# Forces misconception hammer and nail

eulerddx4
Can someone please explain how a hammer can drive a nail. A person swings a hammer in the air and exerts a force on a nail but newton's third says the nail exerts the same force back on the hammer. So if newton is right then how does the nail accelerate.

I just don't get it.

Can someone please explain how a hammer can drive a nail. A person swings a hammer in the air and exerts a force on a nail but newton's third says the nail exerts the same force back on the hammer. So if newton is right then how does the nail accelerate.

I just don't get it.

What exactly don't you get about it?

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Gold Member
Can someone please explain how a hammer can drive a nail. A person swings a hammer in the air and exerts a force on a nail but newton's third says the nail exerts the same force back on the hammer. So if newton is right then how does the nail accelerate.

I just don't get it.

The hammer does get accelerated backwards (as in up). What do you think stops the motion of the hammer as you slam down on the nail?

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eulerddx4
I guess my question might be is the hammer able to exert a force on the nail because it has mass and acceleration?
Also if the nail exerts the same force back then how does the nail accelerate

eulerddx4
If i have a coffee mug on a table why am i able to push it with my hand if whenever i push it the coffee mug pushes back.

eulerddx4
Thats what im trying to get at and i feel extremely stupid right now but im just not getting it

Also if the nail exerts the same force back then how does the nail accelerate
Why should the force on the hammer prevent the nail from accelerating?

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eulerddx4
because the force on the hammer is equal to the force on the nail

eulerddx4
so shouldnt the forces on the nail and hammer just go away if newtons law is true

Gold Member
If i have a coffee mug on a table why am i able to push it with my hand if whenever i push it the coffee mug pushes back.

You exert the same force that the coffee mug exerts on you. However, since you have a far far greater mass, by F = ma, the coffee mug will provide a very small (and to you, unnoticeable) acceleration back on you compared to the acceleration you provide to the mug.

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eulerddx4
oooooo

because the force on the hammer is equal to the force on the nail
But it is acting on the hammer. Why should it affect the nail?

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so shouldnt the forces on the nail and hammer just go away if newtons law is true
Why? They act on two different objects.

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eulerddx4
well im thinking that theres a force acting on the hammer just as theres a force acting on the nail

well im thinking that theres a force acting on the hammer just as theres a force acting on the nail
Yes, and therefore they both are accelerated in opposite directions.

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eulerddx4
i just dont get why theres acceleration if the force of the hammer is the same and opposite the force on the nail. To me it seems like the force should just go away if thats the case

eulerddx4
says to self: "why is this so hard for me to understand"

eulerddx4
You exert the same force that the coffee mug exerts on you. However, since you have a far far greater mass, by F = ma, the coffee mug will provide a very small (and to you, unnoticeable) acceleration back on you compared to the acceleration you provide to the mug.

but why should i be providing acceleration if the force is canceled. Doesn't there have to be some outside force. When i push on a car the car pushes on me. The only way for me to move the car / accelerate it is if i push on the ground really hard.

i just dont get why theres acceleration if the force of the hammer is the same and opposite the force on the nail. To me it seems like the force should just go away if thats the case
They don't cancel, because they act on different objects.

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Mentor
2021 Award
When i push on a car the car pushes on me. The only way for me to move the car / accelerate it is if i push on the ground really hard.
This is not correct. If the ground were frictionless so that neither you nor the car could push on the ground then when you push on the car you would accelerate in one direction and the car would accelerate in the opposite direction.

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eulerddx4
so then how does someone push something like a car or a box

eulerddx4
last year when i took physics my physics teacher said if you have a game of tug of war, the only way to win is if one side pushes harder on the ground because when you pull on the other side the other side pulls with the same exact magnitude in the opposite direction. Is my physics teacher completely misinformed???

eulerddx4
i dont understand why there is any acceleration at all. In my mind there has to be a net force for there to be acceleration but i see no net force here

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i see no net force here
Draw the free-body diagrams for the problem and label all of the forces acting on each body. Then you should clearly see net forces.

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freemovement
I think eulerddx4's confusion is pretty understandable, and most of you really aren't helping by acting like the answer to his problem is so obvious.

So I'm going to try to actually help him out, please correct me if I make any mistakes...

The term "net force" has to do with what you make your system. Here your system is the hammer and the nail, and there are external forces on the system: your hand, gravity, and contact forces in the wood you're nailing. These EXTERNAL forces are transmitted through the hammer and nail, and cause acceleration. The force between the hammer and the nail is an internal force, and causes no acceleration of the system as a whole. So if there was truly no net force - no external force - that is the hammer was flying at the nail in space - it becomes a question of conservation of momentum. The hammer knocks into the nail, giving it a certain amount of momentum. In this case, the center of mass of the system remains at a constant velocity (no force), but remember, your system is NOT just the nail, its the hammer AND the nail. If you're only looking at the nail, you have an external force - the impulse given by the hammer.

But in the case of "driving" the nail, what's really happening is your hand is applying an external force to the system - the force between the nail and hammer does "cancel out" in the sense that it does not affect the motion of the center of mass of your system.

Does this help dude?

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eulerddx4
Yes thank you for taking the time to answer the question! No one would give me a legit answer haha

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The carpenter who hits his thumb with the hammer will tell you that no net force hurts like a sonuva...

harrylin
so shouldnt the forces on the nail and hammer just go away if newtons law is true

Perhaps it's mostly a matter of precise formulation. According to Newton's laws forces do not "just go away"!

