This is more of a conceptual problem than a mathematical one (Note that this is purely for conceptual purposes of my own and probably doesn't really hold any practical value). I was just curious to know that if we imagine a book of mass m1 resting on any flat surface on Earth and then put on top of it another book of mass m2, then the greater weight of the stack obviously seems a direct result of the additional mass (the book) added on top of the bottom book. But then a thought occurred to me: wouldn't the book on top pressing down on the book on bottom increase the downward acceleration of the bottom book? I turned to mathematics for the answer and I applied two slightly different approaches. Though, the two approaches give the same answer for the total weight of the stack, the values for acceleration that I got don't quite add up.
The two approaches I applied are:
1)Simply adding the two masses together and multiplying by g i.e
2)Finding the extra acceleration a that is caused by the top book pushing down on the bottom book, then adding the resulting value to g and multiplying by the mass of the bottom book only i.e
It seems the problem can be interpreted in two ways that appear, at least on the face of it, equivalent. The first approaches imagines a single system of two books. The second approach reduces the physical book to a downward force, so we're effectively dealing with a single book.
But there must a single correct physical interpretation to this. Is the bottom book being accelerated by 9.8m/s^2 or something more? That's my question.
P.S: I am aware that this is an absolutely pointless exercise, since the net accelerations, whatever the component accelerations, are always going to cancel out in this case no matter what approach we take.