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 $v_0=2m/s$. At $t=0\sec$, the spring of constant $k=100N/cm$ is unstretched and the block has a speed $1m/s$ to left. The maximum extension of the spring (in $cm$ ) is______.

Answer 1

Answer: 6

In the frame (inertial) of the free end of spring, the initial velocity of block is $3m/s$ 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 $A=\sqrt{\frac{m}{k}}v=\sqrt{\frac{4}{10,000}}\times 3=6cm$