Authors: Ajay Sharma
Consider compiling a set of one hundred observations of diverse rebounding bodies on a common surface. These bodies may have identical mass and composition but different shapes, such as spheres, cones, needles flat sheets, and irregular forms, and they rebound to different heights. These experiments are classified into realistic physical systems. In existing physics, motion of bodies is explained by the coefficient of restitution method (CORM), the equations are based Newton’s third law of motion (NTLM) and kinematical equations, which explains phenomena qualitatively. Hertz contact method also explains motion of bodies in very limited range. Under suitable conditions, a spherical ball may rebound nearly to its original height, retracing its path, and the rebound height may be treated as an indicator of reaction force. In contrast, a flat body rebounds to a minimal height whereas irregular bodies rebound along trajectories at varying angles. The typical motions of sphere, flat and irregular bodies may be explained with a single equation quantitatively. Even recoil velocity of gun based on the conservation of momentum, is not quantitatively confirmed at macroscopic level. Thus, NTLM may be used independently to explain the behavior of rebounding bodies, in realistic system NTLM is expressed as Reaction (FBA) = − [Kshape × Kcomposition × Ktarget × Kother] Action (FAB). Accordingly for recoil of gun we get, vgun = - mbullet .vbullet /Zmgun. The proposed generalization may be examined through quantitative experiments involving diverse parameters, where and Z represent experimentally determined coefficients. This law is specifically tailored for rebounding bodies in real-world scenarios, providing a phenomenological framework to describe experimental observations. Distinct theoretical treatments may be required for rebounding bodies in idealized versus real-world systems. The results motivate consideration of an extended interaction framework that incorporates geometric and surface-dependent factors within a Newtonian context.
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