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:
“Now, since our condition accommodates things to itself, and transforms them according to itself, we no longer know things in their reality; for nothing comes to us that is not altered and falsified by our Senses. When the compass, the square, and the rule are untrue, all the calculations drawn from them, all the buildings erected by their measure, are of necessity also defective and out of plumb. The uncertainty of our senses renders uncertain everything that they produce.”
—Michel de Montaigne (1533–1592)
“The addition of a helpless, needy infant to a couple’s life limits freedom of movement, changes role expectancies, places physical demands on parents, and restricts spontaneity.”
—Jerrold Lee Shapiro (20th century)
“The next thing his Lordship does, after clearing of the coast, is the dividing of his forces, as he calls them, into two squadrons, one of places of Scriptures, the other of reasons....
All that I have to say touching this, is that I observe a great part of those his forces do look and march another way, and some of them fight amongst themselves.”
—Thomas Hobbes (1579–1688)