9.4: Elastic-inelastic

We shall often be interested in cases where we transfer both energy and momentum from one particle to another, i.e., we have inelastic collisions where particles change their character – e.g., their rest-mass. If we have, as in Figure \(\PageIndex{1}\), two particles with energy-momentum \(k_1\) and \(p_q\) coming in, and two with \(k_2\) and \(p_2\) coming out, We know that since energy and momenta are conserved, that \(k_1+p_1=k_2+p_2\), which can be rearranged to give \[p_2=p_1+q,\quad k_2=k_1-q.\] and shows energy and momentum getting transferred. This picture will occur quite often!

Figure \(\PageIndex{1}\): A sketch of a collision between two particles.