Net Force - Parallelogram Rule For The Addition of Forces

Parallelogram Rule For The Addition of Forces

A force is known as a bound vector which means it has a direction and magnitude and a point of application. A convenient way to define a force is by a line segment from a point A to a point B. If we denote the coordinates of these points as A=(A_x, A_y, A_z) and B=(B_x, B_y, B_z), then the force vector applied at A is given by

The length of the vector B-A defines the magnitude of F, and is given by

The sum of two forces F₁ and F₂ applied at A can be computed from the sum of the segments that define them. Let F₁=B-A and F₂=D-A, then the sum of these two vectors is

which can be written as

where E is the midpoint of the segment BD that joins the points B and D.

Thus, the sum of the forces F₁ and F₂ is twice the segment joining A to the midpoint E of the segment joining the endpoints B and D of the two forces. The doubling of this length is easily achieved by defining a segments BC and DC parallel to AD and AB, respectively, to complete the parallelogram ABCD. The diagonal AC of this parallelogram is the sum of the two force vectors. This is known as the parallelogram rule for the addition of forces.