If you accelerate a cop of coffee (or a nail), the force that you need to accelerate it is determined by the force with which it (and friction with the table or wall) withstands that acceleration.
So, taking Newton's second and third law together, that tells you that the force with which you must push to accelerate the cup is equal to the force with which the cup pushes back against your hand due to its acceleration - it's the same force, between your hand the cup.

And as others already mentioned, in principle when you accelerate the cup away by pushing against it, also you and the earth accelerate in the opposite direction due to the cup that is pushing back against you.

Does that help?

Harald

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eulerddx4
Ok So now I understand! The forces don't cancel out. They are real, they exist and they act on both the nail and the hammer/ person assembly. when you hit the nail you get pushed back but you don't get moved back very much because you are standing on the ground and you have significant mass so gravity is exerting a relatively large force keeping you in place.

What really made the idea click is a gun. When you shoot a gun the bolt exerts a force on the bullet and the bullet exerts a force back. The gun shoots the force doesn't just go away because there is a force exerted back. This is crazy. Rather you actually feel the force back its the recoil. I really had to come up with an example like this to make it click so i would suggest using something like this example in the future because I was really stumped at first. Anyway I'm glad I understand now! Thanks to the people that pointed me in the right direction and i'm also kind of happy that no one came out and explained the whole thing. I feel like I solved the problem myself in a way by coming up with this example.

zoobyshoe
i dont understand why there is any acceleration at all. In my mind there has to be a net force for there to be acceleration but i see no net force here
I see why you are confused. If we have a law that says every action is met by an equal and opposite reaction it makes it sound like every force is automatically in equilibrium and nothing can ever move anything else. Hehe.

What it actually means, though, is that once object A has moved object B, object A no longer has all the force it had before it moved object B. It now has less force. How much less? Exactly that amount it took to move object B. Object A loses an amount of force exactly equal to the amount it took to accelerate object B. That's what "equal and opposite" means. Exactly what is added to B must be subtracted from A.

It's baby simple: If I give you $5, you experience a change of +$5 and I experience a change of -$5. The changes are equal and opposite! The action and reaction are automatically equal and opposite! It does not mean: If I give you +$5 you must give me +$5. That's not what Newton III is saying at all. Newton III is saying if I give you exactly$5 I automatically suffer a loss of exactly $5. Equal, but OPPOSITE. You: +$5, me: -$5. Newton's Third Law guarantees that if you take x amount of force from me, I lose exactly x amount of force. If I lose x amount of momentum to you, you gain exactly x amount of momentum. No more, no less. It is the foundation of all the conservation laws. You experience a net force of +$5, so to speak, and I simultaneously experience a net force of -$5. Last edited by a moderator: eulerddx4 Wait wait wait, Newton's law says in your example that if you give me 5 dollars i have to give you 5 dollars back. If I push on a wall the wall has to push me back with the same force. If a mack truck hits a bike the mack truck gives a force to the bike and the bike gives that same force back to the truck. That's what it says Mentor 2021 Award It's baby simple: If I give you$5, you experience a change of +$5 and I experience a change of -$5. The changes are equal and opposite! The action and reaction are automatically equal and opposite!

It does not mean: If I give you +$5 you must give me +$5. That's not what Newton III is saying at all. Newton III is saying if I give you exactly $5 I automatically suffer a loss of exactly$5. Equal, but OPPOSITE. You: +$5, me: -$5.

Newton's Third Law guarantees that if you take x amount of force from me, I lose exactly x amount of force. If I lose x amount of momentum to you, you gain exactly x amount of momentum. No more, no less. It is the foundation of all the conservation laws. You experience a net force of +$5, so to speak, and I simultaneously experience a net force of -$5.
I do not like this analogy at all! There are two big problems here.

First, in this type of financial transaction the total money is conserved. There is no conservation of force. There is no sense in which one body takes force from another body which is therefore lost from the first body.

Second, the amount of money is a scalar quantity, not a vector quantity like force is, and that makes a big difference. An object experiencing an external force to the right is not gaining force and an object experiencing an external force to the left is not losing force.

eulerddx4, I do not recommend that you study this analogy.

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Gold Member
The problem with the analogy is that it confuses "force" with "momentum". It is really trying to be an analogy about conservation of momentum. That's a valid lesson-- we can either say that the 3rd law must be true because momentum is conserved, or we can say that momentum is conserved because of the 3rd law. Getting back to the gun, it means we can impart a momentum into the bullet only if we are willing to get that same momentum imparted into our arm (in the opposite direction, so a "negative" momentum), in the form of recoil (though we can pass that momentum along, via our body, into the ground).

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2021 Award
Yes, as an analogy with momentum it is not too bad. Momentum is conserved so if A gives momentum to B then A loses momentum. The scalar/vector bit can be glossed over for 1D "vectors".

zoobyshoe
OK Dale and Ken, if we all agree what I said applies to momentum I'm happy.

I realize I'm on shaky ground suggesting something like "conservation of force". It seemed to make sense when I wrote it if I thought of force in terms of Newtons. It seemed that any agent of force must lose as many Newtons as it succeeds in imparting to something else. I made the assumption that kg*m/s2 are transferable from one body to another just as kg*m/s are. If body A exerts force to accelerate B, B now has the force to accelerate something else. A, it seemed, must have lost some force. A must now not have the ability to produce as much acceleration as it did before. This seems logical. However all that went through my head without much examination and I probably should have stuck exclusively to the concept of momentum.

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