Mechanics for Beginners with Numerous Examples - Bookswagon
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Mechanics for Beginners with Numerous Examples

Mechanics for Beginners with Numerous Examples


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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. 1867 Excerpt: ...right angle, so that OC=OD cos COD: thus when the three components are mutually at right angles a component is equal to the product of the resultant into the cosine of the angle between them. Also by Euclid, i. 47, we have OL=OCi+CI)'L=OCl+OE'1=OUi+OEl+OA2: thus when the three components are mutually at right angles the square of the resultant is equal to the sum of the squares of the three components. 266. The process of Art. 52 for determining the resultant of any number of forces acting on a particle is applicable whether the forces are all in one plane or not; the process in Art. 56 assumes that the forces are all in one plane: we shall now extend the latter process to the case of forces which are not all in one plane. 267. Forces act on a particle in any directions: required to find the magnitude and direction of tlieir resultant. Let O denote the position of the particle; let Op, Oq, Or, Os, ... denote the directions of the forces; let P, Q, R, S, ... denote the magnitudes of the forces which act along these directions respectively. Draw through O three straight lines mutually at right angles; denote them by Ox, Oy, Oz: and resolve each force into three components along these straight lines, by Art. 265. Thus P may be replaced by the following three components: P cos pOx along Ox, P cos pOy along Oy, and P cos pOz along Oz. Similarly Q may be replaced by Q cos qOx along Ox, Q cos qOy along Oy, and Q cos qOz along Oz. And so on. Let X denote the algebraical sum of the components along Ox; so that X--P cospOx + Q cos qOx + R cos rOx + S cos sOx +... Similarly let Y and Z denote the algebraicaf sums, of the components along Oy and Oz respectively. Thus the given system of forces is equivalent to the three forces X, Y, Z which act along three straight lines ...


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Product Details
  • ISBN-13: 9781130629088
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 86
  • Spine Width: 5 mm
  • Width: 189 mm
  • ISBN-10: 1130629082
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 168 gr

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