An Elementary Treatise on Mechanics Volume 1

An Elementary Treatise on Mechanics Volume 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. 1819 edition. Excerpt: directions opposite to those of the forces;, then P, Vj + P3 v3 + = P, -, + P ut + Or we may express it thus; let -, - - vt be the velocities ia the directions of the forces, those which are opposite to them being taken negative; that is, v2=--ua, vt=s---4, .... then P, vt + P, vt + P3v3 + P44 +.... =0, which is called the Principle of Virtual Velocities. To prove this, assume a point any where in the machine; and let us suppose that in consequence of the nature of the system, when the points at which P1tP3 P, P4 act bave velocities v, v3, -, -4 this assumed point has a velocity w. Now since this assumed point is in the system, the force P, considered separately might be balanced by a force Q, acting at this point in a direction opposite to the velocity w, so that P, = Similarly P, will be balanced by 32 acting in the direction of the velocity w, so that Pj will be balanced by Q3 opposite to -/, so that P4 by m the direction of w, so that But since Plf Ptt P3, Pt balance, Q, &, Q3- Q," must balance; therefore Q, + Q3 +.... = & + &+., .. or Q, w+2jw +.... =2, w+Q4w+.... or P, + Psv, +.... = = Ptut + P4-t +.... or P, v, -P, -, + P3v3-Ptut +.... =0; or P, v, + P2 v, + P3 w3 + P4 w4 + =0. T. B. It is here supposed that if a force Q balance a force P, a force equal and opposite to Q will balance a force equal and opposite to P at the same points of the machine. In machines whose parts are flexible this is not true: thus, though two equal forces pulling the ends of a string balance, two equal forces pushing the ends of a string do not. The demonstration, however, will be complete if we suppose, as we may without affecting the conditions of equilibrium, that a string...
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Product details

  • Paperback | 88 pages
  • 189 x 246 x 5mm | 172g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236643089
  • 9781236643087