RESISTANCE OF MATERIALS 69 



SE/ 2 

 clastic work is' L, L being the length of the elastic string. 



QF/ 







FL 



and as from the formula / = ^=, we find the value of the 



tension F. 



/SE 

 F = -y- > therefore by substitution : 





This result shows, on the one hand, that the height of the fall 

 can be increased in such a manner that F can overcome the 

 weight of the larger ball, and on the other hand, that the tension 

 F depends on the modulus of elasticity E, that is to say, on the 

 nature of the string. If we select a string of small modulus, the 

 deformation operates in a very short time, the tension, being the 

 same throughout the length of the string, will raise the larger 

 ball. If the string were non-elastic and inextensible, the shock 

 would break it, or make ineffectual vibrations. 



It can be verified, for instance, that an indiarubber string of 

 10 centimetres in length and 5 square millimetres in section, 

 would have a tension of 102 gr. approximately, if the shock were 

 produced by a weight of 50 gr. only, falling from a total height of 

 50 centimetres. 



The elastic vibrations sometimes attain to a magnitude which 

 makes them dangerous. From the formula above it is evident 

 that the internal tensions increase in proportion to the hardness 

 of materials with a consequent increase in the value of E. It 

 will also be seen that a body has a natural period of vibration. 

 If the external impulses which it receives are of the same, or even 

 approximately, the same period. " Resonance " is produced, 

 with the result that the elasticity of the body may be overcome 

 and fracture may result. 



It is on the above account that bodies of troops break step 

 when crossing a bridge, and there are numerous other applica- 

 tions of the preceding laws in relation to both the utilisation of 

 the accumulation of impulses and also the avoidance of dangerous 

 consequences therefrom. 



