28.] IMPACT OF SPHERES. ! 3 



does the useful work, while (14) is wasteful. This would be the 

 case, for instance, in molding a rivet with a hammer, or in forg- 

 ing a piece of iron under the blows of a steam-hammer. The 

 useful work here consists in the deformation of the bolt or piece 

 of iron. 



It appears from the expressions (14) and (15) that, for the 

 purpose of driving the nail, m should be large in comparison 

 with m', while for molding a rivet it is of advantage to have m' 

 large in comparison with m. 



27. In applying the formulae (11) to (15), and in general all 

 formulae of theoretical kinetics, it should be noticed that the 

 forces are supposed to be expressed in absolute measure, the 

 unit being the poundal or the dyne. Hence, to find the force F 

 in pounds the numerical result obtained from one of these 

 formulae must be divided by the value of g. 



28. Let us now consider the change of the total kinetic energy 

 produced by direct impact in two partially elastic spheres. 

 With the notations of Art. n, we have for the excess of the 

 kinetic energy after impact over that before impact : 



To eliminate v and v' from this expression, square the equations 

 </) and (10), 



multiply the latter by mm', and write it in the form 



mm'(p-v'y+(\-^mm'(p-u')* 

 finally add the former equation, 



whence 



(-')a. (16) 



