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neilparker62

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Introduction

This article follows on from the previous on an alternate approach to solving collision problems. In that article, we determined the equal and opposite collision impulse to have magnitude ##\mu \Delta v## for perfectly inelastic collisions, ##\mu(1+e) \Delta v## for semi-elastic collisions and ##2\mu \Delta v## for elastic collisions which will be the focus here. Reduced mass ##\mu=\frac{m_1m_2}{m_1+m_2}## – where ##m_1## and ##m_2## are the colliding masses – and ##\Delta v## is their relative velocity along the line of collision. e is the coefficient of restitution.

Since the previous article focused on 1-dimensional collisions, the aim here is to develop a method of solving 2-dimensional elastic collision problems using a Cartesian plane in which the x and y axes are defined to be respectively parallel and perpendicular (normal) to the line of collision. The latter is defined by the post-collision direction of the stationary mass since it cannot attain momentum...

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