GENERAL PRINCIPLES 



59 



impulse has not allowed the pull to be transmitted, whereas in 

 the second case the mass M has added its effect to that of the 

 pull (fig. 74). 



42. Certain other passive resistances intervene in movement 

 and oblige the motive power to be increased. First of all the 

 resistance of fluids must be considered. According to whether 

 the movement takes place in the air or in water, there results 

 a resistance proportional to the square of the speed of the current 

 flowing at the surface perpendicularly opposed to the current, 

 and to the density of the fluid. 



Then: 



In taking the density of water in relation to that of air, 



R = KSV 2 

 for the resistance in air. The co-efficient K is approximately 



- ; and S and V are expressed in metres and R in kilogrammes. 

 lo 



For water it will be K '. 



The co-efficients K and K' vary with the form of the body in 

 movement. 



The stiffness of a cord or belt causes it to resist bending 

 around a pulley, a resistance which requires the 

 expenditure of a certain force at a dead loss to 

 get a useful result. This inflexibility is expressed 

 by the force / and it is shown approximately that : 



It increases with the distance Q to be displaced, and 

 the distance d (co-efficiency of inflexibility) ; and 

 it diminishes when the radii of the pulley and of 

 the belt increase (fig. 75). The inflexibility is, 

 however, never a negligible quantity. 



