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. $\sqrt{\frac{m v_{0}^{2}}{2 k}}$
• C. $\sqrt{\frac{9 m v_{0}^{2}}{2 k}}$
• D. None of these

Answer 1

Answer: (C)

$2mv=m2v_{0}-mv_{0}$
$v=\frac{v_{0}}{2}$
$w_{s}=k_{f}-k_{i}$
$-\frac{k}{2}\left(x^{2} - 0^{2}\right)=\frac{1}{2}2mv^{2}-\left(\frac{1}{2} m v_{0}^{2} + \frac{1}{2} m \left(2 v_{0}\right)^{2}\right)$
$=m\left(\frac{v_{0}}{2}\right)^{2}-\frac{5 m v_{0}^{2}}{2}$
$\Rightarrow \, - \, \frac{k x^{2}}{2}=-\frac{9 m v_{0}^{2}}{4}$
$x=\sqrt{\frac{9}{2} \frac{m v_{0}^{2}}{k}}$