! 



12 KINETICS OF A PARTICLE. [25. 



or since, by (10), for inelastic impact v' = v, 



m 



. 



m+m* 



This is the common velocity of hammer and nail after the 

 stroke. We find, therefore, by (13), 



mil 



-^- f .^^ = Fs. (14) 



m+m 1 



25. It will be noticed that while the total kinetic energy 

 of hammer and nail just before striking was ^mu 2 +o, the 

 kinetic energy utilized for driving the nail is only the fraction 

 m/(m+m f ) of this total kinetic energy. The remaining portion 

 of the original kinetic energy, viz. 



(15) 



m + m 1 



must be regarded as spent in producing the slight deformations 

 of hammer and nail and such accompanying phenomena as 

 vibrations of the plank, sound, heat, etc. For it is an experi- 

 mental result of modern physical research that, wherever kinetic 

 energy disappears as such, there is done an exactly equivalent 

 amount of work. The apparently disappearing kinetic energy 

 may either be transferred to some other body, as in the case of 

 the vibrations of the plank, or it may reappear in the form of 

 molecular vibrations, causing sound or heat ; or it may be trans- 

 formed into an equivalent amount of so-called potential energy. 

 This physical fact is known as the principle of the conservation 

 of energy. 



26. In our example the total original kinetic energy, Ji*> 

 resolves itself into two portions, the portion (14) used for driv- 

 ing the nail, and the "wasted" or, as it is often called, "lost" 

 portion (15). It may, however, happen that the portion (15) 



