52 STATICS. [95. 



(12) Two forces acting on a point are represented in magnitude and 

 direction by the tangent and normal of a parabola passing through the 

 point. Find their resultant, and show that it passes through the focus 

 of the parabola. 



(13) The magnitudes of two forces acting on a point are as 2 to 3. 

 If their resultant be equal to their arithmetic mean, what is the angle 

 between the forces? 



(14) What is the angle between a force of i ton and a force of V3 

 tons if their resultant is 2 tons? 



(15) A string with equal weights F attached to its ends is hung over 

 two smooth pegs A, B fixed in a vertical wall. Find the pressure on 

 the pegs : (a) when the line AB is horizontal ; (b) when it is inclined 

 to the horizon at an angle 0. The weight of the string, its extensibility 

 and stiffness, and the friction on the pegs are neglected in this problem 

 as well as in those immediately following. 



( 1 6) The string being hung over three pegs A, B, C, determine graphi- 

 cally the pressures on the pegs. Let the vertical line through B lie 

 between the vertical lines drawn through A and C ; there will be a 

 pressure on B only if B lies above the line AC. If B lies below A C, 

 the pressure may be distributed over the three pegs by passing the string 

 around the peg B from below. 



(17) In Ex. (15), for what position of the line AB are the pressures 

 equal ? 



(18) In Ex. ( 1 6), let A C be horizontal, and let a, /?, y denote the 

 angles of the triangle AB C. What are the pressures on the pegs? 



(19) In Ex. ( 1 8), what must be the position of B to make the 

 pressures on the three pegs equal : (a) when B lies above AC ', (b} when 

 B lies below AC? 



(20) If the string with the equal weights W attached to its ends be 

 strung over any number of pegs, the pressures on the pegs are readily 

 determined, either graphically or analytically, in magnitude and direc- 

 tion ; these pressures depend only on the value of W and on the angles 

 between the successive sides of the polygon formed by the string, but 

 not on the distances between the pegs. 



(21) Suppose the string be closed, its ends being fastened together. 

 Let this string be hung over three pegs A, B, C forming an isosceles 

 triangle in a vertical plane with its base A C horizontal, and let a weight 



