it originates.
The head of a vector is where it goes. The head is the end with the arrowhead.
This method is most easily executed using graph paper. Establish a rectangular coordinate system, and draw the first vector to scale with the tail at the origin. Then, draw the second vector (again, to scale) with its tail coincident with the head of the first vector. Then, the properties of the sum vector are as follows:

The length of the sum vector is the distance measured from the origin to the head of the second vector.
The direction of the sum vector is the angle.

[edit] Example
In the image at the right, the vectors (10, 53°07'48") and (10, 36°52'12") are being added graphically. The result is (19.80, 45°00'00"). (How did I measure out those angles so precisely? I did that on purpose.)

The native vector format for the parallelogram method is the 'polar form'

I hope i didnt repeat