Measure of Forc&s applied to Machines. 27 1 



I 



390. Although we have considered that case only, in which 

 the weight transmits all its resistance to the power, it is not less 

 easy, after what has been said respecting the ratio of the weight 

 to the power in each machine, to determine whether by the aid 

 of a particular machine, a given power will produce a proposed 

 effect. In the wheel and axle, for instance, if the radius of the 

 cylinder be <?, and that of the wheel D ; in order that the weight 

 may move with the velocity i?, it is necessary that the power 



should have a quantity of motion equal to ; and since in 



the time /, the action of gravity would give to the body m the 

 quantity of motion mg t, the power in order to sustain this effort 



must have the force or quantity of motion ^j- ; finally, if the 



friction is equivalent to the part of the weight, m being suppos- 

 ed to be applied at the distance #, the power will require the addi- 

 ct mgtd , 

 tional quantity of motion X ; thus, in order to deter- 



C J.J 



mine whether the power be sufficient to move with the velocity 

 v during the time f, the mass m, upon a wheel and axle of which 

 the radius of the axle is tf, and that of the wheel Z), we must de- 

 termine by experiment, the value of 



D 



by employing at a wheel and axle, of known dimensions and 

 known friction, a man moving a known mass ; then if k is the 



value found by putting for m, r, tf, D, , and /, the values of 



these quantities respectively in the experiment, it will be neces- 

 sary, in every other case, that 



+ /M + A m g'* 



should have a value not exceeding k. 



So also, upon the inclined plane, the power acting parallel 

 to the plane ; if we call i the inclination of the plane, mg t sin i 

 will be the quantity of motion which gravity will communicate 



