A-1-kg-block-is-being-pushed-against-a-wall-by-a-force-F-75-N-as-shown-in-the-figure-The-coefficient-of-friction-is-0-25-The-magnitude-of-acceleration-of-the-block-is-

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Question Number 20579 by Tinkutara last updated on 28/Aug/17

$$\mathrm{A}1\mathrm{kg}\mathrm{block}\mathrm{is}\mathrm{being}\mathrm{pushed}\mathrm{against}\mathrm{a}$$$$\mathrm{wall}\mathrm{by}\mathrm{a}\mathrm{force}F=75\mathrm{N}\mathrm{as}\mathrm{shown}\mathrm{in}$$$$\mathrm{the}\mathrm{figure}.\mathrm{The}\mathrm{coefficient}\mathrm{of}\mathrm{friction}\mathrm{is}$$$$0.25.\mathrm{The}\mathrm{magnitude}\mathrm{of}\mathrm{acceleration}\mathrm{of}$$$$\mathrm{the}\mathrm{block}\mathrm{is}$$

Commented by Tinkutara last updated on 28/Aug/17

Commented by ajfour last updated on 28/Aug/17

$$N=F\cos 37°=75\times \frac{4}{5}=60N$$$$f_{max}=\mu N=\frac{1}{4}\times 60=15$$$$F_y=F\sin 37°=75\times \frac{3}{5}=45N$$$$\mathrm{\Sigma }{F}_y=ma$$$$F_y-mg-f_{max}=ma$$$$\Rightarrow 45-10-15=a$$$$\Rightarrow \mathit{a}=20\mathit{m}/{\mathit{s}}^2.$$

Commented by Tinkutara last updated on 28/Aug/17

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

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