How exactly does Newton’s third law work?

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So, from what I understand, Newton’s third law says that for every action, there is an equal and opposite reaction.

I’m having a very hard time wrapping my head around it, as it seems as though if his law worked the way I interprete it to, pushing an object or denting an object would be impossible.

For example,

If someone were to push a book on a table, the force they applied on the book to push it, should be countered by an equal and opposite reaction force, therefore not allowing them to move the book.

In another example, if someone were to push a piece of metal, there should be an equal and opposite reaction force (normal contact force?) which would not allow the person to move the metal (can’t dent it), no matter how much force they use.

I guess what I would like to know would be why this is not the case in the two above examples, and what is it that I am not interpreting correctly with Newton’s third law.

Thank you!!

In: Physics

11 Answers

Anonymous 0 Comments

Resistance is the opposite reaction. Think of pushing a car on level grounds. All that resistance is the opposite reaction.

Anonymous 0 Comments

Think about what the universe would be like if this WASN’T the case.

I would be able to take a car door, punch it with all my strength to dent it, and my hand will not get injured or even feel a thing because Netwon’s third law no longer applied.

I’d be able to take a flimsy piece of wood and hit a brick wall with it with all my strength but the flimsy piece of wood would not break because Newton’s third law no longer applied.

The two situations above, are of course, not the case in this universe. My hand would most likely be broken, and the flimsy piece of wood would break against the wall because Newton’s third law DOES exist. You can’t exert a force on something without that something exerting a force on you.

Anonymous 0 Comments

When you push a book with your hand, you feel pressure on your hand. That pressure is the equal and opposite force in Newton’s third law. The force deforms your hand a little but otherwise doesn’t do anything noticeable, because it’s not a very strong force. The force you apply to the book moves the book because the book is light and has little friction with the table. The force of the book pushing on you does very little because you are much heavier than it and you have plenty of friction between your feet and the ground. But, importantly: if there was no equal and opposite force at all, then you wouldn’t feel anything while pushing the book (no pressure against your hand).

If you push against something heavier, you may notice that you have to brace yourself. Maybe you have to lean in a little or position your feet so you have more grip on the ground. Now the opposite force is more noticeable. If you do this on a slippery surface (e.g a well-polished floor) the opposing force may be enough to push you back a little.

If you push against something in space, the opposite force is totally obvious. If you pushed against a book in space, the book would go flying in one direction quite fast, and you would drift off in the opposite direction much more slowly. If you push against something that’s the same weight (or *mass*, to be more precise) as you, then you both go flying off in opposite directions at the same speed.

So in short: yes, the opposite force is always there as Newton said. If there is a force from A to B, then there is the same force from B to A. But what these forces do to A and B depends on their properties (mostly their mass). The same force acting on a light thing may cause it to shoot away at speed, while it doesn’t even budge a heavy thing, because it’s not enough to overcome the friction between the heavy thing and the surface it sits on.

Anonymous 0 Comments

The equal and opposite forces are not acting on the same object. You push on the book, and the book pushes on you with the same force.

Anonymous 0 Comments

The forces are the same, but the movement also depends on the mass of the objects. So you push a book with some force, the book is light so it will accelerate in the direction you move it. The book pushes you with exactly same force, but you are much heavier so you accelerate at much smaller rate and barely move. Also you’re countering the acceleration with your body. In space you wouldn’t be able to do it and you would really move (still much slower than the book).

Less ELI5: the formula for acceleration is a = F/m where F is the force (equal for you and the book) and m is the mass (different for each). So you can see that with same force you get different results for you and the book.

Anonymous 0 Comments

You push on the book and the book push on you with the same force. This is why the harder you push the book, the stronger you feel the book.

Now what is important is friction. You see you have friction to the ground and the book have friction to the table. The force you put on the book is higher than the friction the book have with the table, so the book will move, but the force the book put on you is lower than your friction on the ground so you don’t move.

Now if you were to push on a large boulder, while you are on ice, the situation would be different. Now your friction to the ice is low and the friction of this boulder to the ground is very high. So the force you apply to the boulder isn low to the friction of the boulder and it doesn’t move. But the force the boulder push you back with is higher than your friction to the ice, so your feet gonna start to slider back.

Anonymous 0 Comments

You are correct to a point. Remember that these laws apply to rigid bodies in idealized conditions and simplified scenarios.

The scenario is describe is sitting in a chair. You sit in a chair, the chair holds you up, the chair provides and equal force to support you.

Your first example – pushing on a book. In this case the force resisting motion is friction. As long as the force you apply to the book is less than the frictional force, the book stays put. Once you get past the frictional force the book starts to move, part of the force you apply gets expended on the friction and the rest gets expended on the book’s acceleration. The two forces are still equal. You should be able to draw a free body diagram that will zero out the forces.

Last example: Newton’s laws apply to rigid bodies. This law is a simplification of reality. And in many cases this simplification does the trick. This law does not hold up once you start applying enough force that the bodies you are applying a force to is no longer rigid (ie it bends or breaks). At that point you are getting into more advanced dynamics and structural mechanics questions.

Anonymous 0 Comments

As far as the denting, the opposite force will still be exerted, but some of the energy that would have been transferred to the object gets used to squish the object instead.
When 2 pool balls hit each other, since they dont squish, you see almost all the energy transferred, and the opposite force pushes the ball away with lots of energy. However, when 2 cars hit each other, they are designed to absorb the force by deforming the metal. The opposite force is still exerted, but you dont see motion because it is absorbed by permanently changing the shape of the object.

Anonymous 0 Comments

Because momentum being conserved is a property of our universe. That means that the change in momentum of all objects before and after an action has to add up to zero.

In order to change an object’s momentum you must apply a force to that object, but your momentum must also change in the opposite direction, meaning a force must be applied to you as well.

Anonymous 0 Comments

The way I finally got my head around the third law was this:

Imagine you are sitting on a boat in a lake and you push another boat. If the boats are the same mass then both of them will start drifting apart at the same acceleration since an equal and opposite force was applied (a=f/m).

However if this boat you were pushing against was much larger than the one you were on you would both experience a larger acceleration away from the big boat since it is more massive. The same force is applied but one party has a much lower mass so is affected more.