Two blocks A and B, each of mass m, are connected by an ideal spring of stiffness k and placed on a smooth horizontal surface. A ball of mass m moving with a velocity v 0 strikes the block A and get

Question

Two blocks A and B, each of mass m, are connected by an ideal spring of stiffness k and placed on a smooth horizontal surface. A ball of mass m moving with a velocity v 0 ​ strikes the block A and gets embedded to it. Then,

TestHub · Accepted Answer

During the brief inelastic impact, block B has no immediate velocity.

$m v_{0} = (2 m) v_{A}$

$v_{A} = \frac{v _{0}}{2}$

$v_{B} = 0$

$Δ K_{collision} = \frac{1}{2} m v_{0}^{2}$

$- \frac{1}{2} (2 m) (\frac{v _{0}}{2})^{2}$

$= \frac{1}{4} m v_{0}^{2}$

After impact, the 2m and m blocks have a common speed at maximum spring compression.

$v_{C} = \frac{( 2 m ) ( v _{0} /2 )}{3 m} = \frac{v _{0}}{3}$

$\frac{1}{2} k x_{m a x}^{2} = \frac{1}{2} (2 m) (\frac{v _{0}}{2})^{2}$

$- \frac{1}{2} (3 m) (\frac{v _{0}}{3})^{2}$

$= \frac{m v _{0}^{2}}{12}$

$x_{m a x} = v_{0} \frac{m}{6 k}$

All four statements are correct.

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