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Question Number 20412 by Tinkutara last updated on 26/Aug/17

$$\mathrm{A}\mathrm{block}\mathrm{is}\mathrm{placed}\mathrm{on}\mathrm{a}\mathrm{rough}\mathrm{horizontal}$$$$\mathrm{surface}.\mathrm{The}\mathrm{minimum}\mathrm{force}\mathrm{required}$$$$\mathrm{to}\mathrm{slide}\mathrm{the}\mathrm{block}\mathrm{is}$$

Commented by Tinkutara last updated on 26/Aug/17

Commented by ajfour last updated on 26/Aug/17

$$P\cos \theta =f_{max}=\mu N$$$$N+P\sin \theta =mg$$$$SoP\cos \theta =\mu (mg-P\sin \theta )$$$$\Rightarrow P=\frac{\mu mg}{\cos \theta +\mu \sin \theta }$$$$=\frac{\mu }{\sqrt{1+{\mu }^2}}\times \frac{mg}{\sin [\theta +{\tan }^{-1}\left(\frac{1}{\mu }\right)]}$$$$Pisleastwhen\theta =\frac{\pi }{2}-{\cot }^{-1}\mu$$$$orwhen\theta ={\tan }^{-1}\mu$$$$P_{minimum}=\frac{\mu mg}{\sqrt{1+{\mu }^2}}.$$

Commented by Tinkutara last updated on 26/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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