234 MOTION OF SYSTEMS OF PARTICLES 



an infinitesimal time, the rate of change of momentum must be in- 

 finite. By the second law of motion, the rate of change of momen- 

 tum is equal to the force, so that the force itself, while it lasts, 

 must be infinite. Thus an impulsive force may be regarded as an 

 infinite force acting for an infinitesimal time. 



190. At the outset of our study of impulsive forces, it will be 

 well to notice one physical peculiarity of these forces. A perfectly 

 rigid body was defined as one which kept its shape under the 

 action of any forces, no matter how great. At the same time it 

 was mentioned that no perfectly rigid bodies exist in nature. 

 Under the action of infinite, or very great, forces such as occur in 

 impulses, no body may be treated as perfectly rigid. 



The consequence of this is that when any impulsive forces are 

 brought into action, relative motion is set up between the different 

 small particles of which continuous bodies are composed. This 

 relative motion possesses energy of a kind which cannot be regain* 

 from the system by mechanical processes ; in fact, the relative 

 motion of these particles simply represents the he"at of the body. 

 Inasmuch as this energy cannot be recovered from the system as 

 mechanical work, we see that the impulsive forces which do work 

 in producing this energy cannot be treated as conservative forces. 

 Thus we see that 



The sum of the potential and kinetic energies of a system does 

 not remain constant through the action of impulsive forces. 



For clearly part of the total energy is left, after the impulses, in the 

 form of heat. 



Consider, for instance, a lead bullet striking a steel target. Suppose 

 that, before striking the target, the bullet is moving horizontally with 

 velocity v at a height h. Its kinetic energy is ^ raw 2 , its potential energy 

 being mgh. After striking, we may suppose the bullet to have no horizontal 

 velocity, but to fall to the bottom of the target. At the instant at which 

 this fall begins, the kinetic energy is nil, while the potential energy is mgh, 

 as it was before the impact. Thus an amount of energy \ mv 2 has disap- 

 peared from the total energy. This has been used up in producing motions 

 of the particles of the bullet and target relative to one another ; tliese show 

 themselves in the form of heat, and also, perhaps, partly in permanent 

 changes of shape, a dent in the target, or a flattening of the bullet. 



