gravity would be nearer the heavier in the ratio of its greater weight, and were one much heavier than the other, the centre of gravity would be within the larger. This is the case of the sun and the earth, the sun's mass being so much greater that the common centre of gravity of the sun and earth is very near the sun's centre. CHAPTER VII. WORK AND ENERGY. 49. Work.-Newton's first law of motion teaches us that a body at rest cannot set itself in motion, and that a moving body cannot change either the direction or speed of its motion, and that if any of these changes take place it is a proof that the body is acted upon by some external force. In the language of science, a force is said to do work on a body when it produces or maintains motion of any kind against resistance. Merely supporting a weight is not doing work, for there is no motion. produced. Under the term "motion" we must understand the visible motion of sensible masses as well as the invisible motion of the particles of a body. Hence, as will be understood better after other chapters have been read, heat produces motion and does work by moving the particles of a body so as to make it expand, and the electric current does work when it decomposes water or any other compound body. Work, therefore, in its widest sense, is the production of visible motion against resistance, or the production of any physical or chemical change. The mechanical work done by moving bodies against the attractive force of the earth is the simplest kind of work, and this work is measured in units called foot-pounds. A foot-pound is the amount of work done when a weight of 1 lb. is raised through a vertical height of 1 foot. If we raise a weight of 45 lbs. through a height of 7 feet, we do 45 X 7 315 foot-pounds of work. The measure of the work done by a force, therefore, is the product of the force into the space through which the body is moved in the direction of the force. We may say— Work = force X space = but we must be careful to remember that space means the distance through which the body is moved in the line of action of the force. If the body be displaced, not in the direction of the line of action of a force, but at some angle of inclination to it, then the distance in the line of action of the force must be calculated or obtained by geometrical construction. a heavy body is raised along a smooth inclined plane, the work done against gravity is measured by the product of the force into the vertical height of the plane, for gravity acts vertically downwards (par. 46). If a body be moved along a horizontal plane, no work is done against gravity, but work is done against the resistance of friction. As just explained, there are many other kinds of work besides that of moving heavy bodies. Breaking a stick or tearing paper is work done against the resistance of cohesion; heat does work upon a body internally by causing its molecules to have a more rapid vibratory motion, and externally by causing it to expand; and an electric current does work when it overcomes the force of chemical attraction and decomposes water into oxygen and hydrogen. 50. Energy.-Energy is the power of doing work possessed by any body or system of bodies; that is, it is that condition of a body which makes it capable of overcoming resistance of any kind. A body may possess energy either because it is in motion, or because it is in a position of advantage in consequence of work that has been spent upon it to place it in that position. A falling weight possesses the power of doing work, and has therefore energy, for it can move wheels or break asunder the particles of a sheet of glass on which it falls. Consider now a weight of 14 lbs. on the floor; it has no power of doing work, and is therefore devoid of energy. Now lift it up and place it on a shelf 10 feet high. In doing so work has been done upon it, but the work is not lost; it is stored up in the stone, and will be given back when the shelf is withdrawn and the stone allowed to descend. The stone on the floor had no energy, but the stone even at rest on the shelf had energy, for work had been spent upon it, and it was kept in its position of advantage only by the shelf preventing the action of gravity. The energy possessed by bodies is therefore in one of two forms or states: (a) Energy of motion, called also Kinetic or Actual Energy; (b) energy of position, called also Potential or Static Energy. The kinetic energy of a body is its power of doing work in consequence of the actual motion of the body or of its molecules. The potential energy of a body is its power of doing work in consequence of its position of advantage, or the position of advantage of its molecules. A coiled spring possesses potential energy in consequence of the position of advantage relative to each other occupied by the coils; while, when uncoiling and setting wheels in motion, the energy of the spring is kinetic. 51. Examples of the Kinetic Energy of Visible Motion.— Experiment 25.-Place a small weight on a piece of tissue paper stretched across a ring. The weight presses on the paper, but has not enough energy to tear it. Raise the weight about 2 feet and drop it, and its energy of motion now overcomes the resistance of the paper, and there fore does work. In a similar way we shall find that a thread which will support a weight at rest will be broken by the increased energy of the falling weight attached at one end, and that the energy of visible motion possessed by a falling weight fastened by a string to a spring-balance extends the spring of the balance more than when the weight hangs without motion. Other examples of kinetic energy are found in moving water that is able to turn a mill-wheel, in a vibrating tuning-fork that is setting the air in motion and so sending sound-waves through it, in a heated body whose vibrating molecules send out waves of radiant energy that set air in motion or turn water into All moving masses or moving molecules possess kinetic energy, that is, a capacity to do work in virtue of their motion. vapour. 52. Examples of Potential Energy. Whenever a body is raised to a height against the action of gravity, it possesses in its elevated position a stored-up power of doing work termed Potential Energy, or Energy of Position. This is the condition of a raised weight or a head of water in a reservoir. Similarly, whenever a body is in a state of strain in consequence of work done upon it it possesses, in consequence of the position of its molecules, potential energy. A coiled or stretched spring, a mass of compressed air in a gun, and a bent bow all possess potential energy, for they are all in a position to do work. As the body at a height falls to a lower position, or as the strained body recovers its size and shape, its energy becomes kinetic, and it gives up again the work that has been done upon it in order to place it in its position of advantage. 53. Transference of Energy.-Energy is often transferred from one body to another. When a body in motion strikes another at rest, a part of the motion possessed by the first body is transferred to the second, that of the first body being proportionately diminished. Kinetic energy or energy of motion has therefore been trans ferred from one body to another. Sus Experiment 26. Potential energy may also be transferred from one body to another. may be made to raise a weight, and in so doing the spring loses potential energy, and the raised mass gains it. Again, the potential energy of one body is often passing to another and becoming changed into kinetic, or vice versa. Examples of this transference and change will shortly be seen. It must be noted that in these transferences of energy there |