Читать книгу Experimental Mechanics - Robert S. Ball - Страница 24

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72. In one case, however, two parallel forces have no resultant; this occurs when the two forces are equal, and in opposite directions. A pair of forces of this kind is called a couple; there is no single force which could balance a couple,—it can only be counterbalanced by another couple acting in an opposite manner. This remarkable case, may be studied by the arrangement of Fig. 23.

Fig. 23.

A wooden rod, a b 48"×0"·5×0"·5, has strings attached to it at points a and d, one foot distant. The string at d passes over a fixed pulley e, and at the end p a hook is attached for the purpose of receiving weights, while a similar hook descends from a; the weight of the rod itself, which only amounts to three ounces, may be neglected, as it is very small compared with the weights which will be used.

73. Supposing 2 lbs. to be placed at p, and 1 lb. at q, we have two parallel forces acting in opposite directions; and since their difference is 1 lb., it follows from our rule that the point f, where d f is equal to a d, is the point where the resultant is applied. You see this is easily verified, for by placing my finger over the rod at f it remains horizontal and in equilibrium; whereas, when I move my finger to one side or the other, equilibrium is impossible. If I move it nearer to b, the end a ascends. If I move it towards a, the end b ascends.

74. To study the case when the two forces are equal, a load of 2 lbs. may be placed on each of the hooks p and q. It will then be found that the finger cannot be placed in any position along the rod so as to keep it in equilibrium; that is to say, no single force can counteract the two forces which form the couple. Let o be the point midway between a and d. The forces evidently tend to raise ob and turn the part o a downwards; but if I try to restrain o b by holding my finger above, as at the point x, instantly the rod begins to turn round x and the part from a to x descends. I find similarly that any attempt to prevent the motion by holding my finger underneath is equally unsuccessful. But if at the same time I press the rod downwards at one point, and upwards at another with suitable force, I can succeed in producing equilibrium; in this case the two pressures form a couple; and it is this couple which neutralizes the couple produced by the weights. We learn, then, the important result that a couple can be balanced by a couple, and by a couple only.

75. The moment of a couple is the product of one of the two equal forces into their perpendicular distance. Two couples tending to turn the body to which they are applied in the same direction will be equivalent if their moments are equal. Two couples which tend to turn the body in opposite directions will be in equilibrium if their moments are equal. We can also compound two couples in the same or in opposite directions into a single couple of which the moment is respectively either the sum or the difference of the original moments.