FRICTION IN MECHANICS. 173 



of friction is to keep the body at reft, or prevent it from 

 moving either way : this being premifed, there will be 

 little difficulty in the following. 



PROBLEM I. 



Having given the weight of the body to be fuftained, 

 the inclination of the plane, and the ratio of the friction 

 co the prefl'ure ; to find the force requifite to fuftainthe 

 weight in a given direction. 



In the foregoing figures, draw PR and PD at right 

 angles to the horizon and plane reflectively, PR repre- 

 fenting the weight; take PD to DQ as the preflfure to 

 the frittion, and let DO be taken upwards or down- 

 wards as the requifite force is motive or fufpenfive ; 

 join PQ, and draw the line Rm in the given direction 

 meeting PQ in m; then Rm is the force required. 



Corollary 1. If the friction be the n part of the 

 preffure, and W be the weight, 5 and c the fine and cofine 

 of the plane's elevation, then the moving force parallel 

 to the plane will be W (s+ c: nj and the fufpending 

 force W (s — c : n .) 



Corollary 2. If the direction of the force be parallel 

 to the horizon, and t be the tangent of the plane's ele- 

 vation, then W (tn+i) : (n — t) will be the moving 

 force, and W (tn — 1) : (n-\-t) the fufpending force, 

 and Wt the force excluding fri&ion. 



Example. If the weight be a ton, the friction ■§• of 

 the preffure, AB=5, BC=3, and AC=4, then the 

 moving force will be 3235 pounds, the fufpending 



force 



