Solve the following :

Question:

Consider the situation of the previous problem. Suppose each of the blocks is pulled by a constant force $F$ instead of any impulse. Find the maximum elongation that the spring will suffer and the distances moved by the two blocks in the process.

Solution:

If ${ }^{x_{1}}$ and ${ }^{x_{2}}$ is travelled by $m_{1}, m_{2}$ under $F$

Work done $=F\left(x_{1}+x_{2}\right)$

Use C.O.E.L $\Rightarrow \frac{1}{2} k\left(x_{1}+x_{2}\right)^{2}=F\left(x_{1}+x_{2}\right)$

$\Rightarrow x_{1}+x_{2}=\frac{2 F}{k}$

Use C.O.L.M $\Rightarrow m_{1} x_{1}=m_{2} x_{2}$

$\Rightarrow x_{1}=\frac{2 F}{k}\left(\frac{m_{2}}{m_{1}+m_{2}}\right) \& x_{2}=\frac{2 F}{k}\left(\frac{m_{1}}{m_{1}+m_{2}}\right)$

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