146 Statics. 



vertical drawn through the centre of gravity shall make at the 

 point D, with the surface of the axle, an angle equal to that of 

 friction. Then any increase of the power will cause the pul- 

 ley to turn. 



By the position which the weight has taken, it will tend to 

 turn the axle upon its centre J 1 , with a force, the moment of 

 which will be p X FE, FE being perpendicular to a vertical 

 passing through D. Now we have already seen, that 



this moment, therefore, will bepd cosy*. But in order that the 

 power, by its augmentation, which I shall call 2', may be upon the 

 point of overcoming this effort, it is necessary that the moment 

 Z* X FG of the force z' ', with which it tends to cause a rotation 

 172. about F, should be equal to the moment pd cos/ ; we have, 

 therefore, by calling the radius FG, Z), 



= pd cos/, 

 and consequently, 



/ _ p cos/ 

 ~D~~' 



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

 less according as the radius of the axle is less than that of the 

 pulley, and in the same ratio. 



It will hence be easy to determine the effect of friction in the 

 different systems and combinations of pulleys. Suppose that 

 the question related to one similar to that represented in figure 

 92, the weight p being equal to 400 lb , and the radius d of the 

 axle as well for the fixed as for the moveable pulleys being a 

 fifth part of the radius D of the pulley. 



The two cords 1, 2, sustain half of the weight or 200 lb j 

 thus, if in the value of z, we put for p 200u>, j D for d, and 

 on the supposition that the friction is one fourth of the pressure, 

 which would give the angle of friction equal to 75 58', and the 

 os/or cos 75 58, equal to 0,24249,* or simply 0,24, we shall 

 have, 



* See table of natural sines and cosines, Topography. 



