150.] 



PLANE STATICS. 



8 9 



with, the axis of the joint A ; AC = h. Find the position of equilibrium 

 and the pressure on the axis of the joint A. (Fig. 40.) 



To reduce to a purely statical problem, cut the string between B and 

 C and introduce the tension, which is = P- } also, replace the pressure 

 A by its horizontal and vertical components A x , A y . Then, if ^ ACB 

 = </>, %.jBAC=0, the conditions of equilibrium give 



A x = Ps'm<f>, A y = W- /'cos <, 





From the last equation, 



sm> = /^ 

 sin0 ~ h P 9 



while from the triangle ABC, 

 sin < 2 / 



sin0 



hence 

 sented 



= zhP/W, i.e. if we take ^ to represent W, Pwill be repre- 

 C. 



For the total pressure A we have 



i.e. A is the third side of a triangle having W and P for the two other 

 sides, and < for the included angle. The magnitude of A is therefore 

 represented by the median from A in the triangle ABC on the same 

 scale on which Wis represented by h. But this median gives also the 

 direction of A ; for we have 



k BC CQZ& 

 A,, W- 



150. A weightless rod AB rests without friction on two planes 

 inclined to the horizon at angles a, j3 } and carries a weight W at the 

 point D. The intersection (C) of these planes is horizontal and at right 

 angles to the vertical plane through AB. Find the inclination of ^AB 

 to the horizon, and the pressures at A and B. (Fig. 41.) 



