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Unformatted text preview: Collisions The previous example is an example of a collision . Collisions play a central role in many parts of modern physics and are the basis of our current understanding of particle physics. The essential effect of collisions is to redistribute the total momentum of the colliding objects. We can classify all collisions into one of three categories: 1. Elastic collisions , which conserve kinetic energy, 2. Inelastic collisions , which do not conserve kinetic energy, and 3. Completely inelastic collisions , in which the objects stick together afterwards. No matter what type of collision occurs, we can study them all in the same way. The guiding principle is that of conservation of linear momentum. A simple way of dealing with collisions is to use the concept of the center of mass. Suppose we have a collection of n particles, with a mass of m 1 , m 2 ,..., m n respectively. Also, let the position of the particles be given by ( x 1 , y 1 ), ( x 2 , y 2 ),...,( x n , y n ). Then recall that the center of mass for this system is at x m x m CM i i i n i i n = = = 1 1 We can now replace all of our equations of motion with equations involving the center of mass; thus m p m v m m m dt x d v CM n i i n i i i n i i n i dt x d i CM CM i = = = = = = = = 1 1 1 1 (14.1) and...
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