Frictionless Slide Propulsion

Classical Mechanics Level 4

The part of mass \(m\) in the figure above slides down the frictionless surface through height \(h\) and collides with the uniform vertical rod of mass \(M\) and length \(d\), sticking to it. The rod pivots about the point \(o\) through the angle \(\theta\) before momentarily stopping. Then \(\theta \) can be expressed as

\[ \theta = \cos^{-1} \left[ \alpha - \frac{ \beta m^2 h } { d ( \gamma m +M) \times ( \nu m + M ) } \right] \]

What is the value of\(\alpha+\beta+\gamma+\nu\)?

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