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[blocks in formation]

153. From the result of Problem 152, find the steam pressure per square inch if V is 11⁄2 in. in diameter on the bottom where exposed to the steam.

154. Figure 56 shows the clutch pedal for an automobile. What must be the length of the power arm a in order that a foot pressure of 15 lb. can open the clutch against a spring pressure of 60 lb. having an arm of 3 in.?

155. Figure 57 shows an old-fashioned windlass for raising water.

If

the crank is 15 in. long and the drum is 5 in. in diameter, what pressure will be needed on the crank to raise a pail of water weighing 30 lb.?

156. Figure 58 represents in an elementary way the levers of a pair of

5 lbs.

1000 lbs.

h

-301

FIG. 58.-Elementary diagram of levers on platform scales.

platform scales. How far from the fulcrum must the 5-lb. weight be placed to balance the 1000-lb. weight located as shown?

157. The hoist of Fig. 52 has an 18-in. crank; the drum is 10 in. in diameter; the diameter of the large gear is 30 in. and of the small gear 6 in. What weight can be raised by a force of 25 lb. on the crank?

158. Calculate the pull required on the crank of the windlass of Problem 155, assuming that the efficiency of the apparatus is 75%.

CHAPTER XIII

TACKLE BLOCKS; THE INCLINED PLANE AND SCREW

91. Types of Blocks.-When a heavy weight is to be raised or moved through any considerable distance, either a windlass, such as described in Chap. XII, or tackle blocks can be used. As shown in the illustrations of the tackle blocks in this chapter, the revolving part is called the pulley or sheave; the framework surrounding the pulleys is called the block and, as generally used, includes both the frame and the sheaves contained in it.

W

FIG. 59. Single pulley arranged FIG. 60. Single pulley arranged to to give no mechanical advantage. give mechanical advantage of 2.

In Fig. 59 we have a single pulley, which serves merely to give a change of direction. There is no mechanical advantage in a single fixed pulley such as this. The pull on the rope at P is transmitted around the pulley and supports W on the other side. We can look at the pulley in this case as a lever with equal arms. P on one end must equal W on the other end. Such a block would be used solely for the convenience it affords, since it is usually easier to pull down than up.

In Fig. 60 the pull P is in the same direction that W is to be moved and is only one-half of W. As explained in Art. 88, the M.A. of a machine can be obtained by comparing the distances moved by the force and the weight. If a force must move five times as far as it lifts the weight, then the M.A. is 5, and the force is one-fifth of the weight. In Fig. 60 the M.A. is 2. This can be seen by raising W a certain distance. The rope on each side will be shortened this same distance and, therefore, P must be drawn up twice this distance. Since P moves twice as far as W, the force P will be one-half of W, and the M.A. will be 2.

W

W

FIG. 61. Single pulley attached to weight arranged to give mechanical advantage of 2. Upper pulley merely changes direction of pull on rope.

FIG. 62.-System of pulleys arranged to give mechanical advantage of 4.

In Fig. 61 we have merely added, to the device of Fig. 60, a fixed block above to change the direction of P. It makes no change in the relation of P and W, except as to direction.

In Fig. 62 we have two pulleys in the fixed block and two in the movable block. More pulleys might be used, but the principle is the same. A general rule for calculating their M.A.'s can be worked out for all cases. Proceeding as before, let us imagine that W and the movable block of Fig. 62 are lifted 1 ft. The

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