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Question

A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k = 50 N / m$ . The maximum compression of the spring would be (in m)

Moderate

Solution

The kinetic energy of mass is converted into potential energy of a spring
$\frac{1}{2} {mv}^{2} = \frac{1}{2} {kx}^{2} \Rightarrow x = \sqrt{\frac{{mv}^{2}}{k}} = \sqrt{\frac{0 .5 \times {(1 .5)}^{2}}{50}} = 0 .15 m$

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