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I have recently been doing some work around Newtons third law. And I was thinking about a question revolving around the topic. It is a common question of how can we move at all if all forces are equal and opposite, all movement must cancel out in that case. I searched it up and all answers say 'Action and reaction forces do not cancel each other because they act on different objects.' However I do not quite understand why this is the case. At first I thought it was due to a persons reaction to a force. For example lets take someone pushing against a ball, the person does not move due to the friction force against him on the ground; the ball moves because there is no frictional force applied back to it. Though, I am unsure if this is the correct understanding.

I'd really appreciate if someone could give a more descriptive answer on why Newtons Third Law does not cancel out. Or at least give a real life example of why it's the case.

Sorry it's a simple question but i'd like to have a clearer understanding.

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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.

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All Newton's 3rd law is really saying is that every force is two sided.

Forces don't act like this

$\longrightarrow$

they act like this

$\longleftrightarrow$

Or this

$\longrightarrow \longleftarrow$

Either pulling two things together or pushing two things apart.

It's not really saying there are two forces. It's saying that whenever there is a force, two objects both feel it.

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You accelerate less than the ball does partly because of the frictional force (as you noted) but also partly because (in most cases) your mass is greater than the ball's, so the same force produces less acceleration.

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Let me describe a setup that makes friction effect way smaller than exerted force:

There is a demonstration apparatus called 'air table'

It consists of a plate with small holes in it, spaced closely apart, and from underneath air is pumped. A glider positioned on the air table is lifted onto an air cushion. Even a very thin air cushion is already enough to make motion near frictionless.

Imagine an air table large enough so that it can support gliders large enough to carry a person.

Let's say you are sitting down on a glider like that, using one leg or both legs to push away another glider. If the other glider has less mass than you then the other glider will get more velocity than you. Conversely, if the other glider had additional mass added, to make it much heavier than you, then your pushing will for the most part result in giving yourself a velocity away from the other glider.

What you are accustomed to in everyday life is that you always have enough friction to prevent yourself from pushing yourself backward, rather than pushing the other object forward. And if you can see in advance that you will probably not have enough friction then you find a way to brace yourself.

But if you are on a glider: the whole point of the glider is that friction is not a factor, and that you have no brakes or anything.

When you are on a glider then the only leverage you have comes from your own inertia. When you push another glider both you and the other glider will get velocity. (The distribution of the velocities is determined by the mass ratio.) I emphasize: when you are on a glider you still have leverage to push; leverage that comes from your own inertia.

For simplicity let's take the case where you are on a glider and there is also a person on the other glider, and the two of you are pushing off against each other, and the two of you have the same mass. The amount of acceleration is proportional to the force, according to $F=ma$

It doesn't matter if only one is actively pushing and the other is just blocking the push; the result is the same no matter what. If there is a pushing force both will undergo change of velocity, in accordance with $F=ma$

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