Collision Test Revisited with F=Ma and Amended Newton’s Third Law

Lim SK

Published on: 2023-10-28

Abstract

This paper aims to revisit the “rigid body” collision because it hasn’t been carefully studied as conventional method of study introduced the concept of elastic behavior which shall be the property of material. In this paper, reader shall learn how to define in what cases F=ma or Rectified Newton’s Third Law [1] is applicable, follow by the proof of conservation of linear momentum simply is the consequence of application of F=ma.

Keywords

Collision; Rigid Body; F=ma; Rectified Newton’s Third Law; Conservation of linear momentum; Law of motion

Introduction

When talking about collision tests between two objects, scholars always start the study by first introducing the principles of conservation of energy and conservation of momentum in conjunction with F=ma and Newton’s Third Law. The collision is considered “elastic” if the kinetic energy is conserved. The meaning of "elastic,” as described by Feynman in his lecture, is excerpted

"...two bodies of equal mass that collide at equal speeds and then rebound. For a brief moment, they are in contact, and both are compressed. At the instant of maximum compression, they both have zero velocity, and energy is stored in the elastic bodies, as in a compressed spring. This energy is derived from the kinetic energy the bodies had before the collision, which becomes zero at the instant their velocity is zero. The loss of kinetic energy is only momentary, however. The compressed condition is analogous to the cap that releases energy in an explosion. The bodies are immediately decompressed in a kind of explosion and fly apart again, but we already know that case—the bodies fly apart with equal speeds. However, this speed of rebound is less, in general, than the initial speed because not all the energy is available for the explosion, depending on the material. If the material is putty, no kinetic energy is recovered, but if it is something more rigid, some kinetic energy is usually regained. In the collision, the rest of the kinetic energy is transformed into heat and vibrational energy—the bodies are hot and vibrating. The vibrational energy is soon transformed into heat. It is possible to make the colliding bodies from highly elastic materials, such as steel, with carefully designed spring bumpers, so that the collision generates very little heat and vibration. In these circumstances, the velocities of rebound are practically equal to the initial velocities; such a collision is called elastic. [2]

Thus, the introduction of “spring energy” in the collision had a direct consequence of the concept of potential energy being brought into their analysis. But is that the highest level of study on collisions?

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