COEFFICIENT OF FRICTION 31 



belt and that T\ is increased and TV is decreased so as to 

 cause rotation of the pulley. The difference of the tensions, 

 Ti T2, is represented in Fig. 4 by a weight being lifted as 

 the pulley is rotated. With given values of Ti and TV the 

 tensions in the belt will gradually decrease from T\ at the 

 point where it first comes in contact with the pulley to Tz 

 at the point t n where it leaves the pulley. The decrease in 

 tension in successive inches of length of contact may be 

 represented by the quantities (to 1\), (/ 2 /i), etc., and the 

 sum of these differences will equal the total difference in 

 tension Ti T-2, which is the same as the effective pull or 

 tractive force, p. 



With a given sum of the tensions T \-\-Tz = W, the limit 

 to the tractive force p, or to the weight that can be lifted 

 without serious or objectionable slipping of the belt, depends 

 upon the length, a, of the belt in contact with the pulley 

 expressed in radians, and upon the coefficient of friction /. 

 The relation existing between the four quantities Ti, T2, 

 f and a is expressed by the exponential formula 



^ =efa - ( J ) 



1 2 



This equation is derived by means of the calculus, and 

 those interested in the mathematical discussion involved are 

 referred to Church's " Mechanics of Engineering," Rankine's 

 " Machinery and Millwork " and other works on applied 

 mechanics. 



Coefficient of Friction. The coefficient of friction is 

 defined as the ratio of the force required to cause one surface 

 to slide upon another to the pressure with which the surfaces 

 are in contact. In the case of belting it is evident from an 



T 



inspection of the formula =- = /a > that the influence that the 



12 



coefficient of friction exerts on the power transmitted by a 

 belt is very great. The value given by experimenters from 

 the time of Morin up to the experiments of Lewis and Ban- 



