Newton's 3 Law: Analyzing Equal & Opposite Forces

[omin]

Newton's 3 Law: Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

Since the magnitude of force applied is said to be exactly the magnitude returned and the direction is said to be exactly opposite, shouldn't no truly equal and opposite collision change the velocity of the second object?

It seems to me that the slightest change of velocity of the second object implies that equal and opposite forces didn't occur. For a velocity change of the second object to be sensed after the collision, it seems the objects must disconnect before equal and opposite actions may finish (during the time the objects touch, the action/reaction acceleration periods).

 

[quantumdude]

Since the magnitude of force applied is said to be exactly the magnitude returned and the direction is said to be exactly opposite, shouldn't no truly equal and opposite collision change the velocity of the second object?

That's definitely wrong. If a force acts on the second object, then according to Newton's second law, there is a change in momentum. This must either manifest itself as a change in mass, or as a change in velocity.

 

[russ_watters]

...equal and opposite collision...

What do you mean by that? That's not how collisions are typically described, so I'm thinking that's where the misunderstanding lies. Maybe you could be more specific about this collision...

 

[robphy]

Newton's 3 Law: Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

Since the magnitude of force applied is said to be exactly the magnitude returned and the direction is said to be exactly opposite, shouldn't no truly equal and opposite collision change the velocity of the second object?

It seems to me that the slightest change of velocity of the second object implies that equal and opposite forces didn't occur. For a velocity change of the second object to be sensed after the collision, it seems the objects must disconnect before equal and opposite actions may finish (during the time the objects touch, the action/reaction acceleration periods).

Let's clarify the Third Law.

$\vec F_\text{on A due to B}=-\vec F_\text{on B due to A}$
Assuming no other forces act,
$\vec F_\text{net on A}=\vec F_\text{on A due to B}$ and $\vec F_\text{net on B}=\vec F_\text{on B due to A}$.

So, (assuming constant masses)
$$\begin{align*} m_A\vec a_A\stackrel{N2}{=}\vec F_\text{net on A}=\vec F_\text{on A due to B} \stackrel{N3}{=}-\vec F_\text{on B due to A}=-\vec F_\text{net on B}\stackrel{N2}{=}-m_B\vec a_B \end{align*}$$
That is, assuming nonzero forces, each object in this collision experiences its own acceleration, and, thus, a change in its own velocity.

 

[joyful55]

That's definitely wrong. If a force acts on the second object, then according to Newton's second law, there is a change in momentum. This must either manifest itself as a change in mass, or as a change in velocity.

Well actually, a change in momentum could also manifest itself as a change in both mass and velocity as in the case of rocket fuel using up and thrsuting itself into space.

 

[quantumdude]

Well actually, a change in momentum could also manifest itself as a change in both mass and velocity as in the case of rocket fuel using up and thrsuting itself into space.

Right, take my "or" statement in the inclusive sense.

 

[Cyrus]

your problem is the frame of refrence. You can push on an object but the object pushes back on YOU too. So If were on an ice rink, and I give YOU as shove, you feel a force I gave to you, and you go drifting off. But at the same time, I feel you pushing me equally and oppositely, so I also go flying off in the OPPOsite direction as you do. So we both go flying, even though I pushed on you. The force will act equally on each of us, just in different directions. The equal and opposite forces act on each body, not the same body. WoW tom is a SUPER mentor, I think he has a cape, all the other mentors are so jealous

 

[omin]

That's definitely wrong. If a force acts on the second object, then according to Newton's second law, there is a change in momentum. This must either manifest itself as a change in mass, or as a change in velocity.

Here's how I'm seeing this in steps:

1. Two objects not touching but on a collision course.

2. Objects impact, but no force exists yet.

3. Object one exerts a force upon object two.

4. Object two exerts a force on object one.

5. Objects separate.

I've read action and reaction may be simultaneous, but that seems to ignore spatial dimension, so I'm assuming there are spatial coordinates which implies an order in action and reaction.

In step 3 the first object impress a force upon the second object (action). If this force is returned equal and opposite in step 4 (reaction), why should the second object have any change in momentum, except during the impulse period (where force is exerted upon it but returned in exact magnitude and opposite direction, resulting in no velocity change?

 

[quantumdude]

In step 3 the first object impress a force upon the second object (action). If this force is returned equal and opposite in step 4 (reaction), why should the second object have any change in momentum, except during the impulse period (where force is exerted upon it but returned in exact magnitude and opposite direction, resulting in no velocity change?

You just answered your own question. The second object suffers a velocity change because there is a force acting on it.

 

[omin]

You just answered your own question. The second object suffers a velocity change because there is a force acting on it.

