(By "distance," as used in the equation, is meant the distance from the fulcrum; "Power distance meaning the distance of the power from the fulcrum.) Suggestive Applications of the Use of the Lever 370. 1. A man bears down 150 lb. on the outer end of a bar of iron 6 ft. in length, which he has pushed under a heavy stone, and supported by a fulcrum 6 in. from the stone. How many pounds of load does he lift on the stone? 2. A man using a 6-ft. bar of iron for a lever, pushes its end 6 in. under a heavy weight and raises up on the outer end, using 150 lb. of power. How much weight does he raise? 6 IN. 72 IN. 3. As one of the horses of his team is much stronger than the other, a farmer adjusts the evener SO that the stronger horse shall do the harder work. It is adjusted as shown in In a load of 2900 pounds how many pounds does each horse draw? 4. In a steelyard 24 inches long the distance from the weight hook to the fulcrum is 2 inches. How heavy a body can be weighed with a pound weight? 5. Two boys have a plank 18 ft. long, and wish to teeter, but one weighs 100 lb. and the other only 50 lb. Where will they fix the support that they may balance? 371. The wheel and axle and the windlass or capstan are but applications of levers. Power x length of crank = load x radius of the axle. 1. The diameter of the wheel, in a wheel and axle machine, is 8 feet, the diameter of the axle being 6 inches. What weight can be raised by a power of 100 pounds? 2. A horse pulls 100 pounds at the end of a lever 20 feet long, which turns an axle having a radius of 6 inches. What load is drawn on the rope around the axle? 372. The pulley is used either to change the direction of the pull or to increase its force. LIT CHANGE OF DIRECTION INCREASE OF FORCE P:W=1:2. P: W-1:4 373. To calculate the increase of force by the use of pulleys, we may use the equation: Power x the number of separate parts of the rope that sustains the weight = the force or load. 1. A man wishing to raise a piano to the secondstory window, adjusts the pulleys so that the weight is sustained by 4 parts of the rope. If the piano weighs 1000 pounds, how much power will it take to raise it when these pulleys are used? 374. The inclined plane is used to raise or lower heavy loads, by rolling them up or down an incline. To calculate the gain by its use we may use the proportion: = Power: load height raised: length of incline. 1. A man wishing to load a barrel of flour weighing 208 pounds (barrel included) into a wagon 3 ft. in height places a 12-ft. plank from the wagon to the ground and rolls the barrel up the incline. How many pounds of power does it take to move the barrel? 2. A man wishing to unload a barrel weighing 300 pounds from a wagon 3 ft. in height uses a 12-ft. plank as an incline, and also passes a rope around the barrel and fastens one end of the rope to the wagon, holding the other end. How much power does he use to hold the barrel as it rolls down the incline? (The wagon holds of the load by this arrangement.) Note. As the exercises in mechanical powers are only intended to be suggestive, further applications and the use of other powers is left to the teacher and pupils. SUMMARY Algebra deals with general applications, so that the solution of one problem forms a type for the solution of all similar problems. Some of its elementary principles may well be used, however, to aid in the solution of the problems which may also be solved by arithmetic. In the solution of a problem by algebra, we first form a statement from the terms of the problem, and in the form of equations which show the relation of the given to the required terms. Then from these equations we find the value of the required terms. Transposition is changing a quantity from one side of the equation to the other. This may be done by changing its sign as we pass the equation sign. Equations having terms expressed in fractional form may be cleared of fractions by multiplying each term by the least common multiple of the denominators of the fractions. When there are two or more unknown quantities in a problem, we must form from its conditions as |