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Question Number 109167 by Dwaipayan Shikari last updated on 21/Aug/20

	Answered by mr W last updated on 21/Aug/20

	$b a l l :$ $b e f o r e c o l l i s i o n v_{i} = \sqrt{2 g l}$ $a f t e r c o l l i s i o n v_{f} = \sqrt{2 g l (1 - \cos θ)}$ $b l o c k :$ $b e f o r e c o l l i s i o n V_{i} = 0$ $a f t e r c o l l i s i o n V_{f}$ $\frac{1}{2} (2 m) V_{f}^{2} = μ (2 m) g \times \frac{3 l}{2}$ $\Rightarrow V_{f} = \sqrt{3 μ g l}$ ${e v}_{i} = v_{f} + V_{f}$ $e \sqrt{2 g l} = \sqrt{2 g l (1 - \cos θ)} + \sqrt{3 μ g l}$ $\Rightarrow \frac{2}{3} = \sqrt{1 - \cos θ} + \sqrt{\frac{3 μ}{2}} . . . (i)$ ${m v}_{i} = - {m v}_{f} + (2 m) V_{f}$ $v_{i} + v_{f} = 2 V_{f}$ $\sqrt{2 g l} + \sqrt{2 g l (1 - \cos θ)} = 2 \sqrt{3 μ g l}$ $\Rightarrow 1 + \sqrt{1 - \cos θ} = \sqrt{6 μ} . . . (i i)$ $\Rightarrow μ = \frac{25}{96}$ $\Rightarrow θ = \cos^{- 1} \frac{15}{16} \approx 20.36 °$
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