Q.
The figure shows the top view of a block $B$ of negligible size and mass $m=2\, kg$ lying on a smooth horizontal plane. The board $A C$ moves with a constant acceleration $a_{0}=10\, m / s ^{2}$ in the direction shown. The coefficients of friction between the board and the block are $\mu_{s}=0.6$ and $\mu_{k}=0.5$. Calculate acceleration (in $m / s ^{2}$ ) of the block relative to the board at the instant shown.
Laws of Motion
Solution:
w.r.t. board $A C$
$N=20 \cos 37^{\circ}=20 \times 4 / 5=16$
$f_{s \max }=9.6, f_{k}=8$
$20 \sin 37^{\circ}-f_{k}=2 a$
$20 \times 3 / 5-8=2 a$
$\Rightarrow a=2\, m / s ^{2}$
