The American Mathematical Monthly; The Official Journal of the Mathematical Association of America Volume 2

The American Mathematical Monthly; The Official Journal of the Mathematical Association of America 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. 1895 edition. Excerpt: ...department should be sent to him. SOLUTIONS OF PROBLEMS. 20. Proposed by CHAS. E. MYERS, Canton, Ohio. A flexible cord of given lcogth is suspended from two points whose co-ordinates are (x, y, ) and (-', y'). What, must be the condition of the cord in order that it may hang in the arc of a circle? Solution by WILLIAM HOOVER, A. M-, Ph. D Professor of Mathematics and Astronomy, Ohio University, Athens, Ohio. Taking the lowest point for origin, and the horizontal and vortical lines through it for axes of x and y, and s--ap...... (1) for the intrinsic equation to the circle. If?r= the constant horizontal component of tension at all points of the cord, the law of mass as given by Theoretical Mechanics is (3). dx cosp dx Cob cp ds dx a cos3 p Then (2) gives m=---: ----=.----(4), or the mass unit g a-cos9- (a--y)' varies inversely as the s(iiare of the distance below the horizontal diameter. Exoellnt solutions of this problem were also received from W. B. M. ZEBU, and /. P. MA TZ. 21. Proposed by J. A. CALDERHEAD, Superintendent of Schools, Limaville. Ohio. 1 Show that, In the wheel and axle, when a force P, acting at the circumference of the wheel, supports a weight Q upon the axle, /.(/i, q=psinf) = (Jr psme) TJ'psinf, where It, r, and p are the radii of the wheel, the axle, and their common axis respectively, and f is the limiting angle of resistance. Solution By 6. B. M. ZERR, A. M., Prinoipal of High Sohool, Staunton, Virginia; and F-P. MATZ, M. So., Ph. D., Professor of Mathematics and Astronomy in New Windsor College, New Windsor, Maryland. Let TP=weigbt of wheel and axle, /7=the angle between /'and Q and also between P and TF since and Ware parallel. The resultant of /' W due to friction is W) + P +-2J(+ Hos/-x more

Product details

  • Paperback | 110 pages
  • 189 x 246 x 6mm | 213g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236494369
  • 9781236494368