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Mechanics for practical men; containing explanations of the principles of mechanics, the steam engine, with its various proportions, parallel motion, ... with practical rules, adapted to the commones - Softcover
Synopsis
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. 1833 Excerpt: ...give rotation to a body or system the weight of which is W, and the distance of the centre of gyration from the axis of motion equal = d, then the accelerating force._ Pf' J p r« + W d2 But if the body or system be put in motion by a power P acting over a pulley, then the inertia of P is nothing. The distance d of the centre of gyration, in some of the most useful cases, is as follows:--In a circular wheel of uniform thickness. d = r /2 In the circumference of a circle revolving about diameter--"'A '-d = % r A/2 In the plane of a circle ditto---d = i r In a solid sphere ditto---d = r t/% In a circular ring, the radii of which are R and r revolving about the centre d = vl--1 In a cone revolving about its vertex d = Z(3 ffl2 + y r2) In a cone revolving about its axis-d = r / In a straight lever, the arms of which are R andr.....-d = vQJ In a paraboloid, the radius of the base of which is R d = R1/J Example 1. A cylinder, the weight of which is 80 lbs. is put in motion by a weight of 20 lbs. attached to a string which is coiled round the cylinder. How far will the weight descend in 6 seconds? The accelerating force/ =----. Here, P = 20 lbs. W = 80 lbs. and d = $ r V2. Pr2 P J-2 P 20 + 40 That is, the accelerating force is g of the accelerating force of gravity; and by formula, page 82, s = 16ft ft-16 x h x 6 = 193 feet. If the cylinder had been put in motion by a power P without inertia, such as the exertion of animal strength, then, since the inertia of P is nothing, we have the acce In Dr. Gregory's Mathematics for Practical Men, this is 3--_ ); but it may be reduced so as to agree with the above, as follows:--.( R4-r =.S (R + r ) x (R-r ) ) V2R--2r' V 2(R2--r ) J taring force = £ = = =-. And the angular velocity may be found as follows r--Eve...
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