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(1818-1889) t

English physicist, born at Manchester; most prominent figure in the establishment of the doctrine of the conservation of energy; studied chemistry as a boy under John Dalton, and became so interested that his father, a prosperous Manchester brewer, fitted out a laboratory for him at home; conducted mostofhis researches either in a basement of his own house or in a yard adjoining his brewery; discovered the law of heating a conductor by an electric current; carried out, in connection with Lord Kelvin, epoch-making researches upon the thermal properties of gases; did important work in magnetism; first proved experimentally the identity of various forms of energy


JAMES WATT (1736-1819)

The Scotch instrument maker at the University of Glasgow, who may properly be considered the inventor of the steam engine; for, although a crude and inefficient type of steam engine was known before his time, he left it in essentially its present form. The modern industrial era may be said to begin with Watt

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This picture shows the relative sizes of Stephenson's original locomotive, the Rocket, which ran in October, 1829, between
Manchester and Liverpool, and the largest locomotive thus far built, the Virginian Mallet, constructed in the shops of the
American Locomotive Company at Schenectady, New York, for use on the Virginian Railroad. The Rocket weighed 4 tons
and won a £500 prize by drawing a coach containing thirty people at a rate of from 26 to 30 miles per hour. The Virginian
Mallet weighs 450 tons and has a tractive power of 176,600 pounds. Its horse power is approximately 5100


2 A


is lifted from the first position in Fig. 141 through a height of 1 m. and placed upon the hook H at the end of a cord which passes over a frictionless pulley p and is attached at the other end to a second kilogram weight B. The operation of lifting A from position 1 to position 2 has required an expenditure upon it of 1 kg. m. (100,000 g. cm., or 98,000,000 ergs) of work. But in position 2, A is itself possessed of a certain capacity for doing work which it did not have before; for if it is now started downward by the application of the slightest conceivable force, it will, of its own accord, return to position 1, and will in so doing raise the kilogram weight B through a height of 1 m. In other words, it will do upon B exactly the same amount of work that was originally done upon it.


FIG. 141. Illustration of potential


146. Potential and kinetic energy. A body may have a capacity for doing work not only because it has been given an elevated position but also because it has in some way acquired velocity; for example, a heavy flywheel will keep machinery running for some time after the power has been shut off, and a bullet shot upward will lift itself a great distance against gravity because of the velocity which has been imparted to it. Similarly, any body which is in motion is able to rise against gravity, or to set other bodies in motion by colliding with them, or to overcome resistances of any conceivable sort. Hence, in order to distinguish between the energy which a body may have because of an advantageous position, and the energy which it may have because it is in motion, the two terms "potential energy" and "kinetic energy" are used. Potential energy includes the energy of lifted weights, of coiled or stretched springs, of bent bows, etc.,-in a word, potential energy is energy of position, while kinetic energy is energy of motion.

147. Transformations of potential and kinetic energy. The swinging of a pendulum and the oscillation of a weight attached to a spring illustrate well the way in which energy which has once been put into a body may be transformed back and forth between the potential and kinetic varieties. When the pendulum bob is at rest at the bottom of its are, it possesses no energy of either type, since, on the one hand, it is as low as it can be, and, on the other, it has no velocity. When we pull it up the arc to the position A (Fig. 142), we do an amount of work upon it which is equal in gram centimeters to its weight in grams times the distance AD in centimeters; that is, we store up in it this amount of potential energy. As now the bob falls to C this potential energy is completely transformed into kinetic energy. That this kinetic energy at C is exactly equal to the potential energy at A is proved by the fact that if friction is completely eliminated, the bob rises to a point B such that BE is equal to AD. We see, therefore, that at the ends of its swing the energy of the pendulum is all potential, while in the middle of the swing its energy is all kinetic. In intermediate positions the energy is part potential and part kinetic, but the sum of the two is equal to the original potential energy.





FIG. 142. Transformation of potential and kinetic


148. General statement of the law of frictionless machines. In our development of the law of machines, which led us to the conclusion that the work of the acting force is always equal to the work of the resisting force, we were careful to make two important assumptions: first, that friction was negligible; second, that the motions were all either uniform or so slow that no appreciable velocities were imparted. In other words,

we assumed that the work of the acting force was expended simply in lifting weights or compressing springs, — that is, in storing up potential energy. If now we drop the second assumption, a very simple experiment will show that our conclusion must be somewhat modified. Suppose, for instance, that instead of lifting a 500-gram weight slowly by means of a balance, we jerk it up suddenly. We shall now find that the initial pull indicated by the balance, instead of being 500 g., will be considerably more, — perhaps as much as several thousand grams if the pull is sufficiently sudden. This is obviously because the acting force is now overcoming not merely the 500 g. which represents the resistance of gravity, but also the inertia of the body, since velocity is being imparted to it. Now work done in imparting velocity to a body, that is, in overcoming its inertia, always appears as kinetic energy, while work done in overcoming gravity appears as the potential energy of a lifted weight. Hence, whether the motions produced by machines are slow or fast, if friction is negligible the law for all devices for transforming work may be stated thus: The work of the acting force is equal to the sum of the potential and kinetic energies stored up in the mass acted upon. In machines which work against gravity the body usually starts from rest and is left at rest, so that the kinetic energy resulting from the whole operation is zero. Hence in such cases the work done is the weight lifted times the height through which it is lifted, whether the motion is slow or fast. The kinetic energy imparted to the body in starting is all given up by it in stopping.

149. The measure of potential energy. The measure of the potential energy of any lifted body, such as a lifted pile driver, is equal to the work which has been spent in lifting the body. Thus, if h is the height in centimeters and M the weight in grams, then the potential energy P.E. of the lifted mass is



Mh gram centimeters.


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