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Two boxes are stacked, box $A$ is placed on a horizontal surface with no friction, box $B$ is placed on box $A$ with unknown coefficient friction between the two. Box $A$ does not slide relative to box $B$, what is the acceleration of both boxes?

We are given the weight of box $A$, $48$ kg, and box $B$, $11$ kg. We are also given the force that is being applied on box $A$, is $149 N$.

The roadblock with this question is how are we supposed to find the acceleration of both boxes if they do not move relative to each other and we are not given the coefficient of friction between the two boxes.

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    $\begingroup$ TIP - Consider both the boxes $A$ and $B$ as a single object with mass $48+11$ $\endgroup$ – SmarthBansal May 12 '19 at 6:31
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Remember Newtons third law.Every action has an equal and opposite reaction.

So now the is friction acting on box B.Where is its other counterforce.Its on box A.

If the boxes do not move realtive to each other ,what does it really mean?They have the same accelerations.

So now you know the net force acting on both these objects.

Simply use F=ma to get your answer.

Tip- mark all the forces acting on each object seperately to get a better understanding of whats happening.

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