Force and rate of change of momentum

[alkaspeltzar]

My question is simply..if force does equate to the rate of change of momentum, then why is it not taughted as this rate rather simply a push or pull?

Is it becuase really they are the same thing and it is much easy to explain/work with? Just curious

Guess up until now I didn't even think of force as a rate of change of momentum...maybe I'm old school

Thanks

 

[Chestermiller]

Force is still push or pull. Only NET force (vector sum of pushes and pulls) is rate of change of momentum.

 

[alkaspeltzar]

Okay, so it is only the NET force which can be considered equal to the rate of change of momentum. Got it!

Is it probably because in most applications(or at least what I work with in school and engineering) we only worry about the simple forces that then this relationship doesn't apply, so force is simply the push pull and we leave the rate of change of momentum out of it?

I do understand the relationship between force and momentum now...I guess what is bothering me is that for years, I have been able to think and do my calcs and never needed to use the relationship until now. Guess it has me confused if I should be thinking of force differently than classic F=ma, push pull that has been drilled into my head.

Thank you

 

[Chestermiller]

Is it probably because in most applications(or at least what I work with in school and engineering) we only worry about the simple forces that then this relationship doesn't apply, so force is simply the push pull and we leave the rate of change of momentum out of it?

You can, of course, leave out ma if it is a static equilibrium problem. But, in dynamic situations, ma needs to be included.

 

[A.T.]

so force is simply the push pull and we leave the rate of change of momentum out of it?

An individual force is the rate of momentum transfer.
Net force is the rate of total momentum change.

Guess it has me confused if I should be thinking of force differently than classic F=ma

The F in F=ma stands for net force, which is the rate of total momentum change.

 

[alkaspeltzar]

Okay but my main question is a physical force the same as a rate of change in momentum? Like if I hit a wall with a force is that the same as saying I hit the wall with a rate of change of momentum?

Or is simply rate of change of momentum related to force therefore we can calculate with one or the other?

 

[Chestermiller]

Okay but my main question is a physical force the same as a rate of change in momentum? Like if I hit a wall with a force is that the same as saying I hit the wall with a rate of change of momentum?

Or is simply rate of change of momentum related to force therefore we can calculate with one or the other?

A push force or a pull force is sometimes (infrequently) referred to as a rate of momentum transfer. But you can't represent it as mass times acceleration unless it the only (net) force acting.

 

[HallsofIvy]

Okay, so it is only the NET force which can be considered equal to the rate of change of momentum. Got it!

Is it probably because in most applications(or at least what I work with in school and engineering) we only worry about the simple forces that then this relationship doesn't apply, so force is simply the push pull and we leave the rate of change of momentum out of it?

I do understand the relationship between force and momentum now...I guess what is bothering me is that for years, I have been able to think and do my calcs and never needed to use the relationship until now. Guess it has me confused if I should be thinking of force differently than classic F=ma, push pull that has been drilled into my head.

Thank you

"Force equals the rate of change of momentum" means that $F= \frac{d(mv)}{dt}$. In the special (but important) case that mass, m, is constant, that is the same as $F= m\frac{dv}{dt}= ma$.

 

[A.T.]

An individual force is the rate of momentum transfer.

Okay but my main question is a physical force the same as a rate of change in momentum?

I answered this just above.

 

[alkaspeltzar]

Sorry bear with me but I am just not getting it.

So are you saying that the physical force(what we long ago defined as a push or pull) is exactly the same as rate of change in momentum, aka the rate of momentum transfer?

Don't you have to have a force to have a rate of change in momentum? Part of me thinks if a body has acceleration, then there must be a force. Likewise, if a body has a rate of change in momentum, it must have a force causing it...so aren't they two separate things, just related since one can't exist without the other?

And if they are the same, why don't we use one name...why say force if it is really a rate of momentum transfer or visa versa?

I guess I m looking for a simple explanation, please no math at this point.

 

[Chestermiller]

Sorry bear with me but I am just not getting it.

So are you saying that the physical force(what we long ago defined as a push or pull) is exactly the same as rate of change in momentum, aka the rate of momentum transfer?

Don't you have to have a force to have a rate of change in momentum? Part of me thinks if a body has acceleration, then there must be a force. Likewise, if a body has a rate of change in momentum, it must have a force causing it...so aren't they two separate things, just related since one can't exist without the other?

And if they are the same, why don't we use one name...why say force if it is really a rate of momentum transfer or visa versa?

