Question

A block of mass $2\, kg$ is being pushed against a wall by a force $F = 90\, N$ as shown in the figure, If the coefficient of friction is $0.25$. then the magnitude of acceleration of the block is_____
$(g = 10 \, ms^{-2} ) \left( \sin \, 37^{\circ} = \frac{3}{5} \right)$

• A. $16 \, ms^{-2}$
• B. $8 \, ms^{-2}$
• C. $38\, ms^{-2}$
• D. $54 \, ms^{-2}$

Answer 1

Answer: (B)

Block's weight (downward), $w=2 \times 10=20\, N$
Vertical component of applied force (upwards),
$F_{V}=F \sin \theta=90 \times 3 / 5=54 N$
Maximum frictional force,
$F_{r} =\mu F \cos \theta=0 \cdot 25 \times 90 \times 4 / 5$
$=18\, N$
$\therefore $ Net vertical force, $F_{\text {net }}=F_{V}-\left(F_{r}+w\right)=m a$
$\therefore F_{\text {net }}=54-18-20=16\, N =m a$
$\Rightarrow a=\frac{16}{2}=8\, m / s ^{2}$