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New in this study is the mathematical formula for calculating energy dissipated due to sliding under the action of Coulomb kinetic friction in the context of Impulse Momentum Planar Collision (IMPC) with isotropic restitution. The surface sliding dissipated energy theorem established here is precisely consistent with the laws of physics underlying IMPC. A principal goal of distinguishing between surface sliding energy dissipation and energy dissipation due to vehicle crush is to improve the rational basis for use of crush energy analysis with IMPC. Also new in this study is a consistent interpretation of Newton's, Poisson's and Stronge's restitution hypotheses as they apply to IMPC with Coulomb kinetic friction. While this paper adds to the understanding of energy dissipation, the IMPC method presented here is not new.

Externally applied unbalanced forces and their corresponding impulses are generally excluded from consideration in regards to the evaluation of the collision phase events for a system comprised of two motor vehicles undergoing collinear impact. This exclusion is generally warranted secondary to the fact that the collision force and its corresponding impulse are dominant during the collision phase. Conceptually, two exclusions exist to this approach. The first is the situation in which significant physical restraints are present to the displacement of one or both collision partners and are of sufficient magnitude as to require inclusion. Generally, this represents the exceptional case and includes, but is not limited to, situations in which one vehicle is snagged, in a non-eccentric manner, by a rigid narrow-width object such as a pole or other similar restraint, prior to the occurrence of the subsequent vehicle-to-vehicle collision under evaluation.

Accident reconstruction typically requires estimating the change of velocity (Delta-V) imparted to vehicles during collision. Estimating Delta-V commonly involves measuring or estimating the deformation of the vehicles involved in a collision. Material coefficients, which relate barrier equivalent velocity (BEV) to deformation for the two vehicles, are then interpolated or extrapolated from barrier crash test data. Finally, the Delta-V for each of the two vehicles is usually calculated using single-degree-of-freedom (SDOF) impact mechanics formulas. This paper presents a derivation of SDOF impact mechanics formulas applicable to one-dimensional vehicle collisions. The governing equations presented are new, more complete and more efficient than previously published efforts. In particular, Newton's third law of physics concerning collision force is proportionally expressed as the product of vehicle weight, crush progression behavior and BEV.