Question

A block of mass $5\, kg$ is pulled by a force $F$ as shown in the figure. If the coefficient of friction is $0.1,$ then the force needed to accelerate the block to $3\, m / s ^{2}$ to the right is close to

• A. 12 N
• B. 22 N
• C. 32 N
• D. 42 N

Answer 1

Answer: (B)

Component of force accelerating the block is $F \cos \theta$
Net force on block, $F_{\text {net }}=F \cos \theta-\mu\, N$
$=F \cos 30^{\circ}-0.1 \times 5 \times 9.8$
$=\frac{\sqrt{3} F}{2}-4.9$
From, $F_{\text {net }}=m a$, we have,
$\frac{\sqrt{3}}{2} F-4.9=5 \times 3$
$\Rightarrow F=\frac{19.9}{\sqrt{3}}=22.9\, N$