Friction. 145 



(D sin 

 -p~ 



D sin 6 d cos/ sin 6 

 D' 



d cos f sin 6 I)' d cos / 



-- z 



Therefore, since when there is no friction, the value of the power is 

 ^7, if we call z the augmentation which the power must receive 

 on account of friction, we shall have 



p(D+ d cos/) pD 

 jy __ $ cos/ "S 7 "' 



cos/) p DEr + pD$ cos/ 

 ' 



D (D' d cos/) 



. . 



-- cos/) : 



from which it will be seen, that the effect of friction will be 

 less according as the radius of the axle is less, although it does 

 not diminish exactly in proportion to this radius. 



241. This solution adapts itself to the lever, by regarding 

 Jy and D as the distances of the directions of the two forces from 

 the fulcrum. It is applicable also to the fixed pulley, by sup- 

 posing D 1 = Z>, which would give, 



2p cos/ 

 = 



Although in the wheel and axle we have supposed the direc- 

 tions in the same plane, the solution is not the less adapted to the 

 ordinary construction of this machine in which the weight and 

 power are exerted in planes but little distant from each other. 



242. To ascertain the effect of friction in the moveable pulley 

 we proceed thus. In order that the power q may be upon the Fig.130. 

 point of causing the pulley to turn about its axis F, it is necessa- 

 ry that it should receive an augmentation sufficient to overcome 

 the friction. Now by this augmentation, the power causes the 

 weight p to depart from its position to such a degree, that a 

 Mech. 19 



