A treatise on analytical statics; with numerous examples

by Isaac Todhunter

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. 1858 ...which, passing over the upper surface of the cylinder, has one end attached to a fixed point and the other to a weight W which hangs freely; if a be the inclination of the plane to the horizon, and 0 the inclination to the vertical of that part of the string which is fastened to the fixed point, the weight of the cylinder is 2jyrgjnjcogJtt+ig).. sin a 26. An inextensible string binds tightly together two smooth cylinders whose radii are given; find the ratio of the pressure between the cylinders to the tension by which it is produced. Result. '2; where r1 and r2 are the given radii. Tl + T2 27. A ball of given weight and radius is hung by a string of given length from a fixed point, to which is also attached another given weight by a string so long that the weight hangs below the ball; find the angle which the string to which the ball is attached makes with the vertical. Result. Let Q be the weight of the ball, P the weight which hangs below the ball, a the radius of the ball, I the length of the string; then the inclination of the string to the vertical is sin-1-=5---=.--7 P+Q a+l. 28. A ring whose weight is P is moveable along a smooth rod inclined to the horizon at an angle a; another ring of weight P is moveable along a rod in the same vertical plane as the former and inclined at an angle a to the horizon; a string which connects these rings passes through a third ring of weight 2 W; shew that the system cannot be in equilibrium unless Ptan a-P tan a' + IF (tan a.-tan a') = 0. 29. A right cone whose axis is a and vertical angle is placed with its base in contact with a smooth vertical wall, and its curved surface on a smooth horizontal rod parallel to the wall; shew that it will remain at rest if the distance of the rod from the wall be not greater than...

80 pages, Paperback

First published August 20, 2015

About the author

English mathematician known for his writings on the history of mathematics.