This is called a _graphic representation_ since it represents by a line
the quantity in question. If another weight of 5 lbs. were hung from the
first one, the graphic representation of both forces would be as in Fig.
56_b_. Here the first force is represented by _AB_ as before, _BC_
representing the second force applied. The whole line represents the
_resultant_ of the two forces or the result of their combination. If the
two weights were hung one at each end of a short stick _AC_ (Fig.
56_c_), and the latter suspended at its center their combined weight or
_resultant_ would of course be applied at the center. The direction
would be the same as that of the two weights. The resultant therefore is
represented by _ON_. In order to exactly balance this resultant _ON_, a
force of equal magnitude but opposite in direction must be applied at
the point of application of _ON_, or _O_. _OM_ then represents a force
that will just balance or hold in equilibrium the resultant of the two
forces _AB_ and _CD_. This line _OM_ therefore represents the
_equilibrant_ of the weights _AB_ and _CD_. The resultant of two forces
at an angle with each other is formed differently, as in Fig. 57 _a_.
Here two forces _AB_ and _AC_ act at an angle with each other. Lay off
at the designated angle the lines _AB_ and _AC_ of such length as will
accurately represent the forces. Lay off _BD_ equal to _AC_ and _CD_
equal to _AB_. The figure _ABCD_ is then a parallelogram. Its diagonal
_AD_ represents the resultant of the forces _AB_ and _AC_ acting at the
angle _BAC_. If _BAC_ equals 90 degrees or is a right angle, _AD_ may be
_computed_ thus: _AB² + BD² = AD²_. Why?
and _AD_ = √_([line]AB² + [line]BD²)._
[Illustration: FIG. 56.--Graphic representation of forces acting along
the same or parallel lines.]
[Illustration: FIG. 57.--Graphic representation of two forces acting
(_a_) at a right angle, (_b_) at an acute angle.]
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