Question

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

• A. $16m{s}^{-2}$
• B. $8m{s}^{-2}$
• C. $38m{s}^{-2}$
• D. $54m{s}^{-2}$

Answer 1

Answer: (B)

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