Question

In the figure shown, a block of mass $60kg$, connected 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 $(g=10m/s^2)$

Answer 1

Given,
Mass of the block $m=60kg$
Natural length $=8m$
Compressed length, $x_o=2m$
$\mu =\frac{1}{2}$
$k=200N/m$
From work-energy theorem
$W_{\text{n}et}=\Delta KE=0$
$\Rightarrow \frac{1}{2}(x_0^2-x^2)-\mu mgx=0$
$\Rightarrow \frac{1}{2}\times 200(2^2-x^2)$
$\frac{1}{2}\times 60\times 10x\Rightarrow x=1m$
Also, at this moment, $f_{max}>kx$.

Hence, block will not move.
So, total distance travelled $=2+1=3m$
Final answer: $3$