# The Mechanics of Engineering

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1908 edition. Excerpt: ...potential energy would be gained. In unstable equilibrium, then, the potential energy is a maximum. I If potential energy is neither lost nor gained, the equilibrium is said to be indi erent, and the particle in its new position is still in equilibrium. Now when potential energy is lost, kinetic energy is gained, and conversely. Hence if a particle is in equililirimzz, static or molecular, all t/1! acting' forces must constitute a system of forces in equilz'brz'm/z. If tlzr potcntial cncrgy 13' ll Illitililllllflli I/If F911!'/IV rium is stable and t/ze kinetic energy, if any, a ma.ri/mun. If the potential energy is a 1/zaximum, t/te equilibrium is unstable and the kinetic energy, if any, a minimum. If I/ze potential energy does not e/iange, t/ie equilibrium is indiflerent and t/ie kinetic energy, if any, does not e/range. I1luSt1'ati0n.--Take the case of a pendulum. Let 1 be the length and m the mass of-the bob. Disregard the mass of the string. When the bob is at the lowest point the potential energy is 1 mg. It. For every possible displacement /1 increases and the potential energy increases. The potential energy is then a minimum. This, then, is a position of stable equilibrium. If the bob is at rest, 5;, Eh it is in stable static equilibrium. If the pendulum swings, when it---------'--------arrives at its lowest point the kinetic energy is a maximum and the potential a minimum, and at the instant it is in stable kinetic equilibrium. When the bob is at the highest point the potential energy is a maximum. This, then, is a position of unstable equilibrium. If the bob is at rest, it isin unstable static equilibrium. If in motion, when it arrives at the highest point the kinetic energy is a minimum and the...