Question

A block of mass 1 kg is horizontally thrown with a velocity of 10 $m{s}^{-1}$ on a stationary long plank of mass 2 kg whose surface has a $\mu =0.5$. Plank rests on frictionless surface. Find the time when $m_1$ comes to rest w.r.t. plank.

Answer 1

Consider the common velocity of the system= $V$

By conservation of Momentum:-

$1\times 10=(2+1)V$

So, $V=10/3$

Force on block= $\mu mg=5\times 1\times 10=5N$

De-acceleration of block a= $5a/1=5m/s^2$

Let time to change the velocity from $10$ to $10/3$ is $t$ then,

$10-10/3=at=5t$

or, $t=\frac{20}{5\times 3}=\frac{4}{3}s$

Even at sliding condition, limiting friction is acting.