STATICS. 2G3 



over the common vertex, and Q is on the point of motion down 

 the plane ; prove that the weight which may be added to P 

 without producing motion is 



sin (a ) sin (/? c) ' 



a, ft being the angles of inclination to the horizon, and tan e the 

 coefficient of friction. 



1265. A uniform rod rests with one extremity against a rough 

 vertical wall (a = ^J, the other extremity being supported by a 



string three times the length of the rod attached to a point in the 

 wall ; prove that the angle which the string makes with the wall 

 in the limiting position of equilibrium is 



tan- 7 or tan- 1 . 



12G6. A weight W is supported on a rough inclined plane of 

 inclination a by a force P, whose direction makes an angle t with 

 the plane, and whose component in the piano makes an angle 

 with the line of greatest inclination in the plane; pm\v that, for 



iibrium to be possible, 



' a sin* 6 cos* i 



IL >. -- . 

 1 + coe 2a cos 2i - sin L . os 



12<>7. A given weight, resting upon a rough inclined plane, 

 is connected with a weight P by means of a string passing over a 

 peg, P hanging freely. The coefficients of friction for the 

 peg and plane are tan A, tan A', that th<- ii 



6 string to the plain- in limiting njuilil.riuui, when 7* is 

 a maximum or minimum! is A A'. 



