88 STATICS. [148. 



Eliminating F from (i) and (3), we have 



__ 



e /sin 2 

 hence from (2) , 



e/sm 2 O 

 and finally from (i), 



148. A cylinder of length 2! and radius r rests with the point A of 

 the circumference of its lower base on a horizontal plane and with the 

 point B of the circumference of its upper base against a vertical wall. 

 The vertical plane through the axis of the cylinder contains the points A, 

 B, and is perpendicular to the intersection of the vertical wall and the 

 horizontal plane. If there be no friction at A and B, what horizontal 

 force F applied at A will keep the cylinder in equilibrium ? When is this 

 force F = o ? 



Let G be the centre of gravity of the cylinder ; W its weight ; A, B 

 the reactions at A, B ; and 9 the given 

 angle between AB and the horizontal plane. 

 B Then B F o, A W o, and taking 



moments about A, 



If either the dimensions of the cylinder, or the angle 6, be such as to 

 make tan B = l/r, no force F will be required to maintain equilibrium ; 

 G and A will then lie in^the sarne vertical line. 



149. The homogeneous rod AB = 2 1 of weight W is jointed at A, so 

 as to turn about A in a vertical plane. A string BC attached to the 

 end B of the rod runs at C over a smooth pulley^ and carries a weight P. 

 The axis of the pulley C is parallel to, and in the same vertical plane 



