Читать книгу Experimental Mechanics - Robert S. Ball - Страница 13

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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.

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.