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Question Number 46180 by ajfour last updated on 22/Oct/18

Commented by ajfour last updated on 22/Oct/18

$$Ifthestickisreleasedinthe$$$$positionasshownindiagram,$$$$endAslidesonyzwallthen$$$$losescontactwithitatP.Find$$$$coordinatesofP.Assumeall$$$$surfacesfrictionless.$$

Commented by ajfour last updated on 22/Oct/18

Commented by ajfour last updated on 22/Oct/18

$$LetA(0,y,z);B(x,0,0)$$$$N_1=m\frac{d^2\left(x/2\right)}{{dt}^2}=\frac{{ma}_1}{2}....\left(i\right)$$$$N_2=\frac{{ma}_2}{2};N_3-mg=\frac{{ma}_3}{2}...\left(ii\right)\mathrm{\&}\left(iii\right)$$$$x=l\cos \theta \cos \varphi ;$$$$y=l\cos \theta \sin \varphi ;z=l\sin \theta$$$$....\left(iv\right),\left(v\right),\left(vi\right)$$$$(N_1\sin \varphi -N_2\cos \varphi )\frac{l}{2}\cos \theta$$$$=\frac{d}{dt}\left(\frac{{ml}^2{\omega }_{\varphi }\cos {}^2\theta }{12}\right)....\left(vii\right)$$$$(N_1\cos \varphi +N_2\sin \varphi )\frac{l}{2}\sin \theta$$$$-N_3\left(\frac{l}{2}\cos \theta \right)=\left(\frac{{ml}^2}{12}\right)\frac{d^2\theta }{{dt}^2}..\left(viii\right)$$$$unknowns{N}_1,N_2,N_3,x,y,z,$$$$\theta ,\varphi .$$

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