A-block-of-mass-1-kg-is-pushed-against-a-rough-vertical-wall-with-a-force-of-20-N-coefficient-of-static-friction-being-1-4-Another-horizontal-force-of-10-N-is-applied-on-the-block-in-a-direction-p

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Question Number 21759 by Tinkutara last updated on 03/Oct/17

$$\mathrm{A}\mathrm{block}\mathrm{of}\mathrm{mass}1\mathrm{kg}\mathrm{is}\mathrm{pushed}\mathrm{against}$$$$\mathrm{a}\mathrm{rough}\mathrm{vertical}\mathrm{wall}\mathrm{with}\mathrm{a}\mathrm{force}\mathrm{of}20$$$$\mathrm{N},\mathrm{coefficient}\mathrm{of}\mathrm{static}\mathrm{friction}\mathrm{being}\frac{1}{4}.$$$$\mathrm{Another}\mathrm{horizontal}\mathrm{force}\mathrm{of}10\mathrm{N}\mathrm{is}$$$$\mathrm{applied}\mathrm{on}\mathrm{the}\mathrm{block}\mathrm{in}\mathrm{a}\mathrm{direction}$$$$\mathrm{parallel}\mathrm{to}\mathrm{the}\mathrm{wall}.\mathrm{Will}\mathrm{the}\mathrm{block}\mathrm{move}?$$$$\mathrm{If}\mathrm{yes},\mathrm{with}\mathrm{what}\mathrm{acceleration}?\mathrm{If}\mathrm{no},$$$$\mathrm{find}\mathrm{the}\mathrm{frictional}\mathrm{force}\mathrm{exerted}\mathrm{by}\mathrm{wall}$$$$\mathrm{on}\mathrm{the}\mathrm{block}.(g=10\mathrm{m}/{\mathrm{s}}^2)$$

Answered by ajfour last updated on 03/Oct/17

Commented by ajfour last updated on 03/Oct/17

$${block}^{\prime }saccelerationbea.$$$$Normalfromwall=20N$$$$\left(notinfigure\right)$$$$sincenetappliedforcealong$$$$thewall/surfaceisgreaterthan$$$$maximumvalueofstaticfriction$$$$kineticfriction={\mu }_{k}Ncomesinto$$$$play.$$$$if{\mu }_k={\mu }_s=\frac{1}{4},then$$$$f={\mu }_{k}N=\frac{1}{4}\times 20=5$$$$So$$$$10\sqrt{2}-5=1\times a$$$$a=14.14-5=9.14m/s^2.$$

Commented by Tinkutara last updated on 04/Oct/17

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

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