95-] INTRODUCTION. 53 



W be suspended from the lowest point D of the string. If AC=$ ft, 

 AB=BC 2.5 ft., and the length of the string 2/= 14 ft, find the 

 tension of the string and the pressures on the pegs. 



(22) If, in Ex. (21), the triangles AB C and ADC be equilateral, 

 what would be the tension and the pressures on the pegs ? 



(23) In Ex. (21), the triangles ABC and ADC being isosceles and 

 their common base AC horizontal, what must be the relation between 

 the angles 2 (3 at B and 28 at D to make the pressures on the three 

 pegs A, B, C equal? The pressures being made equal, what angle 

 gives the least pressure ? 



(24) Show, both analytically and geometrically, that a force whose 

 components PI, P 2 make an angle 6 can be resolved into two rectangular 

 components (P l + P 2 ) cos (0/2), (Pi P 2 ) sin (0/2 ). 



(25) In the toggle-joint press two equal rods CA, CB are hinged at 

 C ; a force F t bisecting the angle 2 a between the rods forces the ends 

 A, B apart. If A be fixed, find the pressure exerted at B at right angles 

 to F \iF- 100 Ibs. and a= 15, 35, 65, 85, 90. 



