Question

How large must $F$ be in the figure shown to give the $700\, g$ block an acceleration of $30 cm / s ^{2} ?$ The coefficient of friction between all surfaces is $0.15 .$

• A. 2.18 N
• B. 3.18 N
• C. 4 N
• D. 6 N

Answer 1

Answer: (A)

Frictional force on $200 g$ block, $f_{1}=\mu(0.2 g)$
Frictional force on $700 g$ block and table, $f_{2}=\mu(0.9 g)$
The free body diagrams of blocks are shown in the figure.

Their equations of motion are
$T-\mu(0.2 g)=0.2 a \,\,\,\, (i)$
$F-T-\mu(0.2 g)-\mu(0.9 g)=0.7 a \,\,\,\,\, (ii)$
Adding $(i)$ and $(ii)$, we get
$F-2 \mu(0.2) g-\mu(0.9 g)=0.9 a$
or $ F=0.9 a+\mu(1.3 g)=0.9 \times 0.3+0.15 \times 1.3 \times 9.8=2.18 N$