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=(Ax, Ay, Az) and B=(Bx, By, Bz), 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.
Read more about this topic: Net Force
Famous quotes containing the words rule, addition and/or forces:
“You will find that reason, which always ought to direct mankind, seldom does; but that passions and weaknesses commonly usurp its seat, and rule in its stead.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Depend upon it there comes a time when for every addition of knowledge you forget something that you knew before. It is of the highest importance, therefore, not to have useless facts elbowing out the useful ones.”
—Sir Arthur Conan Doyle (1859–1930)
“And whoever forces himself to love anybody
begets a murderer in his own body.”
—D.H. (David Herbert)