122 G. F Becker — Impact Friction and Faulting. 

 the contact being taken as origin, may therefore be written 



2 V (n+l) J 



(n+lj' 



If the origin is transferred to the free extremity of the rod by 

 substituting x+a for a-, this becomes 



2 



n+l 



If —f- 1 is taken as the unit of energy and c 1 as the unit distance, 

 A 



n + l ' 



a form of very satisfactory simplicity. If n = l Cj=2c, or the 



length which the entire impinging mass would assume were it 



uniformly compressed to the density at the contact when the 



passive mass is infinite. 



V 

 In the following diagram the area marked — is] the energy 



potentialized in the passive mass, or half the entire^ energy 

 potentialized in the system. 



When the mass 2M strikes the mass 2??M the kinetic energy 

 of the entire system at the moment of maximum compression 

 is, say 



n + l 



2 



and this is manifestly twice the integral of the area marked 



T 



— in the diagram. If T, is the kinetic energy of the passive 



u 



mass alone at this moment, it is readily seen that 



If V is the energy potentialized in the entire system and E 

 the total energy, the fundamental energy equation 



V=E-T, 







becomes 



2/wdx=z — - — / £~ X / Ci dx I e x / Cl dx. 



J n-\-\ J n+l J 



) My_ a 



'~~2~ 



Mv 2 l 

 "IT n + l 