I guess I m looking for a simple explanation, please no math at this point.

Historically, using terms like "rate of momentum transfer" to represent a contact force (push or pull) came about when people began realizing the analogy between the differential equations for the force balances in continua, and the differential equations for heat- and mass transfer. In these sets of equations, the forces per unit area appear in the same locations in the equations as the rate of heat flow per unit area and the rate of mass flow per unit area. So, it became natural for them to start referring to the force per unit area as the rate of momentum flow per unit area (or the rate of momentum transfer per unit area).

 

[alkaspeltzar]

Historically, using terms like "rate of momentum transfer" to represent a contact force (push or pull) came about when people began realizing the analogy between the differential equations for the force balances in continua, and the differential equations for heat- and mass transfer. In these sets of equations, the forces per unit area appear in the same locations in the equations as the rate of heat flow per unit area and the rate of mass flow per unit area. So, it became natural for them to start referring to the force per unit area as the rate of momentum flow per unit area (or the rate of momentum transfer per unit area).

that is not helping me, I am sorry that is more advanced than I can understand. Can you or someone please explain what I have asked above? I just want to know if really, they are the same thing, regardless of name or the math. Looking to have someone explain how a rate of change in momentum really is a contact force

 

[A.T.]

...change in momentum, aka the rate of momentum transfer?...

Change and transfer are not the same. Change is the sum of all transfers: the net effect.

And if they are the same, why don't we use one name...why say force if it is really a rate of momentum transfer or visa versa?

For the same reason we use the word "velocity" instead of "rate of position change".

 

[Chestermiller]

that is not helping me, I am sorry that is more advanced than I can understand. Can you or someone please explain what I have asked above? I just want to know if really, they are the same thing, regardless of name or the math. Looking to have someone explain how a rate of change in momentum really is a contact force

In the normal context of applying physics at the level you are asking about, I would never refer to an individual force as a rate of change of momentum, unless it was the only force acting on a body, in which case it would also then be equal to the rate of change of momentum of the body. But, if there are multiple forces acting on a body, I would only consider the resultant of these multiple forces (i.e., the net force) as being equal to the rate of change of momentum of the body, and I would not consider each one individually as being the same thing as a rate of change of momentum.

Now this may differ from how A.T. looks at it, but that is just a matter of personal taste and preference.

 

[alkaspeltzar]

A.T., so are you saying that rate of change of momentum is not the same as rate of momentum transfer?

Assuming net forces; "Force equals the rate of change of momentum" means that F=d(mv)dt' , does that mean the FORCE IS PHYSICALLY the rate of change of momentum or is this just a math relation?

 

[alkaspeltzar]

So Chestermiller, what you are saying is that yes, the force and rate of change of momentum are the same, assuming it is the only force(or total net force)?

Doesn't the force CAUSE the rate of change of momentum, so they are different entities still?

 

[Chestermiller]

So Chestermiller, what you are saying is that yes, the force and rate of change of momentum are the same, assuming it is the only force(or total net force)?

That's how I view it.

Doesn't the force CAUSE the rate of change of momentum, so they are different entities still?

I would agree with this interpretation also.

 

[A.T.]

does that mean the FORCE IS PHYSICALLY the rate of change of momentum or is this just a math relation?

What is the difference and why should we care?

Doesn't the force CAUSE the rate of change of momentum,

Since both happens simultaneously, how would you know which is the cause and why should we care?

 

[alkaspeltzar]

That's how I view it.

I would agree with this interpretation also.

If they are different entities though, won't they have different units? Unit for rate of change of momentum are same as force, how come?

 

[alkaspeltzar]

What is the difference and why should we care?

Since both happens simultaneously, how would you know which is the cause and why should we care?

Well since high school, college and now engineering, force has always been a push or a pull, calculated by F=Ma, with the understanding that a change in acceleration or momentum is cuased by a force. Hearing a force said it is a rate of change of momentum seems foreign and is outside my understanding, so I am asking trying to understand how or why it is or isn't the same thing.

 

[Chestermiller]

If they are different entities though, won't they have different units? Unit for rate of change of momentum are same as force, how come?

Different entities don't have to have different units. In Newton's 2nd law, they are on the two opposite sides of the equation, so they have to have the same units.

 

[A.T.]

Well since high school, college and now engineering, force has always been a push or a pull, calculated by F=Ma...

