STATICS. 2G1 



of equilibrium are when one axis is vertical ; and that, if 

 c > bJ2 < v /2, the positions in which an axis is vertical are 

 stable, and there are unstable positions of equilibrium in which 

 the pegs are at the extremities of conjugate diameters. 



IV. Friction. 



1255. Find the least coefficient of friction between a given 

 elliptic cylinder and a particle, in order that, for all positions 

 of the cylinder in which the axis is horizontal, the particle may 

 be capable of resting vertically above the axis. 



1256. Two given weights of different material are laid on a 

 given inclined plane, and connected by a string in a state of 

 tension inclined at a given angle to the intersection of the plane 

 with the horizon, and the lower weight is on the point of motion; 

 determine the coefficient of friction of the lower weight, and the 

 magnitude and direction of the force of friction on the upper 

 weight. 



1257. A weight w rests on a rough inclined plane (/i< 1) 

 supported by a string, which, passing over a smooth pulley at the 



-t point of tin- plain-, sustains a weight > pw<w hanging 

 vertically; prove that the angle between the two positions of the 

 plane in which to is in a state bordering on motion is 



1258. Two weights of similar material connected by a fine 

 a rough vertical circular arc on which the string 

 lies; prove that the angle subtended at the centre by the distance 

 between the limiting positions of either weight is 2 tan" 1 /x. 



nif'Tin rod rests with <>ne rxtrnnity against a 

 rough vertical wall, the other being supported by a string of equal 



