Measure of Forces applied to Machines. 267 



and, putting 50 for w, and 32,2 for g, we shall have 

 met 1000 1000 100 5 



or ^ == 



that is, such a force would support a weight of 50 lb only about 

 of a second. 



386. Let us now suppose that it is required not only to sup- 

 port the mass m during the time J, but also to move it during 

 same time with a uniform and known velocity v. 



It is manifest that in communicating the velocity &, either succes- 

 sively or at once, to the body m, there must have been expend- 

 ed a quantity of motion equal to m v ; and to maintain this veloc- 

 ity v during the time f, the action of gravity is to be resisted all 

 the while just as if the body had remained at rest ; that is, there 

 must have been expended an additional quantity of motion equal 

 to vngt] therefore to maintain in the mass m the velocity v dur- 

 ing the time , the agent must be capable of producing a quantity 

 of motion equal to m v + mgt* 



387. It is ascertained by actual trial, that a man can work at 

 a machine like that represented in figure 97, for 8 hours success- 

 ively, and cause the winch to make 30 turns a minute, the radi- 

 us of the cylinder and that of the winch being each 14 inches, 

 and the weight applied at the surface of the cylinder being 25 lb . 

 This experiment determines the value of 



m v -f- m g t, 



and consequently the limit to be observed in estimating the force 

 of a man working at a machine, and for a definite period of time. 

 Indeed, since the radius of the winch and that of the cylinder are 

 equal, the weight in this case passes through the same space with 

 the power. Thus, the radius being 14 inches, at each turn the 

 power passes through 28 X 3,1416, or 88 inches nearly ; ; 

 since it makes 30 turns a minute, it describes 44 inches a second, 

 or f | of a foot ; that is, the velocity 



44 _ 11 

 12 3* 



The mass 



