A Treatise on Statics; With Applications to Physics Volume N . 1

A Treatise on Statics; With Applications to Physics Volume N . 1

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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. 1907 edition. Excerpt: ...the point from which the forces emanate; let m, n, p be the feet of perpendiculars from O on AD, DC, CB, respectively; let Q be the foot of the perpendicular from / on DC; let IQ meet mO in L and pO in M; and let the forces in Oni, On, Op be k. AD, k.DC, k. CB. If AD turns round A through the small angle bf, the displacement of D is AD.bf; and if DC turns round / through 8co, the displacement of D is ID. 8co. Hence AD.bf = ID.ba. Similarly BC.80 = IC. Sco, if 80 is the angle through which BC turns round B. Now the equation of virtual work is k. AD. Am. Sf + k. DC. In. bw. cos InQ-k. BC.Bp. 80 = 0; or, by the first two equations, Am.ID + DC.nQ-Bp.IC = 0. (1) Now Im.ID= LI.IQ, and Ip. IC = IQ. IM; therefore Im.ID-Ip. IC = DM.IQ. (2) Adding (2) to (1), we have AI. ID-BI.IC = LM. IQ-DC.nQ. But the right side of this equation is zero, since the triangles DCI and LMO are similar (nQ is the altitude of the latter). Hence the quadrilateral ADCB is inscribable in a circle; and in this circle lie also the quadrilaterals DC BE, CBEF, ... and therefore the whole polygon. 10. Six equal heavy bars are freely jointed at their extremities; one bar is fixed in a horizontal position, and the system hangs in a vertical plane; the middle points of each pair of adjacent non-horizontal bars are connected by two strings in a state of tension. Show by the principle of work that, if the hexagon is regular in its position of equilibrium, the tension of each string is three times the weight of a bar. 11. Four bars whose weights may be neglected are jointed together by smooth pins and form a quadrilateral, ABCD, in a vertical plane. The joint A is fixed, while the lateral joints B and D rest each against a smooth fixed vertical plane. A given vertical force being applied at..show more

Product details

  • Paperback | 128 pages
  • 189 x 246 x 7mm | 240g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 123660346X
  • 9781236603463