A-ladder-of-mass-m-is-leaning-against-a-wall-It-is-in-static-equilibrium-making-an-angle-with-the-horizontal-floor-The-coefficient-of-friction-between-the-wall-and-the-ladder-is-1-and-that-betw

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Question Number 22479 by Tinkutara last updated on 19/Oct/17

$$\mathrm{A}\mathrm{ladder}\mathrm{of}\mathrm{mass}m\mathrm{is}\mathrm{leaning}\mathrm{against}\mathrm{a}$$$$\mathrm{wall}.\mathrm{It}\mathrm{is}\mathrm{in}\mathrm{static}\mathrm{equilibrium}\mathrm{making}$$$$\mathrm{an}\mathrm{angle}\theta \mathrm{with}\mathrm{the}\mathrm{horizontal}\mathrm{floor}.$$$$\mathrm{The}\mathrm{coefficient}\mathrm{of}\mathrm{friction}\mathrm{between}\mathrm{the}$$$$\mathrm{wall}\mathrm{and}\mathrm{the}\mathrm{ladder}\mathrm{is}{\mu }_1\mathrm{and}\mathrm{that}$$$$\mathrm{between}\mathrm{the}\mathrm{floor}\mathrm{and}\mathrm{the}\mathrm{ladder}\mathrm{is}{\mu }_2.$$$$\mathrm{The}\mathrm{normal}\mathrm{reaction}\mathrm{of}\mathrm{the}\mathrm{wall}\mathrm{on}\mathrm{the}$$$$\mathrm{ladder}\mathrm{is}{\mathrm{N}}_1\mathrm{and}\mathrm{that}\mathrm{of}\mathrm{the}\mathrm{floor}\mathrm{is}{\mathrm{N}}_2.$$$$\mathrm{If}\mathrm{the}\mathrm{ladder}\mathrm{is}\mathrm{about}\mathrm{to}\mathrm{slip},\mathrm{then}$$$$\left(1\right){\mu }_1=0,{\mu }_2\ne 0\mathrm{and}{N}_2\tan \theta =mg/2$$$$\left(2\right){\mu }_1\ne 0,{\mu }_2=0\mathrm{and}{N}_1\tan \theta =mg/2$$$$\left(3\right){\mu }_1\ne 0,{\mu }_2\ne 0\mathrm{and}{N}_2=\frac{mg}{1+{\mu }_1{\mu }_2}$$$$\left(4\right){\mu }_1=0,{\mu }_2\ne 0\mathrm{and}{N}_1\tan \theta =\frac{mg}{2}$$

Commented by Tinkutara last updated on 19/Oct/17

Commented by ajfour last updated on 19/Oct/17

$$\left(3\right)and\left(4\right)arecorrect.$$$$SeeQ.22481forsolution.$$

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