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Question Number 208741 by Tawa11 last updated on 22/Jun/24

Answered by mr W last updated on 22/Jun/24

Commented by mr W last updated on 22/Jun/24

$$\tan \varphi =\mu =0.3$$$$\frac{SC}{BC}=\frac{\sin (\theta +\varphi )}{\sin (\frac{\pi }{2}-\varphi )}=\frac{\sin (\theta +\varphi )}{\cos \varphi }$$$$\frac{SC}{AC}=\frac{\sin (\frac{\pi }{2}-\theta -\varphi )}{\sin \varphi }=\frac{\cos (\theta +\varphi )}{\sin \varphi }$$$$\frac{\sin (\theta +\varphi )}{\cos \varphi }=\frac{\cos (\theta +\varphi )}{\sin \varphi }$$$$\tan (\theta +\varphi )=\frac{1}{\tan \varphi }$$$$\frac{\tan \theta +\tan \varphi }{1-\tan \theta \tan \varphi }=\frac{1}{\tan \varphi }$$$$\frac{\tan \theta +\mu }{1-\mu \tan \theta }=\frac{1}{\mu }$$$$\Rightarrow \tan \theta =\frac{1-{\mu }^2}{2\mu }=\frac{1-0.3^2}{2\times 0.3}=\frac{91}{60}$$$$\Rightarrow \theta \approx 56.6°(ans.iii)$$$$R_1=mg\cos \varphi$$$$N_1=R_1\cos \varphi =mg{\cos }^2\varphi$$$$=30\times 10\times \frac{1^2}{1+0.3^2}=275.2N(ans.i)$$$$R_2=mg\sin \varphi$$$$F_2=R_2\sin \varphi =mg{\sin }^2\varphi$$$$=30\times 10\times \frac{0.3^2}{1+0.3^2}=24.8N(ans.ii)$$

Commented by Tawa11 last updated on 22/Jun/24

$$\mathrm{Wow},\mathrm{have}\mathrm{tried}\mathrm{several}\mathrm{time}.$$$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Commented by mr W last updated on 22/Jun/24

$$doyouhavesameresults?$$

Commented by Tawa11 last updated on 22/Jun/24

$$\mathrm{Yes}\mathrm{sir}.$$

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