Solve the following :


A block of mass $2 \mathrm{~kg}$ is pushed against a rough vertical wall with a force of $40 \mathrm{~N}$, coefficient of static friction being $0.5$. Another horizontal force of $15 \mathrm{~N}$, is applied on the block in a direction parallel to the wall. Will the block move? If yes, in which direction? If no, find the frictional force exerted by the wall on the block.


Net driving force on the block

$F_{\text {driving }}=\sqrt{(m g)^{2}+(15)^{2}}$

Limiting friction force $=\mu R=0.5 \times 40=20 \mathrm{~N}$

$\approx F_{\text {driving }}>f f_{(\mathrm{lm})}$ block will move.

For acceleration,

$F_{\text {Net }}=25-20$

$m \times a=5$

$2 \times a=5$

$a=2.5 \mathrm{~m} / \mathrm{s}^{2}$

Direction w.r.t $15 \mathrm{~N}$ force

$\tan \phi=\frac{20}{15}=\frac{4}{3}$

$\phi=53^{\circ}$ with $15 \mathrm{~N}$ force.

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