direction does the wind seem to come, and what velocity does it seem to have? 16. A weight of 300 lb. is suspended from a pole resting on the shoulders of two men. If one man carries three fifths of the load, and is 4 ft. from the weight, how far is the other man from it? 17. Two parallel forces, one of 36 lb. and one of 64 lb., act on one side of a wooden bar at a distance of 9 ft. from each other. Where must a third parallel force be applied to keep the bar in equilibrium? How great a force must it be and in what direction must it act? 18. A weight of 32 lb. is suspended from a hook at A, by a cord AB. A second cord is tied at B and this is pulled horizontally in the direction BC until the cord AB makes an angle of 30° with its original vertical position. Find the pull on BC and the tension on A. Solve graphically. Suspend any weight, attach the hook of a spring balance at B, and prove experimentally. 19. An ocean steamer is going northeast at the rate of 400 mi. per day (24 hr.). How far north is she going per hour? How far east? BC 326 FIG. 46 causes it to take a What is the hori 20. A balloon rises with a vertical velocity of 138 ft. per minute, while the wind path making an angle of 60° with the ground. zontal velocity of the wind? What is the speed of the balloon? Solve graphically. 21. Three boys carry a boat that weighs 250 lb. The center of gravity or point of application of the weight of the boat is 8 ft. from the stern. One boy lifts from the stern and the other two from a cross stick placed underneath the boat. How far from the center of gravity must the cross stick be placed if each boy lifts the same amount? How far must it be if the two boys carry three fourths of the boat? 22. At New York a ball weighing 9 lb. is swinging around a circle 5 ft. in diameter with a velocity of 22 ft. per second. What pull must be used to keep the ball in its path? 70. Energy. II. ENERGY AND WORK The head of a pile driver (Fig. 47) falling upon a pile forces the pile into the ground to a depth which FIG. 47. Pile Driver depends upon the weight of the head and the height from which it falls. Increase either, and its capacity for doing work, that is, its energy, is increased, and the pile is driven farther into the ground. If we watch the engine of a pile driver while it is pulling the iron head to the top of the frame, we shall see that it is doing work. When the head has been raised and is held in position, the work of the engine stops, but the steam pressure is still there ready to be used at short notice. Steam under pressure is said to possess energy. Energy may be defined as the capacity for doing work. It is measured by the amount of work it is capable of doing. 71. Potential Energy.-We have only to loosen the catch which holds the head in place to find that the head also is ready to do work. When the catch is loosened, the head falls, strikes upon the top of the pile, and its capacity for doing work is shown by driving the pile into the ground. If the head is again raised, but only half as high, it will be found on dropping it that but half as much work is done. This shows that the height from which the head falls must be taken into account, as well as the weight of the head itself. The energy that a body has on account of its position is called potential energy. The work that has been done on a body to place it in a certain position is the measure of its potential energy. This measure is expressed by the equation P.E. Wh, = (19) in which W is the weight of the body and h is its vertical height above the point with reference to which its potential energy is measured. Energy is measured in the same units. as work. For instance, the potential energy of a 10-lb. weight ready to fall 6 ft. is 60 foot pounds. 72. Kinetic Energy. When the head strikes the pile, the work that had been stored up as potential energy in raising the head to its position of rest becomes available on account of the velocity acquired in the fall. This form of energy which is dependent upon the velocity of a body is called kinetic energy. The work that has been done on a body to give it a certain velocity is a measure of its kinetic energy. We have already learned that work force X distance, and that force (in absolute units) = mass X acceleration; hence we may write as an expression of kinetic energy, = = But (Formula 4) Sat2; hence K.E. Ma22, and = in which is the velocity per second, and K.E. is expressed in absolute units. If K.E. is to be expressed in gravity units, Since g (at New York) is 32.16 ft., the formula may be when the weight is given in pounds, the velocity per second in feet, and the result is required in foot pounds. 73. The Transformation of Energy. The pendulum affords a ready means of showing that potential energy may C P A E FIG. 48 B be changed into kinetic, and vice to raising it through the vertical distance DB. At B it has potential energy only, and if it is allowed to swing, it will move down the arc, losing potential energy and gaining kinetic, until it reaches A, when its energy will all be kinetic and will be sufficient to carry it up the other branch of the arc to the point C, a distance CE above the horizontal line, practically equal to DB; and here its energy is again all potential. If a spiral spring, the spring for a screen door, for example, is used as the suspending cord, and a kilogram weight for the pendulum bob, a further transformation takes place, the to-and-fro vibration changing into a vertical vibration and then back again repeatedly. The kinetic energy of the pendulum is employed in raising it against the force of gravity and restoring its potential energy. The case of a rifle ball striking against a stone wall is somewhat different. The motion of the ball is stopped and its kinetic energy is transformed chiefly into mechanical work and heat, for the ball itself is shattered, the wall is defaced, and if the velocity is very great, heat enough is produced to melt part of the ball. The potential energy stored in coal may be transformed into heat energy by combustion, this into kinetic energy, if applied to a boiler and steam engine, and this into electrical energy, if the engine is used to turn a dynamo. When a ball is fired 74. The Conservation of Energy. from a rifle, none of the energy that is developed by the combustion of the powder is lost, but it is all transformed into other forms of energy. Both the rifle and the ball are put in motion, producing kinetic energy; the air is thrown into vibration, producing sound; the ether is thrown into vibration, producing light; and to these results must be added the heat of the combustion. The sum of all these forms of energy is equal to the potential energy of the powder, and there is no loss. By extending the consideration to all kinds of transformation of energy, scientists have reached the conclusion that energy can neither be created nor destroyed, and hence that the total amount of energy in the universe is constant. The pile driver is a good example of both the transformation and the conservation of energy. As the head rises from the top of the pile the work of the engine gives it potential energy. The measure of this is the amount of work it is capable of doing. This is changed into kinetic energy as |