Question

The friction coefficient between the horizontal surface and each of the blocks shown in figure. is 0.20. The collision between the blocks is perfectly elastic. Find the separation between the two blocks when they come to rest. Take $g=10m/s^2$.

Answer 1

$\mu =0.20,g=10m/s^2$

Block of mass 2kg will reach to the 4kg mass with velocity;

$v^2-u^2=2as$

$v=\sqrt{1-\frac{2\times 2\times 16}{100}}$

$v=\frac{3}{5}m/s$

After collision, according to momentum conservation;

$4v_2+2v_1=\frac{2\times 3}{5}$ ............(1)

$v_{sep}=v_{app}$

$v_2-v_1=\frac{3}{5}$ ............(2)

On solving;

$v_1=-\frac{1}{5}m/s$

$v_2=\frac{4}{5}m/s$

Distance travelled by 2kg block;

$s=\frac{u^2}{2\mu g}=\frac{1}{25\times 2\times 2}=\frac{1}{100}$

Distance travelled by 4kg block;

$s=\frac{16}{100}$

$Sep=\frac{16}{100}+\frac{1}{100}=\frac{17}{100}=17cm$