A 0 . 5kg block moving at a speed of 12 ms ^ - 1 compresses a...

Given: Mass of the block $m = 500g$, initial velocity of the block $u = 12m{s}^{- 1}$, and final velocity of the block $v = \dfrac{u}{2} = 6m{s}^{- 1}$.

As non-conservative forces are not acting on the system we can conserve energy.

Thus, loss in kinetic energy of block = Gain in potential energy of spring

$\dfrac{1}{2}m{u}^{2} - \dfrac{1}{2}m{v}^{2} = \dfrac{1}{2}k{x}^{2}$

$\dfrac{1}{2} \times 0 . 5 \times {12}^{2} - \dfrac{1}{2} \times 0 . 5 \times {6}^{2} = \dfrac{1}{2}k \times 0 . {3}^{2}$

$k = 600N{m}^{- 1}$