| Topic: |
Science > Physics |
| User: |
"Andr? Michaud" |
| Date: |
19 Dec 2004 08:21:53 PM |
| Object: |
Newton's second law? |
Androcles a écrit :
"Andr? Michaud" <srp@microtec.net> wrote in message
news:562f286c.0412181513.2828d241@posting.google.com...
Mike a écrit :
François Guillet wrote:
If mass is time depending, is it F=m(t)*dv/dt or F=d(m(t)*v)/dt?
FG
F = dp/dt,p = mv
In general: F = mdv/dt + vdm/dt (rocket equation)
If m is constant it reduces to F = mdv/dt
By the way you should know that Newton's second law is F=dp/dt as
stated in Principia and not F=ma, a result of popular ignorance.
Since t = d/v,
True
both forms of the equation are exactly equivalent,
False.
so F=ma is perfectly legit
False.
It was already explained to you above.
I don't think so.
You are assuming m is constant.
That's precisely what Newton based his 2nd law on.
In the case of a rocket, it is not.
Something as simple as that is usually said to be "not rocket science",
but in this case it is :)
Androcles
To my knowledge, Newton was addressing the question of motion of
stable masses, not the question of rocket launching, this is why
Mike's comment was off the mark.
Rocket launching is a special case. Universal motion of stable
masses is the general case for which the 2nd law was established
by Newton.
The equation that applies to rockets is a simple extension of
the basic 2nd law equation for stable masses.
André Michaud
.
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| User: "Androcles" |
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| Title: Re: Newton's second law? |
19 Dec 2004 10:14:30 PM |
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"Andr? Michaud" <srp@microtec.net> wrote in message
news:562f286c.0412191821.80b9cba@posting.google.com...
Androcles a écrit :
"Andr? Michaud" <srp@microtec.net> wrote in message
news:562f286c.0412181513.2828d241@posting.google.com...
Mike a écrit :
François Guillet wrote:
If mass is time depending, is it F=m(t)*dv/dt or F=d(m(t)*v)/dt?
FG
F = dp/dt,p = mv
In general: F = mdv/dt + vdm/dt (rocket equation)
If m is constant it reduces to F = mdv/dt
By the way you should know that Newton's second law is F=dp/dt as
stated in Principia and not F=ma, a result of popular ignorance.
Since t = d/v,
True
both forms of the equation are exactly equivalent,
False.
so F=ma is perfectly legit
False.
It was already explained to you above.
I don't think so.
You are assuming m is constant.
That's precisely what Newton based his 2nd law on.
In the case of a rocket, it is not.
Something as simple as that is usually said to be "not rocket
science",
but in this case it is :)
Androcles
To my knowledge, Newton was addressing the question of motion of
stable masses, not the question of rocket launching, this is why
Mike's comment was off the mark.
Gunpowder and the cannon's recoil were known to Newton, as were signal
rockets. That is why Mike is correct and your knowledge is deficient.
Mike said:
quote:
In general: F = mdv/dt + vdm/dt (rocket equation)
If m is constant it reduces to F = mdv/dt
unquote.
Note the "If m is constant".
Rocket launching is a special case.
Not at all. It is included in F = dp/dt.
Universal motion of stable
masses is the general case for which the 2nd law was established
by Newton.
You are guessing.
The equation that applies to rockets is a simple extension of
the basic 2nd law equation for stable masses.
Not at all. The second law is F = dp/dt.
F= ma is taught in schools as a precursor to aid understanding.
It is time for you to progress beyond that.
Androcles.
André Michaud
.
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| User: "Lewis Mammel" |
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| Title: Re: Newton's second law? |
19 Dec 2004 11:30:43 PM |
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Androcles wrote:
"Andr? Michaud" <srp@microtec.net> wrote in message
news:562f286c.0412191821.80b9cba@posting.google.com...
Rocket launching is a special case.
Not at all. It is included in F = dp/dt.
I don't believe this can be justified. If you want to justify it, you
have to identify your terms. F is the force of what acting on what?
p is the momentum of what?
Halliday and Resnick ( 1966 ) comment, "It is important to
note that we CANNOT derive a genral expression for Newton's
second las for variable mass systems by treating the mass
in F = dP/dt = d(Mv)/dt as a variable."
