Newtons 3rd Law, not allowing acceleration

Question

I am confused with how acceleration can occur, given Newton's 3rd law of motion. If I apply a force F on some object A, to in turn push another object B, then B will push back on A with the same force (F). Surely then, A (no matter the situation) cannot move - as the force on A forwards (due to me), and the force on A backwards (due to B), would cancel? This would also suggest that B cannot move either?

Edit: to further clarify: I push on object A, which then pushes on object B. Surely the reaction force from B on A, is equal to the force I put on A - meaning that A has no net force and can never accelerate? (And I am trying to find the error in my logic here).

I see a solution to this in the following thread: (Given Newton's third law, why are things capable of moving?) for this question. The answer on this thread however, proposes that the force of the arm on the hand, is greater than the force of the hand on the block (and hence the force backwards on my hand is less than that provided by the arm, there is a net force, allowing for acceleration). Why does it make sense, that the force of my arm on my hand, is less than that of my hand on the block? (In this thread, object A is replaced with my hand, object B is replaced with the block, and I am replaced with the arm).

Similarly, this website (http://resource-bank.nzip.org.nz/draft-under-construction/mechanics/newtons-third-law-misconception-2/) tries to explain this concept with the following diagram:

It does not make sense to me, why if the floor pushes on blue by 80N, that the forces exerted between blue and green is not also 80N (and hence why the forces exerted between green and the floor is not 80N).

I'll say it again: the human body will not help you understand mechanics. Try formulating the question with a springs and masses. — JEB, Oct 13 '21 at 23:42
@JEB I agree. I have edited my post to fit (I still use some references to hands/arms, but that is in reference to another thread that uses those terms). — Jaynindu, Oct 13 '21 at 23:53
The equal and opposite forces do not act on the same object. If they did then there would be no acceleration. But they do not. — hft, Oct 14 '21 at 00:09
Does this answer your question? Given Newton's third law, why are things capable of moving? — Bill N, Oct 14 '21 at 02:31

score 3 · Answer 1 · answered Oct 14 '21 at 00:06

3

I am confused with how acceleration can occur, given Newton's 3rd law of motion.

There can be acceleration because the forces do not act on the same body.

For example:

The earth feels a force from the sun. That force acts on the earth.

The sun also (by Newton's third law) feels a force from the earth. That force acts on the sun (not the earth).

The two forces have equal magnitude and opposite direction. If these two forces acted on the same body, then there would be no acceleration. But because they act on different bodies there is acceleration.

answered Oct 14 '21 at 00:06

hft

19,536

I apologise, I made a mistake in my previous question (mixing up "B" and "A"). To further clarify my question: I push on object A, which then pushes on object B. Surely the reaction force from B on A, is equal to the force I put on A - meaning that A has no net force and can never accelerate? (And I am trying to find the error in my logic here). – Jaynindu Oct 14 '21 at 00:25
"Surely the reaction force from B on A, is equal to the force I put on A" No, this is incorrect. As you note, if A is accelerating, it certainly cannot be true. Why do you think it should be true? – d_b Oct 14 '21 at 00:54
I was under the impression, that when multiple objects are touching (and the system was moving), the force applied by each subsequent object on the next, would be the same? – Jaynindu Oct 14 '21 at 01:40
"moving" can mean moving at a constant speed (no acceleration), in which case the forces can be the same and do cancel. Or "moving" can mean accelerating, in which case the forces do not cancel. – hft Oct 14 '21 at 01:42
What physics textbook are you reading right now? – hft Oct 14 '21 at 01:43
For this situation I don't have a textbook. I just assumed that if I push a trolley, that is connected to another trolley, both would experience the same force forwards - is this not the case? – Jaynindu Oct 14 '21 at 01:46
I apologise I have just learnt my assumption was not the case. Thank you for your help. – Jaynindu Oct 14 '21 at 01:55
Ok. It is helpful to have a good textbook. See, for example, chapter 5 of this textbook: https://salmanisaleh.files.wordpress.com/2019/02/fundamentals-of-physics-textbook.pdf – hft Oct 14 '21 at 02:43

score 1 · Answer 2 · answered Oct 14 '21 at 01:07

In general, there doesn't need to be any relationship at all between different forces acting on an object. You say

It does not make sense to me, why if the floor pushes on blue by 80N, that the forces exerted between blue and green is not also 80N (and hence why the forces exerted between green and the floor is not 80N).

There is no reason why the force exerted by the floor on blue should have any relationship to the force exerted by green on blue, let alone that they should be equal.

Say I throw a ball in the air and then hit the ball with a bat. The force I exert on the ball with the bat doesn't have to have any connection with the gravitational force the Earth exerts on the ball. I can hit the ball as hard or as soft as I want; there is no reason for these forces to be related.

I was under the impression, that when multiple objects are touching (and the system is accelerating), the force applied by each subsequent object on the next, would be the same? — Jaynindu, Oct 14 '21 at 01:44
I apologise, I have just learnt the idea of "contact forces" as per the following video https://youtu.be/Iin29KFE4So. Thank you for your help — Jaynindu, Oct 14 '21 at 01:55

Bob D · Accepted Answer · 2021-10-14T16:04:37.560

It does not make sense to me, why if the floor pushes on blue by 80N, that the forces exerted between blue and green is not also 80N (and hence why the forces exerted between green and the floor is not 80N).

In fact the forces would all be the same if blue and green were in static equilibrium, i.e., if blue and green were not accelerating. See FIG 1 below. Then the static friction forces acting on blue and green, which are external forces acting on the combination of blue and green, would have be the same. So if the static friction force on blue is 80 N then it has to be 80 N on green as well in order for the combination of blue and green to be in equilibrium. Then, since blue and green are also individually in equilibrium the net force on each individually also has to be zero per Newton's 2nd law. Therefore the force that each exerts on the other would also have to be 80 N.

In this example, however, the maximum possible static friction force between green and the ground has apparently been exceeded while that for blue has not. See FIG 2 below. We know this because a free body diagram (FBD) on green alone shows a net force of 30 N to the right, meaning green is accelerating to the right in a direction opposite to the direction of the friction force. That means Green is sliding and the friction force has changed from static to kinetic, or "sliding" friction.

Blue, on the other hand, is accelerating to the right in the same direction as the static friction force acting on it. Only static friction acting as an external force can cause acceleration. The everyday example is the static friction force between a car's drive wheel an the road acting forward on the car causing it to accelerate.

Hope this helps.

Newtons 3rd Law, not allowing acceleration

3 Answers3