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  4. A 0.5 kg block moving at a speed of 12 ms -1 compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be Nm -1.

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Q. A $0.5 \,kg$ block moving at a speed of $12 \,ms ^{-1}$ compresses a spring through a distance $30 \,cm$ when its speed is halved. The spring constant of the spring will be ______ $Nm ^{-1}$.

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Solution:

$U _{ i }+ K _{ i }= U _{ f }+ K _{ f }$
$\Rightarrow 0+\frac{1}{2} m (12)^{2}=\frac{1}{2} K (0.3)^{2}+\frac{1}{2} m (6)^{2}$
$\Rightarrow 0.5\left(12^{2}-6^{2}\right)= K (0.3)^{2}$
$K =600 \,N / m$