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:
“A right rule for a club would be,—Admit no man whose presence excludes any one topic.”
—Ralph Waldo Emerson (1803–1882)
“Napoleon wanted to turn Paris into Rome under the Caesars, only with louder music and more marble. And it was done. His architects gave him the Arc de Triomphe and the Madeleine. His nephew Napoleon III wanted to turn Paris into Rome with Versailles piled on top, and it was done. His architects gave him the Paris Opera, an addition to the Louvre, and miles of new boulevards.”
—Tom Wolfe (b. 1931)
“In literary circles, the men of trust and consideration, bookmakers, editors, university deans and professors, bishops, too, were by no means men of the largest literary talent, but usually of a low and ordinary intellectuality, with a sort of mercantile activity and working talent. Indifferent hacks and mediocrities tower, by pushing their forces to a lucrative point, or by working power, over multitudes of superior men, in Old as in New England.”
—Ralph Waldo Emerson (1803–1882)