CHAMBERS'S INFORMATION FOR THE PEOPLE. 



Fig. 20. 



wheel is used. Theoretically, then, the whole 

 virtue of the pulley resides in the flexible cord. 



It is only with the movable pulley that there is 

 a gain of power. The movable pulley is generally 

 attached to the weight or resistance, and moves 

 along with it. In the annexed 

 cut, a cord is carried from a 

 fixed point at A round a pulley 

 B, from which the weight is 

 suspended ; it is then made to 

 pass over a fixed pulley at C, 

 and the power is represented 

 by a hand drawing downwards. 

 The parts of the cord BA and 

 BC being equally stretched, 

 each sustains evidently half the 

 weight ; but the part of the 

 cord PC has the same tension 

 as the rest, therefore P pulls 

 down with a force equal to half the weight. A 

 single movable pulley, then, doubles the effect of 

 the power. The only effect of the fixed pulley C 

 is to change the direction ; if the hand were at C 

 pulling upwards, it would sustain just half the 

 weight. 



When the two cords, BA, BC, are not parallel, 

 besides sustaining the whole weight, they pull 

 against each other to a greater or less degree, and 

 are therefore stretched with a tension greater than 

 that due to half the weight. Part of the advantage, 

 then, is lost when the strings attached to the 

 movable pulley are not parallel. 



The secret of the saving of power in the mov- 

 able pulley lies in making the hook in the beam at 

 A support the half of the weight. It is as if there 

 were two hands, one at A, and another at C, sus- 

 taining the weight between them ; but, although 

 the hook A can thus act as a substitute for a hand 

 to sustain W at rest, it can take no share in lifting 

 W. In order to lift W one foot, the hand at C 

 must rise through two feet, or which is the same 

 thing the hand at P must descend through two 

 feet. We thus find the same principle in the 

 pulley that has been illustrated regarding the 

 lever. 



Technically, the wheel of a pulley is called a 

 sheaf j for protection and convenience, this sheaf 

 is ordinarily fixed with pivots in a mass of wood 

 called a block; and the ropes or cords are called 

 a tackle. The whole machine, fully mounted for 

 working, is termed a block and tackle. By causing 

 a wheel and axle to wind up the cord of a block 

 and tackle, the power of the lever is combined with 

 that of the pulley in the operation. 



Systems of Pulleys. 



Several pulleys are often used in combination, 

 forming a system of pulleys. There are various 

 modes of arrangement. One of the most com- 

 mon is that represented in fig. 21, and called the 

 ' First System/ in which the same cord passes 

 over all the pulleys, and the pulleys are divided 

 into two sets one set working in the same fixed 

 frame or block, and the other set in a movable 

 block to which the weight is attached. The cord 

 being the same throughout, the tension of all its 

 parts is the same ; and, therefore, neglecting any 

 slight want of parallelism among the cords, the 

 weight is equally distributed among the cords 

 i, 2, 3, and 4. As the cord at P has the same 

 au 



tension as the others, being, in fact, a continua- 

 tion of the same cord, P thus sustains a fraction of 

 W, depending upon the number of cords that join 



Fig. 21. 

 the movable block. 



Fig. 22. 



In the present case, P is 



W 

 one-fourth of W, or P = , or 4? = W ; so 



4 



that a weight of a cwt. at W would be sustained 

 by a weight of 28 Ibs. at P. 



Fig. 22 represents another mode, commonly 

 used in practical operations, of constructing a 

 system of pulleys on the principle of the same cord 

 passing over all the sheaves. As seven cords join 



W 



the lower block, P = . 

 7 



THE INCLINED PLANE. 



If AB (fig. 23) represent a horizontal plane, AC 

 will represent a sloping or iticlined plane. If 

 we suppose AC to be a ( , 



plank resting on the 

 ground at A, and with its 

 other end at C on the 

 edge of a platform, it is a 

 familiar fact, that a man 

 can roll a heavy cask A 

 from A to C, which it Fig. 23. 



would be far beyond his 



strength to lift perpendicularly from B to C. In 

 such a case, the inclined plane is used as a me- 

 chanical power. 



When a cylinder rests on a level plank, its 

 whole weight is supported by the reaction of the 

 plank, and it has no tendency to roll either way ; 

 but if one end of the plank be raised, however 

 slightly, the cylinder begins to roll, and a certain 

 force is required to keep it at rest. As the end is 

 more and more elevated, the restraining force 

 requires to be increased, and at the same time the 

 pressure on the plane becomes less, until, when 

 the plank comes into the upright position, it ceases 

 to sustain any pressure, and a force equal to the 

 whole weight of the cylinder is required to keep 

 the latter in its position. 



In order to find the relation of P to W in a 

 given inclined plane, we have recourse to the 

 resolution of forces. In fig. 24, which represents a 

 cylinder resting on a plane, and kept from rolling 

 down by a weight suspended over a pulley at p y 

 so placed that cp is parallel to AB ; let cf, drawn 



