A simple pendulum consisting of a mass M atta | vedclass

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Question

(B) By the principle of conservation of mechanical energy,the potential energy at the initial position must equal the potential energy at the final po

Vedclass · Accepted Answer

$\cos^{-1}\left[ \frac{L\cos \alpha - l}{L - l} \right]$

Vedclass · Answer

(B) By the principle of conservation of mechanical energy,the potential energy at the initial position must equal the potential energy at the final position.Let the pivot point be the reference level for potential energy $(PE = 0)$.Initial height of the mass $M$ from the pivot is $h_i = -L \cos \alpha$.Final height of the mass $M$ from the pivot after hitting the pin is $h_f = -l - (L - l) \cos 	heta$.Equating the potential energies: $Mg(-L \cos \alpha) = Mg(-l - (L - l) \cos 	heta)$.$-L \cos \alpha = -l - (L - l) \cos 	heta$.$(L - l) \cos 	heta = L \cos \alpha - l$.$\cos 	heta = \frac{L \cos \alpha - l}{L - l}$.Therefore,$	heta = \cos^{-1}\left[ \frac{L \cos \alpha - l}{L - l} ight]$.

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