Elementary Mechanics of Solids and Fluids (Paperback)

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. 1893 edition. Excerpt: ...straight or curved, constrained to turn round a fixed axis called the Fulcrum. Let ACB represent the Lever, C the point where the axis meets the plane of the forces, W the Resistance, P the Driving Force. Draw Cm, Cn perpendicular to Am, Bn, the lines of action ofPandr. If the lever is pivoted on a smooth hinge at C, no work is done by the resistance at C during displacement. Let the weight of the lever be negligible in comparison with P and W. The condition of uniform motion, or of equilibrium, is obtained by taking moments round C, and is P.Cm= W.Cn. Thus a Driving Force P at A can balance a Resistance W at B, and by suitably cboosing the magnitudes of Cm. W and Cn, the rat1o-p can be made as great or as small as we please. W..p-is called the Mechanical Advantage. Levers have been divided into three classes in which the Fulcrum, the Resistance, and the Driving Force respectively occupy the middle position. The crowbar or spade is a lever of the first kind; a pair of nutcrackers, a wheel-barrow, and an oar are levers of the second kind; a pair of tongs, used for lifting coal, is a lever of the third kind. The relation Pvl + JFv2 = 0, shows that, the greater the Vet efficiency, the smaller is the ratio--That is, the greater the efficiency, the slower is the motion of B when the speed of A is constant. This may be expressed by the statement--' what is gained in efficiency is lost in time.' In many cases, the directions of P and W are parallel, and ACB is straight. Then.=-= Mechanical Advantage. 3. The Balance. The Balance is a form of lever, which is employed to determine the mass of a body, by comparison of its weight with the weight of one or more known masses. As the masses of bodies are proportional to their weights, this is...