Question

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

Answer 1

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