Question

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

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

Answer 1

Answer: (A)

Frictional force on $200g$ block, $f_1=\mu (0.2g)$
Frictional force on $700g$ block and table, $f_2=\mu (0.9g)$
The free body diagrams of blocks are shown in the figure.

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