Assuming you place an object so heavy on a table that it breaks it, then according to newtons third law the forces must cancel out (equal magnitude and opposite direction), but if this is true, then how can the object break the table in the first place?
[Physics] Newton’s Third Law Clarification
newtonian-mechanics
Related Solutions
Suppose you and the table are floating in space. If you push the table it will go in one direction and you will go in the other direction. Your and the table's acceleration will be different so you will end up travelling at different speeds. This is obvious from conservation of momentum. The momentum in the centre of mass frame is initially zero, so after the push your velocity $v$ and the table's velocity $V$ are related by:
$$ MV = mv $$
where $M$ is the mass of the table and $m$ is your mass. Your velocity will therefore be:
$$ v = \frac{M}{m} V $$
If you walk up to a table in your living room and push it then other forces come into play. These include the force on the table legs exerted by the living room floor and the force on your feet exerted by the living room floor. You would need to take these into account to analyse the situation properly.
I'd really appreciate if someone could give a more descriptive answer on why Newtons Third Law does not cancel out.
The effect of the forces each object exerts upon the other depends on the application of Newton's second law, not the third law. Newton's second law says the net external force acting on a object equals its mass times its acceleration, or $F_{net}=ma$.
Or at least give a real life example of why it's the case.
See FIG 1 below. A man stands on a surface having friction. Two blocks are in contact with each other are on a frictionless surface, or at least a surface with negligible friction (e.g. ice) compared to the surface the man stands on (e.g., dry pavement). The man applies a force to block A.
In order to analyze all the relevant horizontal forces (there are no net vertical forces) including all pairs of horizontal forces per Newton's 3rd law we draw a free body diagram of the man and each block per FIG 2 below. Note that the equal and opposite Newton 3rd law pairs of forces are (1) between the man and the ground, (2) between the man and block A, and (3) between block A and block B.
To determine the effect of these forces on the man, block A, and block B we need to apply Newton's second law to each individually.
Block B:
Note that the only external horizontal force acting on block B is the force exerted on it by block A, or force $F_{AB}$. From Newton's second law
$$F_{AB}=M_{B}a\tag{1}$$
Where $M_B$ is the mass of block B and $a$ is its acceleration.
Block A:
There are two external horizontal forces acting on block A. The force exerted on it by block B, $F_{BA}$ and the force exerted on it by the man, $F_{CA}$. Thus the net external force acting on A is $F_{CA}-F_{BA}$. From Newton's second law, realizing that since blocks A and B move together they will have the same acceleration $a$, we have
$$F_{NET}=F_{CA}-F_{BA}=M_{A}a\tag{2}$$
Adding equations (1) and (2) we obtain
$$F_{CA}=(M_{A}+M_{B})a\tag{3}$$
Which is the same as saying the only external horizontal force acting on the combination of blocks A and B is the force $F_{CA}$ exerted by the man giving the combination of blocks an acceleration of $a$ per Newton's 2nd law.
This example clearly shows that the equal and opposite forces A and B exert on one another, per Newton's 3rd law, do not "cancel" each other, because there is a net external force acting on the combination of A and B per Newton's 2nd law, causing both blocks to accelerate
So what about the man?
Man:
There are two external forces acting on the man, the force exerted by block A, $F_{AC}$ and the static friction force $f_{s}$ exerted by the ground on the mans feet. The static friction force $f_s$ that the ground exerts on the man is equal and opposite to the force the man exerts on the ground, another Newton's 3rd law pair.
The static friction force $f_s$ will match the force of block A $F_{AC}$ until the maximum possible static friction force is exceeded, in which case the man feet will slip. That would happen if the man pushed too hard on block A. We will assume he doesn't slip, in which case the net force on the man is zero and his acceleration is zero.
But the reason the man doesn't accelerate is not because the equal and opposite pair of forces between him and the ground or between him and block "cancel", but because the two external forces are equal and opposite for a net external force on the man of zero.
Hope this helps.
Best Answer
That is not what the third law says. It says that the force of A on B has the same magnitude but opposite orientation to the force of B on A.
The two forces act on different bodies, so they do not "cancel out". In common situations like the one you mentioned, the 3rd law is valid irrespective of whether the object or table move.