Two blocks of masses `m_(1) = 1 kg` and `m_(2) = 2 kg` are connected by a non-deformend light spring. They are lying on a rough horizontal surface. The coefficient of friction between the blocks and the surface is 0.4. What minimum constant force F has to be applied in horizontal direction to the block of mass `m_(1)` in order to shift the other block? `(g = 10 m//s^(2))`

Explanation

Let the motion of `m_(2)` start when the spring is strefched by x slowlt. Work done by various forces will involve 3 terms, F.x `(-um_(1)g)x and -1/2kx^(2)`
Let the motion of `m_(2)` start when one spring is solwe stretched by x slowly
Work done by various forces `=F.x-(mum_(1)g)x-1/2kx^(2)`
=Change in KE=0
Where k is force constant of the spring