Here is this problem which is bugging me: Q. Two bars of mass m1 and m2 are connected by a non deformed light spring rest on a horizontol plane . coefficent of friction between bars and plane is k . what minimum constant horizontol force has to be applied to bar of mass m1 inorder to move other bar.? A this is what is was trying to do at the time bar m2 moves maximum static friction acts and is equal to LX where X is extension of spring and L Hookes constant of spring for m1 similarly we write force equation in horizontol direction and put LX value from equation for m2. the we get relation in acceleration of block 2 and f the we apply chain rule and write a as -(dv/dx).(dx/dt) as velocity is decreasing as hookes force increases with extension.integrating both sides we get we get relation for kinetic energy of m1. then taking m1 and m2 + spring as system we by using work enery thworem write change in total mechanical energy bis equal to net work done by external force friction and F. well by doing this i get answer F = kg(m1+3/4m2) while correct answer is F= kg(m1+m2/2) i dont know ehere i am doing wrong please help?