I5i.] PLANE STATICS. 9 ! 



(3) A uniform rod AB 2 1 of weight W rests with its upper end A 

 against a smooth vertical wall, while its lower end B is fastened by a 

 string of given length, BC= 2 b, to a point C in the wall. The rod and 

 the string are in the vertical plane at right angles to the wall. Find the 

 position of equilibrium, i.e. the angle $ = ACB, the tension 7"of the 

 string, and the pressure A against the wall. 



(4) A uniform rod AB = 2 /of weight W rests with one end A on a 

 smooth horizontal plane AC, with the other end B against a smooth 

 vertical wall BC, the vertical plane through AB being at right angles to 

 the intersection C of the wall with the horizontal plane. The rod is kept 

 in equilibrium by a string EC. Find the tension Tof this string if the 

 angles CAB = and EC A = <f> are given. 



(5) A weightless rod AB = / can revolve in a vertical plane about a 

 hinge at A ; its other end B leans against a smooth vertical wall whose 

 distance from A is AD = a. At the distance A C = c from A, a weight 

 W is suspended. Find the horizontal thrust A x at A and the normal 

 pressures A y and B at A and B. 



(6) The same as (5) except that at B the rod rests on a smooth hori- 

 zontal cylinder whose axis is at right angles to the vertical plane through 

 AB. In which of the two problems is the horizontal thrust A x at A 

 least? 



(7) The lower end A of a smooth uniform rod AB of weight Wrests 

 on a smooth horizontal plane making an angle with it. At the point C it 

 rests on a smooth cylinder whose axis is horizontal and at right angles to 

 the vertical plane through the rod ; at D the rod is pressed upon by 

 another smooth cylinder whose axis is parallel to that of the cylinder 

 at C. Determine the reactions at A, C, D, if W, 0, AB = 2 /, CD = a 

 are given. 



(8) A smooth weightless rod AB = /rests at C on a smooth horizon- 

 tal cylinder whose axis is at right angles to the vertical plane through 

 the rod ; its lower end A leans against a smooth vertical wall whose dis- 

 tance from C is CD a ; from its upper end B a weight W is 

 suspended. Determine the distance AC = x for equilibrium, and the 

 reactions at A and C. 



(9) A uniform rod of weight W\s hinged at its lower end A, while its 

 upper end B leans against a smooth vertical wall. The rod is inclined 

 at an angle to the vertical, and carries three weights, each equal to 

 w, at three points dividing the rod into four equal parts. Determine 

 the pressure on the wall and the reaction of the hinge. 



