Abstract
It is well established that the law of conservation of momentum is applicable to all interactions between any two bodies during an impact. The law dictates that the total momentum before a collision is the same as the total momentum after the collision (for elastic collisions). This law has been accepted as a fundamental part of Newtonian physics since Newton incorporated Descartes’ work into his own. Scientists rarely question its applicability to kinematics of bodies in the non-quantum world. The law of conservation of momentum is regularly used in vehicle accident reconstruction to calculate a speed of one of the vehicles before or after the collision, assuming that the masses of the vehicles and sufficient other velocities are known. Collisions of vehicles with highly disparate masses pose an interesting dilemma. In such a collision, the speed of the higher mass vehicle will change very little in a collision with a vehicle of much smaller mass and the speed change of the smaller mass vehicle will be large. This is due to the ratio of the masses of the two vehicles which minimizes the effect of the smaller mass vehicle on the vehicle of larger mass. The lopsided nature of the speed change of this kind of collision can lead one to conclude that momentum is not applicable to collisions between vehicles of dramatically different masses. The objective of this work is to investigate the effect of dissimilar masses of vehicles on the effectiveness of momentum to accurately predict speed change. The mathematical formulation of the error associated with dissimilar mass vehicles is presented and quantified to give the reconstructionist guidance in when momentum can be used reliably and when the error resulting from the use of momentum may be larger than desired.
