6. Four men raise an anchor weighing {1 1/2} tons, with a capstan (see Fig. 110) having a barrel 9 in. in diameter. The circle described by the hand-spikes is {13 1/2} ft. in diameter. How much force must each man exert? [Illustration: FIG. 100.--The Capstan.] 7. A bicycle has a 28-in. wheel. The rear sprocket is 3 in. in diameter,[H] the radius of the pedal crank is 7 in.; 24 lbs. applied to the pedal gives what force on the rim of the wheel? What will be the speed of the rim when the pedal makes one revolution a second? [H] Consider the diameter of the front sprocket as 6 inches. 8. Measure the diameters of the large and small pulleys on the sewing-machine at your home. What mechanical advantage in number of revolutions does it give? Verify your computation by turning the wheel and counting the revolutions. 9. What force is required with a single fixed pulley to raise a weight of 200 lbs.? How far will the effort move in raising the weight 10 ft.? What is the mechanical advantage? 10. In the above problem substitute a single movable pulley for the fixed pulley and answer the same questions. 11. What is the smallest number of pulleys required to lift a weight of 600 lbs. with a force of 120 lbs.? How should they be arranged? 12. A derrick in lifting a safe weighing 2 tons uses a system of pulleys employing 3 sections of rope. What is the force required? 13. Name three instances where pulleys are used to do work that otherwise would be difficult to do. 14. Draw a diagram for a set of pulleys by means of which 100 lbs. can lift 400 lbs. (5) THE INCLINED PLANE. EFFICIENCY =126. Efficiency.=--The general law of machines which states that the work done by a machine equals the work put into it requires a modification, when we apply the law in a practical way, for the reason that in using any machine there is developed more or less friction due to parts of the machine rubbing on each other and to the resistance of the air as the parts move through it. Hence the statement of the law that accords with actual working conditions runs somewhat as follows: _The work put into a machine equals the useful work done by the machine plus the wasted work done by it._ The _efficiency_ of a machine is the ratio of the _useful_ work done by it to the _total_ work done on the machine. If there were no friction or wasted work, the efficiency would be perfect, or, as it is usually expressed, would be 100 per cent. Consider a system of pulleys into which are put 600 ft.-lbs. of work. With 450 ft.-lbs. of useful work resulting, the efficiency would be 450 ÷ 600 = {3/4}, or 75 per cent. In this case 25 per cent. of the work done on the machine is wasted. In a simple lever the friction is slight so that nearly 100 per cent. efficiency is often secured.