Question

The figure shows the top view of a block $B$ of negligible size and mass $m=2kg$ lying on a smooth horizontal plane. The board $AC$ moves with a constant acceleration $a_0=10m/s^2$ 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.

Answer 1

Answer: 2

w.r.t. board $AC$
$N=20\cos 37^{\circ }=20\times 4/5=16$
$f_{s\max }=9.6,f_k=8$
$20\sin 37^{\circ }-f_k=2a$
$20\times 3/5-8=2a$
$\Rightarrow a=2m/s^2$