Question

Two blocks of mass $3kg$ and $6kg$ respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant $k=200N/m$. Initially the spring is unstretched and the indicated velocities are imparted to the blocks. Find maximum extension of the spring in $cm$ ?

Answer 1

At the maximum extension, the velocity of both the blocks will be same.

Let the common velocity of the blocks is $v$.

From conservation of linear momentum, it can be written as,

$\left(3+6\right)\times v=6\times 2-3\times 1$

$v=1m/s$

Let the maximum extension in the spring is $x$.

From conservation of mechanical energy, it can be written as,

$\frac{1}{2}\times 3\times {\left(1\right)}^2+\frac{1}{2}\times 6\times {\left(2\right)}^2=\frac{1}{2}\times 200\times {\left(x\right)}^2+\frac{1}{2}\times 9\times {\left(1\right)}^2$

$x^2=\frac{18}{100}$

$=0.3m$

$=30cm$

Thus, the maximum extension in the spring is $30cm$.