IMPACT OF SPHERES. U 



work done upon it by the constant attractive force, Fmg^ of 

 the earth, and we have 



l mv 2 Fs = mgs. 



The kinetic energy \ miP, possessed by a particle of mass m, 

 moving with the velocity v, can therefore always be regarded as 

 equivalent to a certain amount of work. If the motion of this 

 particle be opposed by a constant force or resistance F, the dis- 

 tance s through which it will go on moving until it comes to 

 rest is of course determined from the same equation, 



mv*=Fs. (13) 



It is then said that the kinetic energy of the particle is spent in 

 overcoming the resistance F, or in doing work against the force 

 ^(see Part II., Art. 231). 



23. In the case of direct impact of spheres, as considered in 

 Art. 11, the velocity, and hence also the kinetic energy, of each 

 sphere is in general changed by the impact ; a transfer of kinetic 

 energy can be said to take place. Thus, when a sphere at rest 

 is struck by a moving sphere, kinetic energy is imparted to the 

 former by the impulsive force, and this energy can then be 

 spent in doing work against a resistance. Impact is therefore 

 frequently used for the purpose of performing useful work. 



24. For instance, to drive a nail into a wooden plank, the 

 resistance F of the wood must be overcome through a certain 

 distance s. This might be done by applying a pressure equal 

 to F ; as, however, this pressure would have to be very large, it 

 is more convenient to impart to the nail, by striking it with a 

 hammer, an amount of kinetic energy, ^mv 2 , equivalent to the 

 work Fs that is to be done. Neglecting elasticity, and denoting 

 the mass of the hammer by m, that of the nail by m f , the veloc- 

 ity of the hammer at the moment when it strikes the head of 

 the nail by , we have, by (7), 



mv + m'v' = mu, 



