Question

A plank of mass 10 kg and length L is placed on a frictionless surface. A block of mass 2 kg and negligible size is placed on the plank. Coefficient of friction between the plank and the block is $\mu =0.2$. The block is given sudden horizontal velocity of 2 m/s over the plank. Minimum value of L in meter so that the block does not fall from the plank is $[g=10m/s^2]$ (Write upto two digits after the decimal point.)

Answer 1

Place the frame of reference on the plank.
The acceleration of the plank with respect to ground = $\frac{f}{10}=\frac{mg\mu }{10}=0.4$
The friction $f=4N$

Therefore, the pseudo force on the 2 kg block is $2\ast 0.4=0.8N$

The net force of the 2 kg block is friction + pseudo force = $f+0.8=4.8N$

The decelleration of the block is $\frac{4.8}{2}=2.4m/s^2$
$v^2-u^2=2aS$
$0-2^2=-2\times 2.4\times S$
$S=0.83m$