Which is the rate of momentum change (for constant mass). See post #8

 

[Chestermiller]

Well since high school, college and now engineering, force has always been a push or a pull, calculated by F=Ma, with the understanding that a change in acceleration or momentum is cuased by a force. Hearing a force said it is a rate of change of momentum seems foreign and is outside my understanding, so I am asking trying to understand how or why it is or isn't the same thing.

I totally agree with your perspective. But, on a more advanced level, some people like to refer to a contact force a rate of momentum transfer. However, I respectfully disagree with Halls of Ivy and A. T. in calling each and every contact force a rate of change of momentum. I would only apply this kind of terminology to the NET force acting on a body.

 

[A.T.]

I respectfully disagree with Halls of Ivy and A. T. in calling each and every contact force a rate of change of momentum.

I never did. I called it "transfer", equivalent to "flow".

 

[Chestermiller]

I never did. I called it "transfer", equivalent to "flow".

Sorry. I went back and checked. You're right. Somehow, I got it in my head that you had said the opposite.

Chet

 

[alkaspeltzar]

So let me see if I have this right

So if block A pushes on Block B, not other forces involved, the force(push and pull) is the same as the rate of change of momentum...that is what a force is? Push or pull can be literally thought of as a rate of change of momentum
Yes or no?

 

[A.T.]

So if block A pushes on Block B, not other forces involved, the force(push and pull) is the same as the rate of change of momentum...that is what a force is?

That is what net force is.

 

[alkaspeltzar]

And if so, which I read it Force Net is equal/proportional to the rate of change of momentum of a object, then why are the units not that of rate.

Even a Newton, described as a kgm/s^2, defined not as a rate but as force required to move 1kg at 1m/s^2

Lastly, in my classicl physics class, I was always taught force is a push/ pull, calculated via F=MA, where force was just force, never described as a rate.

Can someone please clarify for me? Looking for basic explanation no heavy theoretical if possible

Thanks

 

[mfb]

"rate of change of momentum" is not the same as "rate". Force can be seen as "momentum change per time".

defined not as a rate but as force required to move 1kg at 1m/s^2

Not move, accelerate. That is an important difference.

 

[alkaspeltzar]

"rate of change of momentum" is not the same as "rate". Force can be seen as "momentum change per time".
Not move, accelerate. That is an important difference.

Okay, what I meant to say is if force is the rate of change of momementum, then force is a rate. But how is that? Rates are typically something per time?

Can you also explain why certain physics books write F=dp/dt...that would make me think it is a rate. Or am I thinking to hard, that equations as such don't physically mean a force is a rate, no more than force is physically mass times acceleration. However, mathematically(abstract) since on causes the other they can equated for calculation purposes?

 

[Dale]

But can you explain why certain physics books write F=dp/dt...that would make me think it is a rate.

Force can indeed be thought of as the rate of momentum transfer, and has the appropriate units. The units for the rate of momentum transfer would be momentum/time. In SI that unit is 1 N.

 

[alkaspeltzar]

Force can indeed be thought of as the rate of momentum transfer, and has the appropriate units. The units for the rate of momentum transfer would be momentum/time. In SI that unit is 1 N.

But why is it from my high school physics class thru college it was never treated or thought of as a rate. Just 100lbs, or 10 N, as in a simple push or pull. Rate was not even thought of.

And am I wrong with my way of thinking? F=ma, force is a push/pull. Is it just in the end, what I know as force can also be thought of as a rate but most of the time isn't due to the fact it isn't necessary?

 

[Dale]

But why is it from my high school physics class thru college it was never treated or thought of as a rate.

I think you would have to ask those teachers.

I assume that acceleration was described as the rate of change of velocity, so multiple of acceleration should already be thought of as a rate. They may have in fact taught that, but the mental connection just took some time to establish.

 

[alkaspeltzar]

I think you would have to ask those teachers.

I assume that acceleration was described as the rate of change of velocity, so multiple of acceleration should already be thought of as a rate. They may have in fact taught that, but the mental connection just took some time to establish.

how come modern units are not rate units then? lb, kg, ton, dyne...where as unit of rate for speed are typically m/s, inch/sec, feet/sec??

 

[mfb]

kg and ton are not forces. The imperial system with pounds, pound-force, slug and whatever is horrible so I won't comment on that. Dyne is just 10^-5 N, same units.

1N = 1kg m/s² - there is your "per second". You can also write it as (1kg m/s)/s where the numerator is momentum and the denominator is time.