ppose to be the angle of friction, so that 

 Un - *, 



thru P _Wm*-ton9WeM*_W sin(g-t) 



'" * 



: " 



ppote we re<i know the least force which will 



office to prevent the body from moving down the plane. 



The expire be least when coa(0 + t) is 



greatest, that ia when + c 0, that is when *= e ; and 



i-f). 



-uppose we reouirc to know the least force which 

 utticc to move the body np the ] xpression 



'. will be lea.- >* (0- 1) is greatest, that is when 



0-c; and then P t -W sin (at -He). 



.is following problem will illustrate the subject of 



plane witn i A weight IF is placed on a 



rough in and is attached by a string to a point 



above the plane: det* iic limiting positions of equi- 



libria 



a be the inclination <>f the piano orizon, the 



n of the 



tance of the plat. body is cpn- 



remain at a constant distance from the fixed point, 



it must 1 situated on the circumference of a certain circle 



lane ; suppose the angular distance of the 



positi :o body from the lowest point of the < ircura- 



e. The forces v body at right angles 



lane are fPcosa, Tsin/9, :\n.l A'. 'Thus 



0... ...... (1). 



forces which act on the body in the plane are TTsiner, 

 T cos ft, and the i 11. Resolve these forces along the 



radius and tangent at the point of the circumference at which 

 the body rests. Thus 



rcoa/9- JPsinaons0-0... ..... (2), 



/J? - W sin a sin 0-0.. ...... (3). 



142 



