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.
Best Answer
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 $F_{\mathrm{applied}}\neq R$.