Question

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

Answer 1

Let the spring is compressed by $y$.

Applying energy conservation principle,

$\frac{1}{2}m{v}^2=\frac{1}{2}k{y}^2$

$\Rightarrow y=\sqrt{\frac{m}{k}}\times v=\sqrt{\frac{4}{100}}\times 10=2\text{m}$

Therefore, final length of the spring$=8-2=6\text{m}$