A Close Examination on Inelastic Collision

TL;DR

This paper provides a detailed analysis of inelastic collisions, deriving quantities like displacement and collision time under constant force assumptions, and applies the theory to experimental data to determine interaction forces.

Contribution

It introduces a detailed model of inelastic collision with constant interaction force, extending traditional short-collision-time assumptions, and applies it to real experimental data.

Findings

Calculated collision time and force from experimental data.

Identified conditions for negligible collision time.

Extended understanding of inelastic collision dynamics.

Abstract

This paper examines the details of an inelastic collision when a bullet shoots a block vertically upward from below. With the assumption of constant interaction force between them, we obtain quantities of interest including the displacement for the block at the end of collision, the collision time, and in particular, the bullet's depth inside the block, which are not studied under the traditional assumption of very short collision time. We identify the condition under which the collision time can indeed be considered as negligibly short. The theory is applied to a well-known demonstration. Using the data extracted from photos of the demonstration, we calculate the magnitude of interaction force and the collision time, which can in no way be easily measured otherwise.