CHAPTER III. 



PRINCIPLES OF GENERAL MECHANICS (Continued). 

 Resistance of Materials. Machines. 



43. Deformation of Bodies : Elasticity. In the foregoing study 

 of equilibrium and the movement of bodies, it has been assumed 

 that they remained indeformable under the actions of forces. 

 But this is a false assumption, and we can, in practice, only 

 study constrained equilibrium ( 13) such as is brought into play 

 by the internal forces of a body. It is therefore necessary briefly 

 to consider the value taken by these tensions under the action 

 of external forces, and to ascertain to what degree the latter can 

 act without entirely overcoming the internal tensions, i.e., with- 

 out breaking the body. The study of the deformation and re- 

 sistance of materials is the necessary complement of the science 

 of work. Under the action of forces, matter is extended, com- 

 pressed, sheared, bent and twisted, and its molecules, in each of 

 these cases, are displaced. If when the effort has ceased, the 

 molecules re-establish themselves in their original positions, it 

 is said that the material is perfectly elastic. If, on the other hand, 

 they re-establish themselves slowly or incompletely, the elasticity 

 is imperfect. The definition of elasticity, therefore., is as follows : 

 The power to return to the initial form after a deforming force 

 has ceased to act. It is evident that the deformation is propor- 

 tional to the effort, as long as the magnitude of that effort has 

 not exceeded a certain value, at which return to the initial state 

 becomes impossible. This value is called the limit of elasticity. 



If the force applied is such as to stress the material beyond 

 the elastic limit, the deformation becomes permanent. The 

 material is said to have received a permanent set. If the force 

 is still further increased rupture of the material will eventually 

 occur. 



A knowledge of the elastic limit of various materials is of prime 

 importance in the study of energetics. For example, the energy 

 stored in a clock spring by the act of winding up will be restored 

 with the greater completeness, in its unwinding, the more that 

 the material of the spring approximates to a, (theoretically), per- 

 fect elastic material. 



