Newton's formulae...

How did Newton derive F = ma ?

On Sat, 17 Apr 2004 10:45:59 +0200, "Mitchell B."
wrote:

How did Newton derive F = ma ?

Key word: apple

But did he even do so?

He didn't do so in that particular symbolic representation, I know
that. What he told us in spelled-out Latin words (maybe he even did
so in English as well somewhere, but the most-quoted statement from
him about this appears in translation) is that the force is
*proportional* to the mass times the acceleration. I doubt that he
ever used your *equal*.

That particular formulation depends on the choice of a system of
units. But there were no "coherent" (as that term is used in
metrology) systems of units in Newton's day. In some other systems
such as the English pound-pound force system, you need a more general
form of the equation, F = kma.

Gene Nygaard
http://ourworld.compuserve.com/homepages/Gene_Nygaard/

He did not.

Newton's 2nd law is a *law*, which means it is a principle of nature that
cannot be derived. Experimentally it was found (also by galileo) that the
accelaration is proportional to the force exerted on an object, and Newton
defined the proportionality constant as the mass of the object.

--
Physics is like sex.
Sure, it may give some practical results, but that's not why we do it.
-R.P.F.

http://www-scf.usc.edu/~kallos

"Timaras" wrote in message
...

Newton's 2nd law is a *law*, which means it is a principle of nature that
cannot be derived.

Says who? In physics a "law" is a rule that has never been observed to be
violated in nature. "Principles" (such as the Principle of Relativity) are
few and far between.

Experimentally it was found (also by galileo) that the
accelaration is proportional to the force exerted on an object, and Newton
defined the proportionality constant as the mass of the object.

Galileo found that falling objects are accelerated independently of their
mass, and that objects retain their velocity unless a force acts upon them.

Newton never "defined" mass. He observed that bodies in rest tended to
remain at rest, and that bodies in motion tended to remain in motion. In
his mind, that connected mass and velocity in the phenomenon of motion, and
he defined "momentum" as the product of the two. Newton quantified
"force."

See my other post in this thread for more info.


Tom Davidson
Richmond, VA

"Gene Nygaard" wrote in message
...
On Sat, 17 Apr 2004 10:45:59 +0200, "Mitchell B."
wrote:

How did Newton derive F = ma ?

Key word: apple

But did he even do so?

He didn't do so in that particular symbolic representation, I know
that. What he told us in spelled-out Latin words (maybe he even did
so in English as well somewhere, but the most-quoted statement from
him about this appears in translation) is that the force is
*proportional* to the mass times the acceleration. I doubt that he
ever used your *equal*.

That particular formulation depends on the choice of a system of
units. But there were no "coherent" (as that term is used in
metrology) systems of units in Newton's day. In some other systems
such as the English pound-pound force system, you need a more general
form of the equation, F = kma.

this is dangerous territory - you could start shead off


Gene Nygaard
http://ourworld.compuserve.com/homepages/Gene_Nygaard/

Newton's 2nd law is a *law*, which means it is a principle of nature
that
cannot be derived.

Says who? In physics a "law" is a rule that has never been observed to be
violated in nature. "Principles" (such as the Principle of Relativity)
are
few and far between.

You're right, I'm just not very efficient using vocabulary yet.



Newton never "defined" mass. He observed that bodies in rest tended to
remain at rest, and that bodies in motion tended to remain in motion. In
his mind, that connected mass and velocity in the phenomenon of motion,
and
he defined "momentum" as the product of the two. Newton quantified
"force."



The very first sentence of principia mathematica is:

"Quantity of matter is a measure of matter that arises from its density and
volume jointly"

And 5 lines after that:

"I mean this quantity whenever I use the term 'body' or 'mass' . It can
always be known from a body's weight, for I have found it to be proportional
to the weight."


And since his 2nd law states that F (such as weight) is proportional to
acceleration, this yields exactly F=ma.

"Timaras" wrote in message ...

Newton's 2nd law is a *law*, which means it is a principle of nature
that
cannot be derived.

Says who? In physics a "law" is a rule that has never been observed to be
violated in nature. "Principles" (such as the Principle of Relativity)
are
few and far between.

You're right, I'm just not very efficient using vocabulary yet.



Newton never "defined" mass. He observed that bodies in rest tended to
remain at rest, and that bodies in motion tended to remain in motion. In
his mind, that connected mass and velocity in the phenomenon of motion,
and
he defined "momentum" as the product of the two. Newton quantified
"force."



The very first sentence of principia mathematica is:

"Quantity of matter is a measure of matter that arises from its density and
volume jointly"

And 5 lines after that:

"I mean this quantity whenever I use the term 'body' or 'mass' . It can
always be known from a body's weight, for I have found it to be proportional
to the weight."


And since his 2nd law states that F (such as weight) is proportional to
acceleration, this yields exactly F=ma.

No! It yields F/a Timaras: That is the ratio F/a is proportional, and
equal to the ratio w/g: As long as there is no frictional resisting
force (uw).

Otherwise: F/a - uw = w/g; where F + uw is the _net_ force [f], that
acts to cause the body's acceleration: To repeat, it's the net force
[f = F-uw] that causes the acceleration.

You're as efficient using vocabulary as most of us: Efficient enough
so that the wool isn't easily pulled over your eyes. That count's good
for you.

Donald G. Shead wrote:


No! It yields F/a Timaras: That is the ratio F/a is proportional, and
equal to the ratio w/g: As long as there is no frictional resisting
force (uw).

How do you come up with this nonsense. Weight is variable and mass is
invariant.

Bob Kolker

"Mitchell B." wrote in message ...
How did Newton derive F = ma ?

He didn't. He postulated and stated that force is the rate of change
of momentum w.r.t time, F = d(mv)/dt. Academia assumed mass invariance
and simply removed m out of the derivative using the product rule for
scalars, F = m dv/dt = ma.

If you assume that rest mass varies with velocity, then you can derive
things a little differently.

For example, if mass varies linearly with velocity

m(v) = m0 + kv
where
m0 = rest mass
k = some constant
v = velocity

So, momentum = p = m(v(t)) v(t)

Force = dp/dt
= d (m(v)v) / dt
= m(v) (dv/dt) + v (dm(v)/dt)
= m(v) a + v (dm/dv)(dv/dt)
= m(v) a + v (dm/dv) a
= ma + v(1/kv)a
= ma + a/k

JS

"Robert J. Kolker" wrote in message news:lsYgc.29247$0b4.38766@attbi_s51...
Donald G. Shead wrote:


No! It yields F/a Timaras: That is the ratio F/a is proportional, and
equal to the ratio w/g: As long as there is no frictional resisting
force (uw).

How do you come up with this nonsense. Weight is variable and mass is
invariant.

Bob Kolker

No Bob, mass isn't invariant. Remember it varies with velocity. But
otherwise I agree.