How an Impetus Impressed in Elastic Bodies is Slowed Down and Extinguished




(1)
Mathematics in Naples, Naples, Italy

 


 Deceased



Anybody who discerns the genius of nature which always carries out similar operations similarly in the simplest and easiest way and does not like changing its method, will easily be persuaded that impetus is not extinguished and annihilated in elastic bodies, no more than it is in absolutely hard and inelastic bodies. Therefore, the theory presented above will not be useless to clear up the matter with as much perspicacity as possible. Beforehand, to start more easily, the nature and property of elastic bodies must be explained. They result from some relatively common instruments such as lever, nail and others of the same kind.


Proposition LXVIII


If the extremity of a lever is impelled by a motive virtue so as to succeed in overcoming the resistance offered at the other extremity of the lever by cohesion or a compressing body, the resistance acts against the impelling force like an opposite motive force resisting without any percussion.

Let the fulcrum of the lever CD be E (Table 16.​1, Fig. 53). At its extremity D there is a resistance B or a weight, either some glue or something else tenacious which must be divided or disrupted. The other extremity C of the lever is impelled by the motive energy or virtue of the body A moving at a velocity V. According to mechanics, there is equilibrium of course if the moment of the motive virtue of A is equal to the moment of the resistance B: the forces being balanced, neither the body A propels the extremity C of the lever nor is it repelled by the energy of the resistance of B. If the moment of A is greater than the moment of the resistance B, the extremity C of the lever is propelled by the force of A and the resistance B is overpowered and expelled or disrupted. It must be seen how the resistance B works. The action of the resistance can certainly be considered as an opposite movement. If the resistance B is removed and replaced by another body M which, in a movement opposite to A and with an equal moment or motive virtue opposes the impulse of A, then unquestionably the forces of the two bodies A and M impelling each other in opposite movements without percussion are balanced. As a result, each of them is immobile and the impetus of each of the two bodies is extinguished. Thus, the impetus of A is refrained and extinguished by the resistance B acting at the extremity D of the lever, as if it were by the direct impelling virtue of the body M driving back the course of A in an opposite movement. Consequently, if the forces of B and M generate the same effect of extinction of the movement of A, their motive forces, not only are equally strong, but, moreover, act in the same way. Both repel and refrain the course of the impetus of A. Consequently, the resistance of the body B, although seemingly inert, nevertheless has and exerts a motive energy which, by an opposite force and impetus, opposes the course of the body A towards C.


Proposition LXIX


A column is fixed to a wall and its extremity is impelled by a motive virtue. The resistance to its breakage at the base close to the wall is placed at the extremity of the deflected lever and the resistance acts similarly in so far as it repels the opposite impulse.

A column CED is supposed to be fixed to the wall RS (Table 16.​1, Fig. 54). At its extremity C it is impelled by the motive virtue of A at a velocity V. The column must also be conceived as a deflected lever FED the centre of which is the extremity E. This centre is sustained by the consistency of the wall. The resistance is a glue or any other retaining force by which the parts of the column are tied to the other adjacent parts fixed inside the wall. This retaining force actually is distributed over all the surface of the base DE. This retaining force is also the resistance which exerts its energy at the centre of its base DE against the blow of the body A. Here also the resistance of this retaining force reacts against the impulse of A in an opposite movement and impetus. It resists indeed in so far as it repels the straight impulse of the body A and so in the collision at the extremity C either extinguishes or slows down the impetus of the propelling body A.

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Oct 7, 2016 | Posted by in GENERAL | Comments Off on How an Impetus Impressed in Elastic Bodies is Slowed Down and Extinguished

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