The Elementary Principles of Mechanics; Statics. 1894 Volume 2

The Elementary Principles of Mechanics; Statics. 1894 Volume 2

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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. 1894 edition. Excerpt: ...sum of the moments about any point in the plane equal to zero. Take the point D and let the lever-arms be n, and n%. Then Ntn, -Nn, = 0 (3) We have from the figure, since -2 and n, are parallel to BC and AC, if 8 is the angle of the rod with the horizontal, ns = b cos (a, --6), ni = a cos (a, -f-6), and from (2) we have N, = sn "'2, . Substituting in (3), we have sin cti b cos (at--fl) = a---cos (a, + 6): sin i expanding and reducing, we obtain tan8 = -c-tg-.-ftcotg.a, (4) Also from (1) we obtain P sin at P sin a, N, = i--. r2--., Nt =-r--.; r (5) sin (a, + at) sin (tr, + a, ) v' If a = 90 and a, --0, or the plane BC is vertical and AC horizontal, we have from (4), 8 = 90, and from (5), N = P and N, = 0. That is, the position of equilibrium is when the rod is vertical and the end A is at C. If it has any other position, there is no equilibrium unless another force is introduced. (17) A rod AB of length I rests upon two smooth planes, one AC horizontal and tlie other BC vertical, and its inclination with the horizontal is 0. A load of P lbs. is applied at a distance AD = a from the end A. The rod is prevented from sliding by a string attached to C and the rod. If the inclination of this string with the horizontal is a, find the stress in it for equilibrium. Weight of the rod neglected. Ans. The forces acting upon the rod are the vertical weight P acting at D, the stress iS in the string, and the normal pressures N and Nt at A and B. We have then for equilibrium the algebraic sum of the vertical components equal to zero, or N-P-Ssin a = 0; (1) the algebraic sum of the horizontal forces equal to zero, or S cos p-Nt = 0; (2) p the algebraic sum of the moments about any point in the plane equal to zero. (18) A body is...show more

Product details

  • Paperback | 122 pages
  • 189 x 246 x 7mm | 231g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236503430
  • 9781236503435