Question

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 _____ $Nm^{–1}$.

Answer 1

$\frac 12 mv^2 = \frac 12kx^2 + \frac 12m(\frac v2)^2$

$\frac 12 mv^2 - \frac 12m(\frac v2)^2 = \frac 12kx^2$

$\frac 38mV^2 = \frac 12kx^2$

$k = \frac 34 \times \frac 12 \times \frac {144}{9} \times 100$

$k = 600$

So, the answer is $600$.