Question

The spring-block system lies on a smooth horizontal surface. The free end of the spring is being pulled towards right with constant speed $v_{0}=2 \,m / s$. At $t=0 \,\sec$, the spring of constant $k=100\, N / cm$ is unstretched and the block has a speed $1\, m / s$ to left. The maximum extension of the spring (in $cm$ ) is______.

Answer 1

In the frame (inertial) of the free end of spring, the initial velocity of block is $3 \,m / s$ to left and the spring unstretched.

Applying conservation of energy between initial and maximum extension state.
$\frac{1}{2} m v^{2}=\frac{1}{2} k A^{2} $
or $ A=\sqrt{\frac{m}{k}} v=\sqrt{\frac{4}{10,000}} \times 3=6\, cm$