26. We shall first illustrate how a single force may be resolved into a
pair of forces; for this purpose we shall use the arrangement shown in
Fig. 10 (see next page).
The ends of a cord are fastened to two small spring balances; to the
centre E of this cord a weight of 4 lbs. is attached. At A and B are
pegs from which the balances can be suspended. Let the distances AE, BE
be each 12", and the distance AB 16". When the cord is thus placed, and
the weight allowed to hang freely, each of the cords EA, EB is strained
by an amount of force that is shown to be very nearly 3 lbs. by the
balances. But the weight of 4 lbs. is the only weight acting; hence it
must be equivalent to two forces of very nearly 3 lbs. each along the
directions AE and BE. Here the two forces to which 4 lbs. is equivalent
are each of them less than 4 lbs., though taken together they exceed it.
[Illustration: FIG. 10.]
27. But remove the cords from AB and hang them on CD, the length CD
being 1' 10", then the forces shown along FC and D are each 5 lbs.;
here, therefore, one force of 4 lbs. is equivalent to two forces each
of 5 lbs. In the last lecture (Art. 19) we saw that one force could
balance two greater forces; here we see the analogous case of one force
being changed into two greater forces. Further, we learn that the
number of pairs of forces into which one force may be decomposed is
unlimited, for with every different distance between the pegs different
forces will be indicated by the balances.
Whenever the weight is suspended from a point half-way between the
balances, the forces along the cords are equal; but by placing the
weight nearer one balance than the other, a greater force will be
indicated on that balance to which the weight is nearest.