Also please note, if you're following Newton, his "force" is
a finite impulse acting, in many examples, in zero time.
His Laws all pertain to finite changes of momentum.
"When a body is falling, the uniform force of its gravity
acting equally, impresses, in equal intervals of time, equal
forces on that body, and therefor generates equal velocities;
and in the whole time impresses a whole force, and generates
a whole velocity proportional to the time."
He reserves infinitesimal reasoning for the analysis of particular
problems. e.g. Proposition I. Theorem I. "...Now let the number of
those triangles be augmented, and their breadth diminished IN INFINITUM; ..."
Universal motion of stable
masses is the general case for which the 2nd law was established
by Newton.
You are guessing.
He certainly considered systems of masses, and the rocket
is easily analysed by considering the system, rocket plus fuel,
using Newton's Corollary III, as I stated.
The equation that applies to rockets is a simple extension of
the basic 2nd law equation for stable masses.
Not at all. The second law is F = dp/dt.
See above.
F= ma is taught in schools as a precursor to aid understanding.
It's not a precursor, it's a reformulation, and it's entirely
equivalent to Newton's Second Law.
Lew Mammel, Jr.
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| User: "Androcles" |
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| Title: Re: Newton's second law? |
20 Dec 2004 06:44:02 AM |
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"Lewis Mammel" <l.mammel@worldnet.att.net> wrote in message
news:41C66430.67D0D2DF@worldnet.att.net...
Androcles wrote:
"Andr? Michaud" <srp@microtec.net> wrote in message
news:562f286c.0412191821.80b9cba@posting.google.com...
Rocket launching is a special case.
Not at all. It is included in F = dp/dt.
I don't believe this can be justified.
You are entitled to you beliefs.
If you want to justify it, you
have to identify your terms. F is the force of what acting on what?
p is the momentum of what?
"If" has an associated "else".
I do not want to justify it.
Halliday and Resnick ( 1966 ) comment, "It is important to
note that we CANNOT derive a genral expression for Newton's
second las for variable mass systems by treating the mass
in F = dP/dt = d(Mv)/dt as a variable."
I note that is what Halliday and Resnick have commented.
'M' is, however, a variable. Fuel is part of the mass, the acceleration
variable dx^2/d^2t is increasing.
Also please note, if you're following Newton, his "force" is
a finite impulse acting, in many examples, in zero time.
Yes indeed. The force that is acting on my rear end at this
very moment as I sit at this desk is finite, in zero time.
If an earthquake or similar disturbance were to occur there
would be a finite time when the force would not be constant.
Else the force is constant.
His Laws all pertain to finite changes of momentum.
If dp/dt then F.
The contrapositive is
If NOT F, then NOT dp/dt.
It is not
If NOT dp/dt then NOT F.
F exists absent dp/dt.
"When a body is falling, the uniform force of its gravity
acting equally, impresses, in equal intervals of time, equal
forces on that body, and therefor generates equal velocities;
and in the whole time impresses a whole force, and generates
a whole velocity proportional to the time."
Yes, I agree. I add:
When a body is NOT falling, the uniform force remains uniform
by definition of uniform. I am not falling, my chair is providing
an equal an opposite force.
He reserves infinitesimal reasoning for the analysis of particular
problems. e.g. Proposition I. Theorem I. "...Now let the number of
those triangles be augmented, and their breadth diminished IN
INFINITUM; ..."
Yes, that is how the calculus is derived.
Universal motion of stable
masses is the general case for which the 2nd law was established
by Newton.
You are guessing.
He certainly considered systems of masses, and the rocket
is easily analysed by considering the system, rocket plus fuel,
using Newton's Corollary III, as I stated.
Then why am I supposed to note Halliday and Resnick ?
The equation that applies to rockets is a simple extension of
the basic 2nd law equation for stable masses.
Not at all. The second law is F = dp/dt.
See above.
F= ma is taught in schools as a precursor to aid understanding.
It's not a precursor, it's a reformulation, and it's entirely
equivalent to Newton's Second Law.
---- IF mass is constant,
ELSE F= dp/dt. If you want to justify it, you have to identify your
terms.
Androcles.
Lew Mammel, Jr.
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