=123. Mechanical Advantage.=--A lever often gives an advantage because by its use one may lift a stone or weight which the unaided strength of man could not move. If the lever is used in lifting a stone weighing 500 lbs., the force available being only 100 lbs., then its _mechanical advantage_ would be 5, the ratio of _w:f_. In a similar way, the mechanical advantage of any machine is found by finding the ratio of the resistance or weight to the effort. What must be the relative lengths of the effort arm and resistance or weight arm in the example just mentioned? Since the effort times the effort arm equals the weight times the weight arm, if _f × D_{f} = w × D_{w}_, then _D_{f}_ is five times _D_{w}_. Hence the mechanical advantage of a lever is easily found by finding the ratio of the effort arm to the weight arm. Important Topics 1. Advantage of machines. 2. Machines cannot create energy. 3. Law of machines. 4. Six simple machines. 5. Lever and principle of moments. 6. Mechanical advantage of a machine. Exercises 1. Give six examples of levers you use. 2. Fig. 88_a_ represents a pair of paper shears, 88_b_ a pair of tinner's shears. Which has the greater mechanical advantage? Why? Explain why each has the most effective shape for its particular work. [Illustration: FIG. 88.--(_a_) Paper shears. (_b_) Tinner's shears.] 3. Find examples of levers in a sewing machine. 4. What would result if, in Art. 122, the 100 g. weight were put 25 cm. from O and the 50 g. weight 45 cm. from O? Why? Explain using principle of moments. 5. How is the lever principle applied in rowing a boat? 6. When you cut cardboard with shears, why do you open them wide and cut near the pivot? 7. In carrying a load on a stick over the shoulder should the pack be carried near the shoulder or out on the stick? Why? 8. How can two boys on a see-saw start it without touching the ground? 9. In lifting a shovel full of sand do you lift up with one hand as hard as you push down with the other? Why? [Illustration: FIG. 89.--The hammer is a bent lever. What is its mechanical advantage?] 10. Why must the hinges of a gate 3 ft. high and 16 ft. wide be stronger than the hinges of a gate 16 ft. high and 3 ft. wide? 11. When one sweeps with a broom do the hands do equal amounts of work? Explain. 12. A bar 6 ft. long is used as a lever to lift a weight of 500 lbs. If the fulcrum is placed 6 in. from the weight, what will be the effort required? Note: two arrangements of weight, fulcrum and effort are possible. 13. The handle of a hammer is 12 in. long and the claw that is used in drawing a nail is 2.5 in. long. (See Fig. 89.) A force of 25 lbs. is required to draw the nail. What is the resistance of the nail? 14. The effective length of the head of a hammer is 2 in. The handle is 15 in. long and the nail holds in the wood with a force of 500 lbs. Only 60 lbs. of force is available at the end of the handle. What will be the result?