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 $g=10m/s^2$.

Answer 1

Answer: 5.00

Velocity when $2kg$ just about to collide.

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

Momentum
$2\times 0.6=-2V_1+4V_2$
$2V_2-V_1=\mathrm{0.6....}(1)$
$V_1+V_2=e(0.6)(e=1)$
$\frac{V_1+V_2=0.6}{3V_2=1.2}.....(2)$
$V_2=0.4m/s$
$V_1=0.2m/s$
Distances when they stop
(1) $\to 0^2=(0.2{)}^2-2(0.2g)\Delta x_1$
$\Rightarrow \Delta x_1=0.01m=1cm$
(2) $\to 0^2=(0.4{)}^2-2(0.2g)\Delta x_2$
$\Rightarrow \Delta x_2=4cm$
Separation b / w them $=1+4=5cm$