This method of determining the resultant by _computation_ may be used
when the two forces are at right angles. (In any case, _AD may be
measured_ using the same scale that is laid off upon _AB_ and _AC_, as
shown in Fig. 57 _b_.) The three cases of combining forces just given
may be classified as follows: The _first_ is that of _two forces acting
along the same line_ in the same or opposite direction, as when two
horses are hitched tandem, or in a tug of war. The _second_ is that of
_two forces acting along parallel lines_, in the same direction, as when
two horses are hitched side by side or abreast. The _third_ is that of
_two forces acting at the same point at an angle_. It may be represented
by the device shown in Fig. 58, consisting of two spring balances
suspended from nails at the top of the blackboard at _A_ and _B_. A cord
is attached to both hooks and is passed through a small ring at _O_ from
which is suspended a known weight, _W_. Lines are drawn on the
blackboard under the stretched cords, from _O_ toward _OA_, _OB_, and
_OW_ and distances measured on each from _O_ to correspond to the three
forces as read on balance _A_ and _B_ and the weight _W_. Let a
parallelogram be constructed on the lines measured off on _OA_ and _OB_.
Its diagonal drawn from _O_ will be found to be vertical and of the same
length as the line measured on _OW_. The diagonal is the _resultant_ of
the two forces and _OW_ is the equilibrant which is equal and opposite
to the resultant.
[Illustration: FIG. 58.--Experimental proof of parallelogram of forces.]
Again, the _first_ case may be represented by a boat moving up or down a
stream; the resultant motion being the combined effect of the boat's
motion and that of the stream. The _second_, may be represented by two
horses attached side by side to the same evener. The resultant force
equals the sum of the two component forces. The _third_, may be
represented by a boat going across a stream, the resultant motion being
represented by the diagonal of the parallelogram formed by using the
lines that represent the motion of the stream and of the boat.
=74. Units for Measuring Force.=--Force is commonly measured in units of
weight: in pounds, kilograms, and grams. For example, we speak of 15
lbs. pressure per square inch and 1033.6 g. pressure per square
centimeter as representing the air pressure. It should be noted here
that the words pound, kilogram, and gram are used not only to represent
_weight_ or _force_ but also the masses of the objects considered. Thus,
one may speak of a pound-mass meaning the amount of material in the
object.
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