Introduction:

In mechanics, the net force is the vector sum of forces acting on a particle or object. The net force is a single force that replaces the effect of the original forces on the particle's motion. It gives the particle the same acceleration as all those actual forces together as described by Newton's second law of motion. It is possible to determine the torque associated with the point of application of a net force so that it maintains the movement of jets of the object under the original system of forces. Its associated torque, the net force, becomes the resultant force and has the same effect on the rotational motion of the object as all actual forces taken together. It is possible for a system of forces to define a torque-free resultant force. In this case, the net force, when applied at the proper line of action, has the same effect on the body as all of the forces at their points of application. It is not always possible to find a torque-free resultant force.

Total Force:

Force is a vector quantity, which means that it has a magnitude and a direction, and it is usually denoted using boldface such as F or by using an arrow over the symbol, such as . Graphically, a force is represented as a line segment from its point of application A to a point B, which defines its direction and magnitude. The length of the segment AB represents the magnitude of the force. Vector calculus was developed in the late 1800s and early 1900s. The parallelogram rule used for the addition of forces, however, dates from antiquity and is noted explicitly by Galileo and Newton.

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