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Question Number 89300 by I want to learn more last updated on 16/Apr/20

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Commented by I want to learn more last updated on 16/Apr/20

Determine the minimum horizontal force required to maintain a 10kg box on a ramp inclined at 30° to the horizontal if the coefficient of friction is 0.2

Commented by mr W last updated on 17/Apr/20

Commented by mr W last updated on 17/Apr/20

$$N=mg\cos \alpha +F\sin \alpha$$$$f=mg\sin \alpha -F\cos \alpha$$$$f=\mu N$$$$mg\sin \alpha -F\cos \alpha =\mu (mg\cos \alpha +F\sin \alpha )$$$$mg(\sin \alpha -\mu \cos \alpha )=F(\mu \sin \alpha +\cos \alpha )$$$$mg(\tan \alpha -\mu )=F(\mu \tan \alpha +1)$$$$\Rightarrow F=\frac{mg(\tan \alpha -\mu )}{\mu \tan \alpha +1}=\frac{10\times 10(\tan 30°-0.2)}{0.2\times \tan 30°+1}$$$$=33.83N$$

Commented by I want to learn more last updated on 17/Apr/20

$$\mathrm{Thanks}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}.$$

Answered by 242242864 last updated on 17/Apr/20

$$\mathit{H}orizontalforce=\mathit{F}$$$$\mathit{R}esolvingalongtheplane$$$$\mathit{F}\cos \propto +\mathit{u}\mathit{R}=\mathit{m}\mathit{g}\sin \propto .......\left(\mathit{i}\right)$$$$\mathit{V}erticallytheplane,$$$$\mathit{F}\sin \propto +\mathit{m}\mathit{g}\cos \propto =\mathit{R}$$$$\Rightarrow \mathit{F}\cos \propto +\mathit{u}(\mathit{F}\sin \propto +\mathit{m}\mathit{g}\cos \propto )=\mathit{m}\mathit{g}\sin \propto$$$$but\propto ={30}^{°}$$$$\mathit{F}\cos {30}^{°}+0.2(\mathit{F}\sin {30}^{°}+10\times 9.8\cos 30°)=10\times 9.8\sin {30}^{°}$$$$0.87\mathit{F}+0.1\mathit{F}+16.97=49$$$$\mathit{F}=\frac{32.03}{0.97}$$$$\mathit{F}=33.02\mathit{N}$$$$$$$$$$$$$$$$$$

Commented by I want to learn more last updated on 17/Apr/20

$$\mathrm{Thanks}\mathrm{sir},\mathrm{i}\mathrm{appreciate}$$

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