This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1851 Excerpt: ...T, acting in the direction BA, and Ta in the direction BC. Hence resolving horizontally and vertically we have, sinTsinfl2 (1) I, cos0, -T2cos0s=-', (2) We shall have two similar equations for each weight; suppose there are n of them, then we shall have 2 n equations. Let us consider how many unknown quantities there ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1851 Excerpt: ...T, acting in the direction BA, and Ta in the direction BC. Hence resolving horizontally and vertically we have, sinTsinfl2 (1) I, cos0, -T2cos0s=-', (2) We shall have two similar equations for each weight; suppose there are n of them, then we shall have 2 n equations. Let us consider how many unknown quantities there will be. There are n + 1 strings, therefore there will be n +1 unknown forces Tt T2 Ta+, and n + 1 unknown angles 0, 02 0 +i; on the whole then there will be 2n + 2 unknown quantities; but there are only 2n mechanical equations, therefore we must have two geometrical. One of these will be the following, which arises from the fact of AG being given, a, sin 0, + a2 sin 0s + + a +, sin 6., = c. (A) The other is obtained thus; let D be the lowest point of the festoon, and let Wr be the weight which hangs at D, then the vertical distance of D from AG is -! cos 0! + a3 cos 02 + &c. + ap cos 0; but the same vertical distance is also equal to oi cos 0, +i + + - +, cos 0.H;.-. 0,0080!+ +flt, cos0, = alH., cos0JH.I + + a +, cos0W, . (B) Thus we have obtained the 2 n + 2 equations required. To complete the solution of the problem so far as it can be completed, let us write down equation (2) and all those of the same class: and to simplify the problem we will consider all the weights equal, then T1 cos 0, -T2 cos 0, = W, T2 cos 0a-T2 cos 03 = W, subtracting the second of these equations from the first, we have Tl cos 0, -2 T, cos 6, + T2 cos 0 = 0. But by (1) T, sin 0, = T2 sin 0, and in like manner, T2ivD.6, -7,3sin02, .." Tl sin 0, = T% sin 6, = T3 sin 03 = suppose;. T _ T =----7 = A "' 'sinff, ' 'sin0, ' 3 sin0, ' Hence our equation becomes A cos 0, X cos 02 x cos 0, _ sin 0l sin 0S sin 0S' or cot 0, + ...
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Add this copy of Elementary Mechanics to cart. $66.41, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2016 by Palala Press.
