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  4. A body of mass 2 kg moves with velocity of 18 m / s hits a spring fixed at other end of force constant 1000 N / m and comes to rest after compressing the spring. The compression of the springs is

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Q. A body of mass $2 kg$ moves with velocity of $18 m / s$ hits a spring fixed at other end of force constant $1000 N / m$ and comes to rest after compressing the spring. The compression of the springs is

Work, Energy and Power

Solution:

Total kinetic energy converted into potential energy
$\frac{1}{2} m v^{2}=\frac{1}{2} k x^{2}$
$\sqrt{\frac{m v^{2}}{k}}=x$
$\sqrt{\frac{2 \times 18 \times 18}{1000}}=x $
$\Rightarrow x=\sqrt{\frac{648}{1000}}=\frac{25.45}{10 \times \sqrt{10}}$
$x =0.80 \,m$