Question

Two blocks A and B each of mass m are connected by a massless spring of natural length L and spring constant K. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B, and collides elasticity with A. Then ?

• A. The kinetic energy of the A-B system at maximum compression of the string, is zero
• B. The kinetic energy of the A-B system, at maximum compression of the spring, is $m{v}^2/4$
• C. The maximum compression of the spring is $v\sqrt{\left(m/K\right)}$
• D. The maximum compression of the spring is $v\sqrt{\left(m/2K\right)}$

Answer 1

The correct option is A The kinetic energy of the A-B system at maximum compression of the string, is zero

$mv=(m+m)v\prime$

$v\prime =v/2$

$mv=(m+m)v\prime$

$\frac{1}{2}{mv}^2=\frac{1}{2}\left(2m\right)(\frac{v}{2}{)}^{2+}\frac{1}{2}k{v}^2$

$v\sqrt{\frac{m}{2k}}$