Question

A ball of mass $4\,kg$, moving with a velocity of $10\,ms ^{-1}$, collides with a spring of length $8 m$ and force constant $100\,Nm ^{-1}$. The length of the compressed spring is $x m$. The value of $x$, to the nearest integer, is ______.

Answer 1

Let's say the compression in the spring by: $y$. So, by work energy theorem we have
$\Rightarrow \frac{1}{2} mv ^{2}=\frac{1}{2} ky ^{2}$
$\Rightarrow y =\sqrt{\frac{ m }{ k }} \cdot v$
$\Rightarrow y =\sqrt{\frac{4}{100}} \times 10$
$\Rightarrow y =2 m$
$\Rightarrow $ final length of spring
$=8-2=6\,m$