1. A cue ball of mass m with kinetic energy K collides elastically with an eight-ball of mass me at rest. Derive the relationship between the deflection angle of the cue ball (0) and its kinetic energy after the collision (p²/2m). That is, express 0 as a function of K' and K.
1. A cue ball of mass m with kinetic energy K collides elastically with an eight-ball of mass me at rest. Derive the relationship between the deflection angle of the cue ball (0) and its kinetic energy after the collision (p²/2m). That is, express 0 as a function of K' and K.
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Transcribed Image Text:### Problem Set on Elastic Collisions
1. A cue ball of mass \( m \) with kinetic energy \( K \) collides elastically with an eight-ball of mass \( m_e \) at rest. Derive the relationship between the deflection angle of the cue ball (\( \theta \)) and its kinetic energy after the collision (\( p'^2 / 2m \)). That is, express \( \theta \) as a function of \( K' \) and \( K \).
2. For the situation described in Problem 1, if \( m < m_e \), then it is possible for \( m \) to bounce directly backwards (i.e., with a deflection angle of \( \theta = \pi \)). However, if \( m > m_e \), then there is a maximum deflection angle. Find this angle.
These problems explore the principles of elastic collisions in physics, encouraging the derivation and understanding of kinetic energy transformations and deflection angles in a practical scenario involving billiard balls.
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