EXAMPLES. 



a rough s .! nl if Q be on the point 



0* P* 

 lit ' put into the opposite scale will DD 



that scale be on the point of descending. 



18. Two equal weights P, /' an- "imrrtrd by a string 

 with ';t which passes over a r>u-h fixed h^ri. 



cylinder: com forces refining to raise /' according as 



P is pushed up or /'' pulled down. 



19. Ay B, C are three rough pe^s in a vertieal ]>'. 

 Pj (?, R are the greatest weights which can be severally 

 rted by a weight II", when connected with it by strings 

 without wri^ht passing over J. //, 6 f , over .1. //. an-l over 

 B, C respectively ; >luw that the coeflicient of fricti-.n 



20. A light thread, whose length is ~". lias its i-x 

 fastcncd t> those of a uniform heavy rod whose length is 

 5a, and wh-n the, thread is passed over a thin round peg, it 

 is found that the rod will hang at rest, provided the point 

 of support be anywhere within a .-pace <i in the middle of 

 the thread ; determine the coefficient of friction l..-t\veen the, 



i and the pc.i; when the, ri-d lianas in a position 1.. 

 ing on motion, and find its inclination to the hori/.ou and 

 the tensions of tin t parts of the string. 



JZexf/'/.s. The coefficient of friction is determined l>y the 

 equation e***'= j. The inclination of the rod to the hori/on 



21. From a fixed point a heavy uniform chain hancrs 

 so that part of the chain rests on a rou^h \IYI/ 



: iind the least length of chain that may be in cm 

 with the plane. 



vy chain of weight W rests entirely in contact 

 with the arc of a rough closed vertical curve in a state hor- 



:; on motion. If tan a be the coefficient of fri- 

 shew that the resultant normal pressure on the circle is equal 



cos a, and that its direction makes an angle a with the 

 vertical. 



