

GENERAL PRINCIPLES 55 



produces the friction 3> =/ X N, and a tangential component 

 T which tends to overcome that friction (fig. 69). Equilibrium 

 is not reached until 



T = 4> =/x N, 

 that is to say, at that moment 



T 



And as T = F sin 9, N = F cos 9. 



T sin 9 



__ or / = - = tang 9. 



N cos 9 



This is the angle of friction or the greatest inclination that 

 the direction of the force can make with the vertical and sliding 

 continue. 



If the force is that of gravity G (fig. 70) , by gradually increasing 



the inclination of the surface S to 

 the horizontal, it will be found that 

 the angle of friction is equal to the 

 angle of inclination but only in 

 equilibrium. 



Rolling friction is exhibited in 

 ' K the haulage of carriages. The 



n ~ M larger the radius of the wheel the 



*'*- 7a - smaller the friction, the haulage 



being produced tangentially. By 



dividing the effort of traction of a vehicle by its weight, the co- 

 efficient of traction is obtained. This co-efficient is 0-005 on 

 railways, that is to say, for a wagon of 10,000 kilogrammes (10 

 metric tons) there must be a tractive effort of 



10,000 X 0'005 = 50 kilogrammes. 

 In railways the tractive effort per metric ton is adopted ( 256) . 



40. Impact. An emission of energy also takes place when a 

 body in movement encounters suddenly a body in repose or 

 moving at a lesser speed. The impact has a very short duration. 

 If a body of mass M and speed V meets a 

 body of a mass m and speed v ; the latter -^ 



experiences percussion at the point of con- f J Q 

 tact (fig. 71). If the movement takes place jSf m 



in the same direction, M is added to m and 

 the new speed will be u. As far as move- fl * 7l - 



ment is concerned we have : 



MV -4- mi) 



MV -f mv = (M -f m) u ; hence u = ^ i w 



