To avoid further fruitless discussion, I'll simply state that the unbalanced force acting on an object is directly proportional to the rate of change of the momentum of an object.
Since momentum is mass x velocity, this is probably where N101N gets his mistaken F=mv from.
The actual equation is slightly more complicated as shown in the attachment.
Since momentum is mass x velocity, this is probably where N101N gets his mistaken F=mv from.
The actual equation is slightly more complicated as shown in the attachment.
Attachments
To explain in more detail where acceleration (a) comes in, here's my take:
Resultant force = rate of change of momentum (as originally expressed by Newton)
> Resultant force = change in momentum/time for change
> F = (mv - mu)/t (where v = final velocity, and, u = initial velocity)
> F = m(v - u)/t (since the mass is constant)
> F = ma
Note: Acceleration is rate of change of velocity i.e. change in velocity/time or (v -u)/t
Resultant force = rate of change of momentum (as originally expressed by Newton)
> Resultant force = change in momentum/time for change
> F = (mv - mu)/t (where v = final velocity, and, u = initial velocity)
> F = m(v - u)/t (since the mass is constant)
> F = ma
Note: Acceleration is rate of change of velocity i.e. change in velocity/time or (v -u)/t
Oh dear . . . I’m reminded of Bertrand Russell’s observation (and I paraphrase) of the arrogance and cocksureness of the ignorant while the intelligent tread far more carefully and with much self-doubt.
Force is equal to the rate of change of momentum. In differential
form this is:
This formula can be used to calculate
the final velocity of a rocket where:
i) dv/dt is the rate of change of velocity
ii) dm/dt is the rate of change of mass, that is, the mass per second of ejected hot gases from the rocket's engines.
form this is:
Code:
F = d[mv]/dt
Since both mass m, and velocity v are functions of time,
the relationship becomes:
F = m.dv/dt + v.dm/dtthe final velocity of a rocket where:
i) dv/dt is the rate of change of velocity
ii) dm/dt is the rate of change of mass, that is, the mass per second of ejected hot gases from the rocket's engines.
Indeed, Newton's equation proves quite satisfactory when it comes to putting satellites into orbit.
Whether Newton was guilty of 'borrowing without authorization' is a matter for historians to discuss.
However, his laws of motion are tried and tested - for all everyday velocities, including those of space rockets, that is. 😉
This psot gives me a little comfort and hope, this because as I have been lectured to about some of the latter aspects, I have always felt doubt - as though it didn't really all just 'snap into place'.
It may seem disrespectful, but recently I have also wondered about certain astronomers, professors in exalted positions, we cannot verify much of what they espouse to be an accurate account of actual realities and events. This means that their performance is not measurable or verifiable.
Much of their status is given to them by their peers, and we watch on.
This is the sort of blanket statement that is easy to make, but perhaps more difficult to justify.
When it comes to cosmology there are few accurate accounts of actual realities and events in the universe, and this very point has been stressed many times in this thread.
Cosmologists are extremely competitive and are constantly testing each other's hypotheses - peer review is active and thorough.
The records seem to show that it was Hooke who ‘borrowed’ and was never able to prove he’d done anything prior to Newton.
This whole anti-science thing is of course nonsense. We have the standard model - driven by QM - describing things as the atomic level. We know QM works exceedingly well since we all use mobile phones choc full of semiconductors whose operation rests squarely on QM.
Describing the Universe at large are Einstein’s Relativity and Maxwells equations describing EMR.
There will be a lot of speculation as science feels its way forward to try to answer newly emerging questions (dark matter, dark energy, a unified theory of everything for example) but trashing existing science as if that will lead to an answer is not the solution. For the most part, the equations I mentioned above are the most accurate in all of science, so they are correct. My guess is we will probably have to reinterpret some aspects of our understanding for a breakthrough - just as Einstein did with a Newton’s and Maxwell did once he formalized Faraday’s discoveries, enabling him to correctly identify light, electricity and magnetism as all stemming from same underlying mechanism.
I posted a link up a week or two ago to Juergen Rens presentation on how Einstein got to Relativity. In that presentation he describes Einstein’s biggest challenge was going from qualitative insights (from his thought experiments) into quantitative results - ie his formalized field equations that allowed accurate, numbers based predictions to be made. That took 5 years and a lot of self doubt. Einstein presented his final paper to the Prussian Academy of Sciences 3 times over a period of three weeks. The first two times, the greatest mathematician of the day, David Hilbert, was in the audience and shook his head at Einstein, indicating that he had not quite got them right. On the third go, Hilbert congratulated him. Hilbert could have solved the equations (primarily Tensor calculus), but the maths came from the insights so it was Einstein that solved the problem by thinking about it and then used math to formalize it.
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I have the impression the basic issue, is some people are rationally uncomfortable with science, as it appears to question and challenge well established hegemonies.
The truth, although it may be considered a virtue, is often ruthless.
The truth, although it may be considered a virtue, is often ruthless.
This is the awesome part. How many before or after can claim the same experience. There should be a chronological account.
I think you are being unnecessarily harsh, given that my comments were speculative and not generalised.
Hegemony is a strong word here, seriously out of date imo, like about 400 years or so.
Thankfully, the truth is always ruthless.
Me? Harsh? I'm just a pussycat compared to some posters! 🙂
This thread is mainly about speculation. Hard facts can be in short supply, but all comments are welcome.
To lighten the mood, I've found the attached image which illustrates how we've always pondered on what is outside our universe.
When it comes to cosmology, there's certainly lots to ponder!
Attachments
As a member of several forums for a while, I am surprised at some of the viciousness which is exhibited, I only want to discuss and learn, and if possible help others.
When searching for PPM driver boards a few days ago I stumbled on a Google Group forum, and I was amazed at the blatant insulting going on which had become detached from subject matter, and was composed of several posts of the worst insults.
When searching for PPM driver boards a few days ago I stumbled on a Google Group forum, and I was amazed at the blatant insulting going on which had become detached from subject matter, and was composed of several posts of the worst insults.
Thankfully we've got effective moderators, but sometimes nastiness can get through when some egos are threatened!
Yep!
We're all poo flinging monkeys at heart.
There's some indication that we (homo sapiens) willfully chose to eradicate the other humanoid races very early on. Not surprising at all, get rid of the competition just in case they decide to move in next door.
It's in all of us, very aggressive. But sometimes a few of us can manage seemingly peaceful and relatively intellectual conversation, when we have satiated our base needs of food, water, sexual stimulus and sleep.
We're all poo flinging monkeys at heart.
There's some indication that we (homo sapiens) willfully chose to eradicate the other humanoid races very early on. Not surprising at all, get rid of the competition just in case they decide to move in next door.
It's in all of us, very aggressive. But sometimes a few of us can manage seemingly peaceful and relatively intellectual conversation, when we have satiated our base needs of food, water, sexual stimulus and sleep.
Bonsai,
I agree that certitude is not a trait of knowledge.
Not making any statements protects you from being wrong and is a wise way to hide ignorance. In his profession, Russell could not refrain from making statements about highly difficult epistemic issues, where adopting a halfhearted stance or exhibiting vagueness is not a virtue. Otherwise he could rather have become a cobbler or something. Russell made quite a few erroneous.statements regarding provability, validity and justification of knowledge.
We express opinions.
What should I have been less cocksure about?
Way back here I followed up one of my posts to say that I was of course merely guessing and that I have no formal education in the subject matter. I was informed that this thread has no intention to be strictly factual but is for venting ideas and wonderings + crazy ideas in general so I was not to worry. Felt good.
Keep it this way?
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Keep it this way?
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