Question

The friction coefficient between the horizontal surface and each of the block shown in the figure is $0.2$. The collision between the blocks is perfectly elastic. Find the separation (in $cm$ ) between them when they come to rest. Take $g=10\, m / s ^{2}$.

Answer 1

Velocity when $2 \,kg$ just about to collide.

$V^{2}=u^{2}+2 \,a s$
$V^{2}=1^{2}+2(-2)\left(\frac{16}{100}\right)$
$V^{2}=1-\frac{64}{100}$
$V^{2}=\frac{36}{100}$
$\Rightarrow V =0.6\, m / s$

Momentum
$2\times 0.6 = -2V_1 + 4V_2$
$2V_2 - V_1 = 0.6....(1)$
$V_1 + V_2 = e(0.6)(e = 1)$
$\frac{V_1 + V_2 = 0.6}{3V_2 = 1.2} .....(2)$
$V_2 = 0.4\,m/s$
$V_1 = 0.2\,m/s$
Distances when they stop
(1) $\rightarrow 0^{2}=(0.2)^{2}-2( 0.2 \,g) \Delta x_{1}$
$\Rightarrow \Delta x _{1}=0.01\, m =1 \,cm$
(2) $\rightarrow 0^{2}=(0.4)^{2}-2(0.2 g ) \Delta x _{2}$
$\Rightarrow \Delta x _{2}=4 \,cm$
Separation b / w them $=1+4=5 \,cm$