Question

In the figure shown, a block of mass $60kg$, connnected to a spring, is released from rest when compression in the spring is $2m$ (natural length of spring is $8m$ ). Surface $AB$ is smooth while surface $BC$ is rough. The block travels $y$ distance before coming to complete rest from the releasing point. The value of $y$ (in metre) is $\left(g=10m/s^2\right)$

Answer 1

Answer: 3

From work-energy theorem,
$W_{\text{net }}=\Delta KE=0$
$\Rightarrow \frac{1}{2}k\left(x_0{}^2-x^2\right)=\mu mgx$
$\Rightarrow \frac{1}{2}\times 200\left(2^2-x^2\right)$
$=\frac{1}{2}\times 60\times 10x$
$\Rightarrow x=1m$
Also, at this moment, $f_{\max }>kx$.
Hence, block will not move.
So, total distance travelled $=2+1=3m$