Question

Two blocks A and B of equal mass m= 1.0 kg are lying on a smooth horizontal surface as shown in figure. A spring of force constant k = 200 N/m is fixed at one end of block A. Block B collides with Block A with velocity v= 2.0 m/s. Find the maximum compression of the spring.

Answer 1

At maximum compression velocity of both block will be same $\left(v\right)$ say.

By momentum conservation let mass of each be $m$.

$m\times 2=(m+m)v$

$v=1$m/s

By conservation of momentum let $x$ be the compression of the spring.

$\frac{1}{2}m{\left(2\right)}^2=\frac{1}{2}m{v}^2+\frac{1}{2}m{v}^2+\frac{1}{2}k{x}^{2}4m-2m=200x^2{x}^2=\frac{2}{200}=\frac{1}{100}x=\frac{1}{10}=10cm$