Classical Mechanics (Kibble & Berkshire) · Problem 10.17

The angular momentum principle — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · collisions

Problem

Some inequalities in elastic collisions Use the elastic scattering formulae to show the following inequalities: (i) When m1>m2m_1 > m_2, the scattering angle θ1\theta_1 is restricted to the range 0≤θ1≤sin⁡−1(m2/m1)0 \leq \theta_1 \leq \sin^{-1}(m_2/m_1). (ii) If m1<m2m_1 < m_2, the opening angle is obtuse, while, if m1>m2m_1 > m_2, the opening angle is acute. (iii) E1E0≥(m1−m2m1+m2)2,E2E0≤4m1m2(m1+m2)2.\frac{E_1}{E_0} \geq \left(\frac{m_1-m_2}{m_1+m_2}\right)^2, \qquad \frac{E_2}{E_0} \leq \frac{4m_1 m_2}{(m_1+m_2)^2}.

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