Do you mean the force that occurs in the action period in step three? What the first object exerts is what it loses, so what the first object loses could be termed to be the opposite reaction of the second object, or not?

I can see that as simultaneous, but not the entire process I've tried to delineate here. What did Newton mean?

 

[Cyrus]

Hey omin, is my post talking about the same topic as your question, or are you talking about something different? I am not sure if your asking what I responded too or not.

 

[joyful55]

Do you mean the force that occurs in the action period in step three? What the first object exerts is what it loses, so what the first object loses could be termed to be the opposite reaction of the second object, or not?

I can see that as simultaneous, but not the entire process I've tried to delineate here. What did Newton mean?

Try picturing your step 3 & 4 as a single step which occurs at the same time.

 

[russ_watters]

Newton's 3rd applies to each object individually. It seems you are thinking that the action happens to one and the reaction happens to another. Each object experiences a force, so each object experiences an acceleration. The forces are equal, the masses are equal, so the accelerations are equal.

 

[omin]

Hey omin, is my post talking about the same topic as your question, or are you talking about something different? I am not sure if your asking what I responded too or not.

I apologize, I didn't mean to seem to ignore your comment. I get an hour a day at the library and I don't have the time to respond to all comments and my posts get sloppy if I don't take my time with them.

You said it like the book, I admit. I'm just not sure where the equal and opposite simultaneousness assertion is in Law 3. I don't know if it's meant to be in step three or meant to occur over the course of the whole the collision phenomenon.

Try picturing your step 3 & 4 as a single step which occurs at the same time.

I tried and I have a bit of a problem fusing them. In step three, the acceleration object one loses is the acceleration object two gains. This I see as simultaneously equal and opposite. But, I don't know if that is what law 3 is supposed to represent, because of step 4 where the second object seems to me not to be able to react until acted upon which implies time duration rather than an instant of simultaneousness.

 

[Cyrus]

Well, whenever any two bodies touch they have to have equal and opposite forces. the moment they no longer act on each other, there is no longer an equal and opposite force. I just like to think about my hand. If i push on somthing i give it a force. But I FEEL myself pushing on that object, so it HAS to be pushing back on me too, otherwise, how would I feel it? The moment I stop touching it, the force goes down to zero on both me and the thing I was pushing.

 

[quantumdude]

Do you mean the force that occurs in the action period in step three?

It doesn't matter which force you call "action" or "reaction". The simple fact of the matter is that each object exerts a force on the other. Since each object has a nonzero force acting on it, each object is subjected to a change in velocity. It's just that simple.

What the first object exerts is what it loses, so what the first object loses could be termed to be the opposite reaction of the second object, or not?

This doesn't make any sense to me. What exactly does either object "lose"?

I can see that as simultaneous, but not the entire process I've tried to delineate here. What did Newton mean?

He meant that forces come in pairs. And yes, they do appear simultaneously.

 

[omin]

It doesn't matter which force you call "action" or "reaction". The simple fact of the matter is that each object exerts a force on the other. Since each object has a nonzero force acting on it, each object is subjected to a change in velocity. It's just that simple.



This doesn't make any sense to me. What exactly does either object "lose"?



He meant that forces come in pairs. And yes, they do appear simultaneously.

I'll have to think about this more, because my original question just isn't being pinpointed and it's my fault because the slight digression on other fine points sourrounding it is moving away from the original point.

 

[Tide]

I'll have to think about this more, because my original question just isn't being pinpointed and it's my fault because the slight digression on other fine points sourrounding it is moving away from the original point.

The "digression" was necessary and not slight because from your original post it was clear you had a fundamental misunderstanding of the principles involved. From my perspective the "other fine points" are right on the mark and necessary to help you understand your original point - or the incorrectness of it.

 

[joyful55]

I apologize, I didn't mean to seem to ignore your comment. I get an hour a day at the library and I don't have the time to respond to all comments and my posts get sloppy if I don't take my time with them.

You said it like the book, I admit. I'm just not sure where the equal and opposite simultaneousness assertion is in Law 3. I don't know if it's meant to be in step three or meant to occur over the course of the whole the collision phenomenon.



I tried and I have a bit of a problem fusing them. In step three, the acceleration object one loses is the acceleration object two gains. This I see as simultaneously equal and opposite. But, I don't know if that is what law 3 is supposed to represent, because of step 4 where the second object seems to me not to be able to react until acted upon which implies time duration rather than an instant of simultaneousness.

First of all, the equal and opposite assertion is meant to occur over the course of the whole collision. Try reading up and relationship b/w impulse, momentum and net force.

Secondly, forget what I said about steps. The whole 3rd law, has only one single mechanism is that the force when acted by a body on another could also be viewed in relative of the other body as in it was acted on the first body. Just infer from Einstein's Relativity.

