FKICTION 



Further, when the two bodies are pressed together in any 

 way it is found that the directkwa^of the reaction can make any 

 angle up to a certain limiting angle with the normal to the 

 plane of separation without sliding taking place, but that as soon 

 as this angle is reached sliding takes place. This -angle is 

 known as the angle of friction. It is clearly the same as the 

 angle through which the plane before considered can be tilted, 

 for the angle between the normal to the plane and the direction 

 of the reaction (i.e. the vertical) is simply the slope of the plane. 



42. In any case in which frictional forces act, let R denote the 

 normal component of the reaction, and let F denote the compo- 

 nent in the plane of the contact which 

 is caused by friction. When slipping is 

 just about to occur, the resultant must 

 make an angle e with the normal, where 

 e is the angle of friction. Thus, if S de- 

 notes the whole reaction, we must have 



R = S cos e, F = S sin e, 

 and hence F = E tan e. 



FIG. 20 



The quantity tan e is called the coefficient of friction and is denoted 

 by the single letter p. Then, when slipping is just about to take 

 place, we have F= E 



It must be clearly understood that this equation gives the true 

 value of the frictional force only when slipping is just about to 

 take place. It sets an upper limit to the value of the frictional 

 force, but does not give the actual value of this force unless we 

 know that the system is on the verge of sliding. 



43. Consider, for instance, the experiment already discussed, in 

 which a particle is placed on a horizontal plane which is gradually 

 tilted up. When the plane is horizontal the particle is at rest, 

 acted on only by gravity and the reaction with the plane. Thus 

 the reaction is vertical, so that here F= 0. Consider next the 

 state of things when the plane makes an angle a with the horizon. 



