I've this question

enter image description here

When asked I was told that we will balance force for $2m$ object

i.e., $(2\mu)2mg=Kx$

And we will conserve energy for $m$ mass

i.e., $Fx=\frac{1}{2}kx^2+\mu mgx$

Both the blocks are attached to the same spring so why is it wrong to balance forces for both the masses. I want to know why can't we do vice versa rather how does the solution work

I am not asking for calculations or answer to a homework question but asking for a concept involved.

  • $\begingroup$ I was writing an answer to your egg question when the question was deleted, so I lost it. Have a look here greekreporter.com/2021/05/01/… . The reason eggs break is 1) air bubbles which are bigger the older the egg, 2) thickness of skin 3) previous undetected cracks $\endgroup$
    – anna v
    May 22 '21 at 5:22
  • $\begingroup$ @annav thank you so much I was getting downvotes so I closed it $\endgroup$
    – imposter
    May 22 '21 at 5:42

The question specifically says that $F$ is the minimum force needed to move the $2m$ mass. As the spring extends by a length $x_{\circ}$, the smaller mass $m$ has an acceleration due to the net force provided $F$, friction and spring force.

As no data about the acceleration is provided in the question we cannot balance any force equation for mass $m$ without knowing its acceleration.


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