# Two boxes that are connected pushed by force - what happens between two boxes?

So when two boxes are connected together, and force is applied, two boxes move with the same acceleration. (assuming force is constant.) My question is, how are forces between two boxes get cancelled out? When force is applied to the first box, it would exert force into the second box which pushes the first box with the same reaction force... And I am not sure afterawards.

"By connected together" I mean that two boxes are stick together literally. There's no string or something like that. It's basically glued together.

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Do you mean to ask why an internal force(like the force between those two boxes) has no net effect on whole system of those two boxes? – udiboy1209 Sep 6 '13 at 15:48
Yeah.. so there are two boxes, but they are like one box (in other world, you can consider those boxes to be one box). Why are the boxes moving at the same acceleration? – user29157 Sep 6 '13 at 15:52
In other words, for any box, there will be internal components that we can think of as separate boxes. These boxes will exert force onto each other, but they cancel out. Why is it the case? – user29157 Sep 6 '13 at 15:53
Because according to newton's law, the forces are exactly equal in magnitude and exactly opposite in direction which is why they cancel out. – udiboy1209 Sep 6 '13 at 15:54
PS why they move with the same acceleration is not because the forces cancel out, but because the glued bonds would break if they didn't. They are constrained by the glue to move with the same acceleration. – udiboy1209 Sep 6 '13 at 15:56

The description you provided in the comments is incorrect. The external force won't get exactly transferred to the next box. The reaction force between the blocks will be different than the external force.

By Newton's third law, you deduce that when the $\mathrm{Box} 1$ pushes $\mathrm{Box} 2$ by a force $R$, $\mathrm{Box} 2$ pushes $\mathrm{Box} 1$ back with the same force $R$.

By Newton's second law you can find out the individual accelerations of the two.
Applying Newton's second law on $\mathrm{Box} 1$, we get: $$F_{\mathrm{applied}}-R_{\mathrm{from Box} 2}=m_1 a_1\tag{1}$$ Applying Newton's second law on $\mathrm{Box} 2$, $$R_{\mathrm{from Box} 1}=m_2 a_2\tag{2}$$

Another equation can be used which constraints the acceleration of the both boxes to be equal. $$a_1=a_2=a\tag{3}$$ Acceleration is equal because the blocks would not stay together if it wasn't.

These three equations can be used to find acceleration or Normal force between the two blocks. You can see that $F_{\mathrm{applied}}\neq R$.

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This is the classic horse and buggy brain teaser. If the horse pulls on the buggy, the buggy must pull back on the horse with an equal force so who moves anywhere? The answer lies in the fact that the buggy pulls back on the horse because it is being ACCELERATED. That is where the force comes from. In the case of the two boxes, the second box (one at the front) is indeed canceling out the force of the first box (the one doing the pushing) but only by being accelerated. Remember, there is always zero net force, but often there are accelerations involved to make that force zero.

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