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A Companion to Wrigley's Collection of Examples; Being Illustrations of Mathematical Processes and Methods of Solution

A Companion to Wrigley's Collection of Examples; Being Illustrations of Mathematical Processes and Methods of Solution


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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. 1861 Excerpt: ... /3 3. Let MKL represent the isosceles triangle on the inclined plane; O its centre of gravity. First suppose that the triangle begins to slide. Let R be the reaction of the plane perpendicular to itself, fi the coefficient of friction, and the inclination of the plane when sliding commences. Eesolving the forces parallel to the plane, we have (iR=W sin (i), and resolving at right angles to the plane, R = IF cos 0 (a), from (i) and (2) we have jj. = tan f. Next suppose that the triangle rolls over the corner K; then the vertical through G will pass through K when A has received the proper value; draw GH&t right angles to the plane; tlien Hence if /a be less than GH rolling. If M_gg-rolling will take place before sliding; and for rolling and sliding to take place simultaneously, we must, Gil have fi =-gg., or /i = = tan3' 4. Let AB be the rod, G its centre of gravity, which (since the rod is uniform) will be at its middle point; R the reaction of the plane CB; R that of the plane CA. Let the angle BAG = 6. Then the forces acting on the rod are, its weight (W) acting at G in the vertical GH, BJ at A, R at B, and the friction. Resolving parallel to BC, we have W-R-(jlro (1), Resolving parallel to CA, we have R-H!E = o (2). Also, taking the moments round G, we have R sin 0 + fiR cos 0-R cos 0 + fi'R.sin 0 = o (3). From equations (1) and (2) we have W and substituting these values in equation (3), we get 8. Let 0 and f represent the inclination to the vertical of the string and beam respectively; and let 1 = length of the beam, c the length of the string, and / the coefficient of friction. Suppose the beam to be on the point of sliding downwards, then it is maintained in its position by the reaction (R) of the plane in the direction BR; by the frictio...


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Product Details
  • ISBN-13: 9781130414677
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 32
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130414671
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 77 gr


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