\VI.IM, i. \\ ii ;: ION. 



180. Wedge with Friction. (See Art. 168.) 



Suppose the wedge to be on the point of moving in the 

 direction in ..'/* urges it, ana 



assume for simplicity that each face 

 is similarly acted on by the obstacle. 



s which maintain the wedge 

 juiliKrium are 2P perpendieoukf 

 to the thick end, R perpendicular to 

 each face, and pR along each face 

 towards the thick end. Hence, re- 

 solvinir the iurees parallel t the <i 

 tion of 2P, 



P = 72 sin a + /-J2 cos a (1). 



Forces equal and opposite to R and pR act on the ob.-' 



h point of contact. If R be the resultant of Ji and ^7/, 

 we have 



X = BJ(l+tf (2). 



Let S be the resolved part of R' along a direction making 

 an angle i with that of R and i' with that of R . 168) ; 



then 



S = R' cost" 



= /Icos'+ffc72.in / (3). 



(1), (2), and (3) will give the ratio of P to R and of P to 8. 



181. Screw with Friction. (See Arts. 109, 170.) 



If the surfaces of the screw arc rough it is kept in r.jui- 

 librium by W, P, a system of forces perpendicular t> the 

 surface of the groove, and a system of forces ari-inir fnun 

 friction. Let R t denote one of the forces perpendicular t<> the 

 surface of the groove, pR, the corresponding irietion ; th 

 makes an angle a with the axis of the cylinder <>n which the 

 . is raised, and fiR t an angle ^TT a with the axis of the 

 cylinder. Suppose IF about to prevail over /'; then resolving 

 the forces parallel to the axis of the cylinder, and taking 

 moments round it, we have 



W- 25 (cos a + /* sin a) = 0, 

 Pa 2-ft (sin a - p cos a) I m 



