r 



103.] CONCURRENT FORCES. 57 



(10) A weightless rod AC (Fig. 21), hinged at one end A so as to 

 be free to turn in a vertical plane, is held in a horizontal position by 

 means of the chain BC. If a weight W be suspended at C, find the 

 thrust Pin AC and the tension T of the chain. Assume AC 8 ft., 

 AB = 6 ft. 



(n) In Ex. (10), suppose the rod AC, instead of being hinged at 

 A, to be set firmly into the wall in a horizontal position ; and let the 

 chain fastened at B run at C over a smooth pulley and carry the 

 weight W. Find the tension of the chain and the 

 magnitude and direction of the pressure on the 

 pulley at C. 



(12) In "tacking against the wind," let Fbe the 

 force of the wind ; a, ft the angles made by the axis | 

 of the boat with the direction in which the wind 



blows, and with the sail, respectively. Determine Fi - ** 



the force that drives the boat forward and find for what position of the 



sail it is greatest. 



(13) A cylinder of weight W rests on two inclined planes whose 

 intersection is horizontal and parallel to the axis of the cylinder. Find 

 the pressures on these planes. 



(14) Find the tensions in the string ABCD, fixed at A and D, and 

 carrying equal weights Wat B and C, if AD=c is horizontal, AB=BC 

 = CD, and the length of the string is 3 /. 



(15) One of the vertices A of a regular hexagon is acted upon by 

 5 forces represented in magnitude and direction by the lines drawn 

 from A to the other vertices of the hexagon. Find their resultant. 



(16) Find the resultant of three equal forces P acting on a point, 

 the angle between the first and second as well as that between the 

 second and third being 45. 



(17) A mass m rests on a plane inclined to the horizon at an angle 

 ; it is kept in equilibrium (a) by a force P^ parallel to the plane ; 

 (b} by a horizontal force P 2 \ (/) by a force P 3 inclined to the horizon 

 at an angle + a. Determine in each case the force P and the pres- 

 sure R on the plane. 



(18) Show that the three forces represented by the vectors OA, OB, 

 QC are in equilibrium if O is the centroid of the triangular area ABC. 