 

[ballooza]

let me tell u something omin, try to punch someone so hard on his shoulder-for example-, ofcourse u exert force there...u were asking like: where is the feedback force? well, don't u feel ur hands get hurt? that's the equal opposite power... sometimes that's unimaginable (if that's even a word) but there's no other explannation...i just read the wuestion of yours and not the answers so maybe u know that now... uneed anything for this answer ask away.

 

[akashdgr8]

Whenever two bodies collide impulsive forces come into play their magnitude is very high thus they don't require much time impart the change in momentum

 

[omin]

Okay, I've thought about it and here is where I'm confused.

It has to do with situations where rebound occurs and where it doesn't.

In a collision where the first object loses all velocity to the second object, a simultaneous equal and opposite reaction seems obvious.

In a collision where there is rebound, where the second object doesn't retain all the velocity, is where there appears not to be not an equal and opposite reaction, over the course of the collision.

Do I look at rebound like this in simultaneous steps:

1. First object collides with second object. First object decelerates equal and opposite to second objects acceleration.

2. Second object decelerates within itself, but accelerates at the same time to create an opposing direction of force toward the first object. (Meanwhile, the first object is unaffected.)

3. Now the second object is going in the direction of the first object. The second object decelerates while first object accelerates.

Am I supposed to take the third law in consideration specifically with fundamental building blocks and only in general with objects that are made up by those building blocks?

Otherwise wouldn't only a truley equal and opposite collision be where the second object gains all the velocity leaving the first object without velocity, where masses are identical?

 

[Doc Al]

collisions

When two objects collide it is the force that they exert on each other that is equal and opposite. Not the resulting accelerations of the objects, which depend on their masses.

A consequence of the forces being equal and opposite is that the net change in momentum of both objects is zero. Whatever momentum one gains, the other loses.

 

[omin]

When two objects collide it is the force that they exert on each other that is equal and opposite. Not the resulting accelerations of the objects, which depend on their masses.

Let me see if I understand this right. Force, as I have read, occurs only during acceleration of an object. Acceleration is change of velocity. Acceleration is measured in standardized units of object displacement, velocity. When force is exerted from a first object, isn't acceleration (velocity units) what we notice and thus the only change in the force equation, unless mass changes during the collision? Why isn't resulting acceleration what is exerted, since it seems to be the only variable changing?

A consequence of the forces being equal and opposite is that the net change in momentum of both objects is zero. Whatever momentum one gains, the other loses.

Ok, isn't it the same thing, nearly, to say that the amount of force exerted from object one to object two is the amount of momentum exerted from object one to object two? The only difference in a non-changing mass collision being that momentum uses velocity exerted and force uses velocity squared exerted?

 

[Doc Al]

Let me see if I understand this right. Force, as I have read, occurs only during acceleration of an object.

No. For the purposes of understanding Newton's 3rd law, consider that every force is an interaction between two objects. Can a force be exerted on an object without the object accelerating? Yes. Consider a book lying on a table. Both the Earth and the table exert forces on the book. Since the net force is zero, there is no acceleration.

Acceleration is change of velocity.

Acceleration is a rate of change of velocity, with the understanding that velocity and acceleration are vectors.

Acceleration is measured in standardized units of object displacement, velocity.

Acceleration is measured in units of "distance per time squared".

When force is exerted from a first object, isn't acceleration (velocity units) what we notice and thus the only change in the force equation, unless mass changes during the collision?

Whether an object accelerates or not depends on the total force exerted on it. If the only force on the two objects is their equal and opposite interaction, then if you know that force you can calculate the acceleration using Newton's 2nd law.

Why isn't resulting acceleration what is exerted, since it seems to be the only variable changing?

I think you'd be better off thinking that they exert equal and opposite forces on each other. (They sure don't exert equal and opposite accelerations!)

Ok, isn't it the same thing, nearly, to say that the amount of force exerted from object one to object two is the amount of momentum exerted from object one to object two?

No. Force can be seen as the rate of change of momentum.

The only difference in a non-changing mass collision being that momentum uses velocity exerted and force uses velocity squared exerted?

Using your own terms like "velocity exerted" and "velocity squared exerted" will only serve to confuse you. It's really simple. Force is exerted. A net force on a object will produce an acceleration and a rate of change of momentum. Since, according to Newton's 3rd law, the two objects exert equal and opposite forces on each other for the same time, one can show that the change in momentum of one object will be equal and opposite to the change in momentum of the other. (Momentum of an object is its mass times its velocity.)

Rather than talk in general terms, perhaps describing a specific example may clarify the concept. Pick one, if you like.

