Question

The arrangement shown in figure is at rest. An ideal spring of natural length $l_{0}$ having spring constant $k=220\, Nm ^{-1}$, is connected to block $A$. Blocks $A$ and $B$ are connected by an ideal string passing through a friction less pulley. The mass of each block $A$ and $B$ is equal to $m=2\, kg$ when the spring was in natural length, the whole system is given an acceleration $\vec{a}$ as shown. If coefficient of friction of both surfaces is $\mu=0.25$, then find the maximum extension (in $cm$ ) of the spring. $\left(g=10\, m s ^{-2}\right)$.

Answer 1

Let the maximum extension in spring be $x$.

Apply work-energy theorem: (Net work done by tension will be zero)
$-\frac{1}{2} k x^{2}-8 x-7 x+28 x-2 x=\Delta KE =0$
$\Rightarrow -\frac{1}{2} \times 220 x^{2}+11 x=0$
$\Rightarrow x=0.1\, m =10\, cm$