Question

The figure shows two blocks of mass $m$ each, connected by an ideal unstretched spring and then placed on a frictionless floor. If the blocks are given velocities $v_0$ and $2v_0$ as shown, then the maximum extension in the spring is

• A. $\sqrt{\frac{m{v}_0^2}{k}}$
• B. $\sqrt{\frac{m{v}_0^2}{2k}}$
• C. $\sqrt{\frac{9m{v}_0^2}{2k}}$
• D. None of these

Answer 1

Answer: (C)

$2mv=m2v_0-m{v}_0$
$v=\frac{v_0}{2}$
$w_s=k_f-k_i$
$-\frac{k}{2}\left(x^2-0^2\right)=\frac{1}{2}2m{v}^2-\left(\frac{1}{2}m{v}_0^2+\frac{1}{2}m{\left(2v_0\right)}^2\right)$
$=m{\left(\frac{v_0}{2}\right)}^2-\frac{5m{v}_0^2}{2}$
$\Rightarrow -\frac{k{x}^2}{2}=-\frac{9m{v}_0^2}{4}$
$x=\sqrt{\frac{9}{2}\frac{m{v}_0^2}{k}}$