i86.] 



FRICTION. 



I II 



enough to equal the limiting friction F. The normal reaction 

 N of the plane is equal and opposite to the weight W. The 

 body is thus in equilibrium un- 

 der the action of the two jDairs of 

 equal and opposite forces ; but 

 motion will ensue as soon as P 

 is increased. If P be decreased, 

 .Fwill decrease at the same rate, 

 so that the equilibrium remains |W 



undisturbed. Fi - 55 - 



The force of friction Fcan be combined with the normal reac- 

 tion Nto form a resultant, 



which represents the total reaction of the horizontal plane. 



If $ be the angle between N and R when F has its limiting 

 value F=pN(Art. 183), we have, since tan< = F/A r , 



tan cf) = fju. 



The angle < thus gives a kind of graphical representation for 

 the coefficient of friction p ; it is called the angle of friction. 



186. If the plane be not horizontal, but inclined to the hori- 



,<* zon at an angle 6, the weight W 

 >/ of the body (regarded as a particle) 

 resting on the plane can be re- 

 solved into a component J^Fsin# 

 along the plane, and a component 

 W cos perpendicular to it (Fig. 

 56). Hence, if no other forces 

 act on the body it will be in equi- 

 librium, provided the component 

 Ws'mO be not greater than the 

 The limiting condition of equi- 



Fig. 56. 



limiting friction F=/J, Wcos 6. 

 librium is, therefore, 



fj, IV cos = Wsin 0, 



or //, = tan ; 



