having work done on it, the ability to do work itself and is able to keep the clock running. That which has been stored in a body and enables it to do work is called energy. The clock spring, in being wound, gains energy; and when it does work in driving the clock, it loses this energy. The work done in lifting the weight of a pile-driver gives it energy. When it falls, it can do work. When a rifle is fired, the exploding gases do work on the bullet, giving it energy; when the bullet strikes an object, it does work and loses its energy. In general, any body that is in such a condition that it is able to do work is said to have energy. 85. Measurement of energy. Today energy is a marketable commodity; it is commonly bought and sold. When one pays his electric-light bill, he pays for the amount of energy delivered to him; for electric meters are so designed that they indicate the amount of energy supplied. Many small factories and mills buy their energy from neighboring concerns. In order to buy and sell energy, methods must be devised for measuring it. Changes in the energy of any body or any machine are always associated with work. A boy throwing a baseball does a certain amount of work on the ball and loses a certain amount of energy; the energy gained by the ball is equal to the work the boy does. (This assumes that there are no frictional losses, that the boy does no work on the air. If he does, then part of the work he does gives some energy to the air.) If a weight of 100 pounds is lifted 10 feet, 1000 foot-pounds of work have been done, and the weight is said to have gained 1000 foot-pounds of energy. In falling it can do 1000 foot-pounds of work. The energy a body possesses is equal to the total work it can do. Energy is not always gained by a body when work is done on it. A wagon drawn at a constant speed on a level road is not gaining or losing energy. In that case all the applied force is used in overcoming friction. The work done is used to develop heat and noise, which are forms of energy. When the wagon goes up a hill or increases its speed, it gains energy, but on account of friction the gain in energy is less than the work done. If 30 per cent of able L the work is lost on account of friction, the energy gained by the wagon is equal to 70 per cent of the total work done and may be said to be equal to the net amount of work done on the wagon. In general, the loss in energy of a body may be measured by the work it does when losing energy, and the gain in energy of a body may be measured by the net amount of work done on it. 86. Two forms of energy. Bodies can possess energy in a great many different ways. In general there are two classes: 1. Bodies in motion have energy, for in losing their speed they can do work. That form of energy which is due to motion is called kinetic energy. A moving train or automobile, a ball or a bullet in flight, a rotating flywheel, have kinetic energy. 2. All other forms of energy are called potential energy. The more common cases of potential energy may be grouped under three heads: (a) Potential energy may be due to the position of a body with respect to the ground. A stone on top of a building, water in an elevated reservoir, and the lifted weight of a pile-driver have potential energy because of their position. (b) Potential energy may be due to the distortion of an elastic body. A stretched or compressed spring has potential energy. (c) Potential energy may be possessed by those substances that can do work through some chemical action. Thus the energy of coal, gasoline, foods, etc. is potential energy of this type. 87. Transformation of energy. Simple observation reveals many cases where energy changes from one form to another. A boy sitting in a swing is pulled out to one side, and thus raised off the ground. The work done gives him potential energy. When released he swings back, losing his potential energy and gaining energy of motion, or kinetic energy. As he passes the lowest point and goes toward the other end, he loses kinetic energy and again gains potential energy. A vibrating clock pendulum is a similar case of the continuous changing of energy from one form to another. In Fig. 72 are shown an axle and a flywheel. When the rope is wound around the axle, the heavy weight is lifted and gains potential energy. When it falls, this potential energy changes into kinetic energy of the flywheel and of the weight. Part of the energy is stored in the wheel. When the weight strikes the floor, the wheel and axle will keep on running, winding the rope up on the axle and lifting the weight. This storing of energy in a flywheel is very common. In a gas engine the energy is not supplied continuously, but at intervals. It is the energy stored in the flywheel that makes it possible to get from this engine a nearly uniform supply of energy. Many types of machines have flywheels which help maintain an approximately uniform speed. where the velocity v is in feet per second. For example, a certain train has a weight of 1000 tons and a speed of 30 miles per hour. A city electric-power plant affords an illustration of complicated transformations of energy. Part of the energy in coal is converted into energy of steam. By means of an engine this is changed into energy of moving machinery, then by the FIG. 72 aid of a dynamo into electrical energy, which is transmitted over wires and, at some distant point, is changed into light, or heat, or energy of moving machines. Since the temperature of a man is usually higher than his surroundings, he is continually losing energy in the form of heat. He loses energy, also, on account of the physical work he does. To compensate for these losses a moderately active man must receive daily about 10,000,000 foot-pounds of en energy (sect. 225). This he must get from the food he eats. 88. Method of computing kinetic energy. The kinetic energy of a body is equal to the net amount of work that must be done on it to give it this energy. By taking a simple case it is possible to prove that this work is equal to (mass of body) × (square of its speed). Suppose that in throwing a baseball a constant force Facts while the ball is displaced a distance s. This force will produce a uniform acceleration a, the force and the acceleration being related by equation (21), F = ma. The work done by the force is, by equation (39), W = Fs, where s is the displacement while the force is acting. If the value of F from equation (21) is substituted in this equation, W=mas. But when a body moves with a constant acceleration (equation (12)), s = at2. Substituting this value of s, W = ma(at2) = 1⁄2 ma2t2. But the velocity the ball acquires when it has a uniform acceleration a is given by equation (11), v=at. If this is now substituted in the preceding equation, we have, as the net work done on the ball, In the C.G.S. system when mass is measured in grams, and velocity in centimeters per second, the energy as computed by this formula will be in ergs. For example, a bullet having a mass of 15 grams and a velocity of 700 meters per second will have a kinetic energy equal to (15) × (70,000)2 = 3.675 × 1010 ergs = 3675 joules. When B.E. units are used, the weight will probably be given in pounds. In that case it will be more convenient to change the form of equation (44), substituting weight/32 for the mass m (see section 66). We then have Kinetic energy in foot-pounds = 1 weight 2 32 Hence Kinetic energy = 1000 × 2000 X 442 = 60.5 × 106 ft.-lb. = 30,250 foot-tons. 89. Method of computing potential energy. The potential energy of anything is always measured by the net work done in giving it that energy or by the work it does in losing that energy. For example, in the case of a weight raised a certain height the potential energy is equal to the product of the weight in pounds times the height in feet. This is true because the product of weight times the height is the work done. For B.E. units the potential energy of an elevated weight is Potential energy = weight X height, (46) giving foot-pounds of energy if the weight is in pounds and the height in feet. If C.G.S. units are used, and the mass m in grams is given, the weight of the mass is mg dynes (sect. 66), and Potential energy = mgh, = 980 mh ergs (approximately) when the height h is in centimeters. (47) In those cases where it is not a case of elevating a weight, the potential energy is determined either by computing the net work required to put the body in the condition where it has the energy or by the total work it does in losing that energy. A wound clock spring may have its energy determined by measuring the forces and distances through which these forces act when it is wound. The potential energy of coal is determined by experimentally measuring how much heat energy it develops when burned. In general, the potential energy of a body can be determined either by the net work done in giving it that energy or by the total work it does when it loses that energy. |