A pulley is merely a modification of the wheel. Figure 15 shows how it may be arranged to correspond to the three orders of simple levers. If the pulley axis is fixed, as in the first order, the effort and weight arms are equal and hence balanced. In the second order the wheel is bodily movable, hence one pound will raise two pounds of weight because the power arm is twice as long as the weight arm, while in the third order it takes two pounds of lift to raise one pound of weight. There is no end of possible combinations of pulleys which will multiply power in the same way that bar levers do when compounded. A common arrangement of block and tackle is given in Figure 16. There is a four-sheave pulley block above and a three-sheave block below, but in order to trace the rope clearly the pulley wheels or sheaves are represented as of different diameters. The arrangement consists of a series of levers of the first order in the upper pulley block coupled to a series of levers of the second order in the lower block. To find the weight that a given power will lift, multiply the effort by the number of strands of rope that are supporting the weight. In this case there are seven such strands, not counting the strand E, to which the effort or pull is applied. This means that a pull of a hundred pounds at E will lift 700 pounds at W. Of course a pull of seven feet at E will raise the weight only one foot.
FIG. 17.—INCLINED PLANE WITH EFFORT PARALLEL TO THE INCLINED FACE
THE INCLINED PLANE AND ITS FAMILY
The inclined plane constitutes a second broad classification of machine elements. The wedge, the screw, the cam, and the eccentric, all belong to the family of the inclined plane.
FIG. 18.—INCLINED PLANE WITH EFFORT PARALLEL TO THE BASE
A simple form of inclined plane is pictured in Figure 17, which shows a weight W being rolled up an incline. The effort required to carry it to the top of the incline depends, of course, upon the steepness of the incline. The drawing shows a rise of 3 feet on a slope 5 feet long, and the weight of the wheel is, say 20 pounds. To find the effort required, the weight is multiplied by the rise (20 × 3 = 60) and divided by the length of the slope (60/5 = 12) and we find that it takes only 12 pounds to roll the 20-pound wheel to the top of the incline. This holds true when the pull is parallel to the inclined face. If the pull is parallel to the base of the incline, as in Figure 18, we must divide by the length of the base instead of the length of the incline (60/4 = 15) and we find that it takes 15 pounds of effort to pull the weight up the incline. If the pull is exerted at an angle both to the base and the inclined face, we have a problem that is slightly more complicated and we need not go into it here because it involves a bit of trigonometry. In all cases, however, it may be noted that the amount of rope that is taken in, in hauling the weight up the incline, bears a definite relation to the amount of effort required to raise the weight. In Figure 17, 5 feet of rope must be pulled in, in order to raise the weight 3 feet, so that ⅗ of 20 or 12 pounds is all that is required to pull up the weight, while in Figure 18, 4 feet of rope is hauled in for a lift of 3 feet, so that ¾ of 20 or 15 pounds is required to pull up the weight. In this respect the inclined plane is exactly like the lever or the pulley, for the effort multiplied by the distance through which it is exerted is always exactly equal to the weight multiplied by the distance through which it moves. Thus in Figure 17, the effort 12 pounds multiplied by the distance 5 = the weight 20 pounds times the distance 3, and in Figure 18, effort 15 x distance 4 = weight 20 x distance 3. Of course, we are ignoring the weight of the rope and the friction which, in actual practice, are important factors to be reckoned with.
