JRICTION IN MECHANICS. I79 



PROBLEM IV. 



If AhqN be the fegment of an equilateral triangle, 

 which, by moving parallel to itfelf and the horizon, 

 generates a folid, upon which a figure hmGEHKpqh 

 moves, touching the former in hm and qp ; requi»ed 

 the effect of the friction ; {till fuppofing it the n part of 

 the pre flu re. 



Let P be the center of gravity of half the body*, and 

 PR its weight as before; then the body by means of its 

 inflexibility is kept together in the fame manner as if it 

 was actuated by a force parallel to the horizon ; but if 

 PDn be perpendicular to Ah, and Rn parallel to the 

 horizontal line AC, meeting PD in n, Pn will be the 

 preflure againft the- fide Ah, and the friction is the n 

 part of Pn; but PR : Pn : : AC : AB; therefore if AC 

 reprefent the weight ol half the body, the n pan of AB 

 willexprefs the weight lequiiite to overcome the friction, 

 for that ha'f; and by doubling the expreflions, they ferve 

 for the whole. Wherefore let W leprefent the weight 

 of the body, f the fecant of the angle BAC ; then Wf 

 will be the preflure againfl the plane AD; and the n 

 part of Wfthe force nectflary to overcome the friction; 

 and as this lait is the force neceflary to draw the body 

 along a horizontal plane, therefore the force neceflary 

 to draw the body along a hoi izontal plane, is to that ne- 

 ceflary to draw it along the body whofe lection is 

 AhqN, as AC to AB, or as 1 to/. 



Becaufe when the angle CAB is given, the ratio of 

 PR to Pn is conftant; therefore when the folid whofe 

 fection is AhqN is elevated, making an angle with the 

 horizon, fo that its bafe forms an inclined plane; PR in 

 that cafe reprefents the preflure in a normal direction 

 to that plane, and Pn the preflure againit the folid; and 



ar 



* Fig. 7; 



