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:
“I make it a kind of pious rule to go to every funeral to which I am invited, both as I wish to pay a proper respect to the dead, unless their characters have been bad, and as I would wish to have the funeral of my own near relations or of myself well attended.”
—James Boswell (17401795)
“The force of truth that a statement imparts, then, its prominence among the hordes of recorded observations that I may optionally apply to my own life, depends, in addition to the sense that it is argumentatively defensible, on the sense that someone like me, and someone I like, whose voice is audible and who is at least notionally in the same room with me, does or can possibly hold it to be compellingly true.”
—Nicholson Baker (b. 1957)
“When we are in love, the sentiment is too great to be contained whole within us; it radiates out to our beloved, finds in her a surface which stops it, forces it to return to its point of departure, and it is this rebound of our own tenderness which we call the others affection and which charms us more than when it first went out because we do not see that it comes from us.”
—Marcel Proust (18711922)