 

[omin]

Consider a book lying on a table. Both the Earth and the table exert forces on the book. Since the net force is zero, there is no acceleration.

Oh, I assumed zero wasn't a quantity, so no force existed. So, I should assume zero is a quantity and assume force exists (although it's zero) .

Acceleration is a rate of change of velocity, with the understanding that velocity and acceleration are vectors.

Sorry, I assumed change implied a quantity, thus implying a rate. Should I always say rate of change versus change for convention?

Acceleration is measured in units of "distance per time squared".

I just didn't get acclerlation comprised with time squared. The squared seems a covience form versus the velocity per standard time.

I think you'd be better off thinking that they exert equal and opposite forces on each other. (They sure don't exert equal and opposite accelerations!)

Magnitude is equal (where one object accelerates and the other decelerates equal magnitudes), but direction component is opposite means equal and opposite, or not?

Using your own terms like "velocity exerted" and "velocity squared exerted" will only serve to confuse you. It's really simple. Force is exerted. A net force on a object will produce an acceleration and a rate of change of momentum. Since, according to Newton's 3rd law, the two objects exert equal and opposite forces on each other for the same time, one can show that the change in momentum of one object will be equal and opposite to the change in momentum of the other. (Momentum of an object is its mass times its velocity.)

Force is the product of mass and acceleration. Acceleration is the only variable that changes in a collision where no mass changes. We can say only force is exerted it sounds like. When I exert something, to me it's like giving, impressing, applying. And velocity is the only variable that changes. If mass was given as well as velocity, then it would make sense that force was exerted. That's how I reasoned it. Where am I going wrong with that reasoning?

 

[Doc Al]

Oh, I assumed zero wasn't a quantity, so no force existed. So, I should assume zero is a quantity and assume force exists (although it's zero)

Think of a force as the interaction of two bodies: a push or a pull. Just because the net force is zero doesn't mean no forces are being exerted. Imagine a heavy weight resting on your toe--I presume you would agree that forces are being exerted on your toe, even though it's not accelerating.

Sorry, I assumed change implied a quantity, thus implying a rate. Should I always say rate of change versus change for convention?

Words in physics have specialized technical meanings. Some things are rates, others are not. The concepts are not interchangeable. Acceleration is a rate of change of velocity.

I just didn't get acclerlation comprised with time squared. The squared seems a covience form versus the velocity per standard time.

"velocity per unit time" is the same units as "distance per time squared".

I think you'd be better off thinking that they exert equal and opposite forces on each other. (They sure don't exert equal and opposite accelerations!)

Magnitude is equal (where one object accelerates and the other decelerates equal magnitudes), but direction component is opposite means equal and opposite, or not?

Absolutely wrong! The forces are equal, not the accelerations. Per Newton's 2nd law, the accelerations are inversely proportional to the masses of the objects.

Force is the product of mass and acceleration. Acceleration is the only variable that changes in a collision where no mass changes. We can say only force is exerted it sounds like. When I exert something, to me it's like giving, impressing, applying. And velocity is the only variable that changes. If mass was given as well as velocity, then it would make sense that force was exerted. That's how I reasoned it. Where am I going wrong with that reasoning?

Where you're going wrong is that you seem to want to make the physics conform to your intuitive sense of what's happening while you continue to use your "ordinary language" to describe things. That way lies madness! Better to learn the language of physics. And understand Newton's laws as written, using the technical (and more precise) language of physics.

 

[bd1976]

Wow this is a seriously cool thread - I had exactly this kind of discussion with my teacher when I was thirteen! The sad truth everyone learns in the end is that physics has little to do with intuition and everything to do with differential equations.

My advice would be to stop thinking and to start doing maths!

 

[russ_watters]

Oh, I assumed zero wasn't a quantity, so no force existed. So, I should assume zero is a quantity and assume force exists (although it's zero) .

Haven't you ever used a bathroom scale?

 

[joyful55]

Wow this is a seriously cool thread - I had exactly this kind of discussion with my teacher when I was thirteen! The sad truth everyone learns in the end is that physics has little to do with intuition and everything to do with differential equations.

My advice would be to stop thinking and to start doing maths!

Well, physics is not all about maths but more of logic and reasoning, most of all, statistics and analysis. It is from the data we analyse that we are able to come up with differential equations. For example, how in the world did we come up with acceleration being dv/dt? Through data collection.

 

[joyful55]

Let me try to set N3L into a much more comprehensive example.
Try pushing your finger on a pin. The force was exerted by you on the pin but you still feel pain as if there is a force acting on your finger from the pin(because that force really exists).

 

[omin]

Thank you all for the comments. I'll keep in mind when I hit the book again.