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Work

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 v₀ = 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 the left. The maximum extension of the spring (in cm) is ________.

Moderate

Solution

In the frame (inertial) of the free end of spring, the initial velocity of block is 3 m/s to the left and the spring unstretched.
Applying conservation of energy between initial and maximum extension state.
$\begin{array}{l} \frac{1}{2} {mv}^{2} = \frac{1}{2} {kA}^{2} \\ Or A = \sqrt{\frac{m}{k}} v = \sqrt{\frac{4}{10, 000}} \times 3 = 6 cm . \end{array}$

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