Suppose there's a block of some mass that is kept on a table. But, instead of staying at rest on the table, it breaks through the table. How does Newton's third law hold up here?
If the block is at rest on the table then the push of the block onto the table due to its weight and the normal force by the table on the block are the action-reaction forces. But what about this case?
Best Answer
The law still applies, but we have to be careful with the forces. If the book has a mass $m$, we cannot simply say that the book applies a force of $F=mg$. If the table broke, then there was some maximum force it could withstand, which was less than $mg$.
The key to remember is that the sum of the forces on an object equals 0 only if that object is not accelerating. It actually always equals $ma$, where $a$ is the acceleration on the object. We write this $\sum F = ma$, with $\sum$ being how we notate summing everything up. It just happens to be that if the object is not accelerating (we say "at rest") $\sum F = m\cdot 0 = 0$
So the reality in your scenario is that the table pushes up with some force equal to exactly the amount of force it could apply without breaking. This is less than $mg$, so the result is that the book is accelerating. Newton's Third Law holds.
Now very soon this book will start moving closer to the atoms in the table. To understand what happens beyond the breaking point, we can't treat the table as one monolithic entity -- the velocity of the different parts can be different, and will be different during breaking. We can analyze the individual pieces of wood, or we can go to extremes and look at the forces on the atoms. But that all goes beyond your question. The fundamental answer is that the sum of the forces does not have to be zero, unless the object is not accelerating.
And much of these questions can be answered by remembering that there's many operations that we think of as "instantaneous" but are not. If the book falls on the table and WHAM! makes a loud sound, we say it "hit" the table at that time. But, if you look in slow motion, you will see that there was a whole lot of bending and wobbling which let that "hit" work out according to Newton's Laws. For example, in cases like these, the table can't "break" right away. It's actually a long series of smaller motions which, over the course of a few milliseconds, result in what we call "breaking."