First Principles of Mechanics

In our last number we had occasion to introduce a single pulley, but without any explanation of the nature thereof, as an illustration of principle. The pulley is one of the many modifications of the lever: this will appear plain when it is observed that two balls suspended by a cord which passes over a pulley, as in Figure 1, they will counterbalance each other in the same manner that the two balls do on a straight lever, as represented in the last number. The small pin in the centre of the pulley is termed the axle, and corresponds to the fulcrum which is used in connection with the straight lever. But if two pulleys are mounted on the same axle, and one of them is twice as large in diameter as the other, as in figure 2, then a ball suspended from the periphery of the large pulley will balance one of double its weight, which shall be suspended from the opposite side of the small pulley: thus the ball B has as great an influence on the pulley, as A, although it is only half as heavy; and the reason of this is, that in case of motion in the pulley, B would move with double the velocity of A:—in other words, A can not descend one inch, without raising B two inches at the same time; hence, the power is equal. On the same principle, if a wheel five-feet in diameter is mounted on a shaft which is only six inches in diameter, then one lb weight suspended from the periphery of the wheel, will be sufficient to counterbalance ten lbs. suspended from the opposite side of the shaft. The ball C in figure 3, is suspended from the axle of the pulley D; and one end of the cord which sustains this pulley is made fast at E, while the other end, after passing over the pulley E, terminates at the ball G: in this case the ball G will sustain a ball of double its own weight at C. In this instance the pulley D being a lever, the fastened end of the cord, is the fulcrum; the force is received from the ball G, and is applied to the ball C: or rather, this would more strictly be the case, if G was a little more than half as heavy as C, so as to produce motion by descending. In figure 4, the cord being made fast at H, passes under two pulleys, and over two. By this arrangement, there is a double leverage gained in each of the pulleys I and J, so that the ball R will sustain four times its weight at L; this fact we shall illustrate by remarking, that the ball L being attached to both pulleys I and J, is suspended by a four-fold cord: so that if this ball is made to descend one inch, the length of each section of the cord, must be extended an inch, making four inches in all; and consequently the ball K will be elevated four inches; reversing the motion, the ball K must descend four inches to raise L one inch. Thus, a man hauling down a cord at K would be able to hoist four times his own weight at L; and this will sufficiently illustrate the principle of pulleys in general. The windlass, which is another modification of the lever principle, is a simple horizontal cylindrical shaft, having a pivot or axle at each end, and several holes in the sides thereof, in which are occasionally inserted a kind of wooden bars called liand spikes, and by means of which the shaft is turned. A powerful draught is thus produced on a rope or chain attached to the shaft, and winding round it. The capstan, is a vertical windlass having a projecting circular head in the periphery of which the hand spikes are inserted, and by which the capstan is made to revolve; the operators walking round in a circle. In our next number we shall introduce the Inclined-plaue, Wedge, Screw and Toggle; and endeavour to show that they are all but so many modifications of the lever principle.