Question

A spring block system is placed on a horizontal rough surface as shown in the figure. The block is given velocity when the spring is in natural length. The total distance travelled by the block before it finally comes to rest is $\frac{2}{k}$ metres. Find the value of k ___

Answer 1

$\frac{1}{2}m{v}^2-\mu mgx=\frac{1}{2}k{x}^2\frac{1}{2}\times 5\times (\frac{16}{25}\times 10)-\frac{3}{5}\times 5\times 10\times x=\frac{1}{2}\times 50\times x^2\Rightarrow 25x^2+30x-16=0x=\frac{-30+\sqrt{900+1600}}{50}x=\frac{2}{5}m.\Rightarrow k=5$