Force and rate of change of momentum

[PeroK]

If you use a force meter in both cases, you would get the same answer in Newtons.; the force that stretches a spring by so much will also cause an acceleration and the sums will give you the same result Imagine a car being towed with a rope. The force stretching the rope is 1000N and the force accelerating the car is also 1000N. You could measure that force in two ways. It's the same thing that you're measuring.
Do you also have the same problem with acceleration and gravity? There is a Principle of Equivalence at work with both quantities. I think you may be confusing 'familiarity' with quantities that you feel 'directly' with scientific significance.

Please read the posts more carefully. I knew if I tried to summarise the OP's view, someone would assume it was my view!

 

[sophiecentaur]

Please read the posts more carefully. I knew if I tried to summarise the OP's view, someone would assume it was my view!

This is a perennial problem on forums like PF but you really don't need to take offence. I was, as always, commenting on the message and not ad hominem (but I see I used the personal pronoun - "you", when I should have written "one". I can't be expected to read through 91 (!) posts to see who is actually responsible for the ideas I come across.
It's good that we are in agreement about the facts of the matter.

 

[PeroK]

This is a perennial problem on forums like PF but you really don't need to take offence. I was, as always, commenting on the message and not ad hominem (but I see I used the personal pronoun - "you", when I should have written "one". I can't be expected to read through 91 (!) posts to see who is actually responsible for the ideas I come across.
It's good that we are in agreement about the facts of the matter.

Yes, it's been a long hard thread!

 

[Dale]

Everyone understands push or pull, I think it would be cruel to start with force as a rate of change of momentum for beginners.

Sure, I am not suggesting starting there, but as soon as you write Newton's second law it is clear that force is a rate.

 

[Dale]

How can we describe the constant tension of a spring as a rate? The static friction holding a block on an incline? The force holding a magnet against a refrigerator?

In each of those cases there are multiple forces with rates of momentum transfer that sum to zero. It may not be a terribly useful concept in those cases, but it also should not be such a surprise either.

 

[BiGyElLoWhAt]

I honestly think this was a semantics question.
Force describes an interaction.
Momentum (and changes of) are a property of matter.
These two cannot be the same, so what must be the case is a cause and effect relationship. The rate of change of momentum w.r.t. time of an object is equal and magnitude and direction to the net force acting on said object, but they are not the same thing. We can equate them mathematically, but an interaction quantity and a property quantity cannot be physically the same thing.

 

[PeroK]

I honestly think this was a semantics question.
Force describes an interaction.
Momentum (and changes of) are a property of matter.
These two cannot be the same, so what must be the case is a cause and effect relationship. The rate of change of momentum w.r.t. time of an object is equal and magnitude and direction to the net force acting on said object, but they are not the same thing. We can equate them mathematically, but an interaction quantity and a property quantity cannot be physically the same thing.

I believe that what you've described is not semantics, but the difference between Physics and Metaphysics. Physics is, essentially, a science of measurement. Yes, you can theorise and use mathematics, but essentially what something "is" in physics is what you measure. Force, like everything else, is ultimately defined by how you measure it.

Metaphysics, on the other hand, is concerned with the fundamental nature of things, so your argument is essentially that force and rate of change of momentum have different intrinsic natures and are different metaphysically.

One example of where metaphysical thinking caused a problem in physics was the development of relativity and the question of "what is time". The great man cut through this by recognising that time is what a clock measures and time has no intrinsic, metaphysical properties. That insight led to special relativity. Without it, the presumed metaphysical nature of time stood in the way of progress towards SR.

 

[BiGyElLoWhAt]

I don't know if I would say that I'm saying something "is" something, intrinsically, unless you consider saying that "force is an interaction quantity" falls into that category.

The semantics here, I believe, is determining whether these two quantities are related via definition, or if it's a cause and effect relationship. I believe that it's the latter.

To expand on what you were saying, we "measure" momentum by measuring velocity and mass, and then calculate momentum. We can also measure changes in these quantities.
We measure force completely differently. For a spring, we measure k, and we measure x. For gravity, we measure m and h, etc.

IMO, $F=\frac{dp}{dt}$ doesn't say that net force is the time rate of change of momentum, it says that a net force induces a rate of change in momentum, and therefore they are "physically" two different things. Additionally, again, not to beat the dead horse, but force describes an interaction, and momentum and changes in momentum describe matter. The latter argument is, IMO, strong evidence that force "is" not the time derivative of momentum, but that the interaction causes the state of matter to change.

On the other hand:
$E=m_0c^2$
IMO says that mass and energy are the same thing. These are two property quantities, that both describe the same piece of matter. So in essence, mass "is" energy.