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Re: [Phys-l] The "why" questions



I believe there is a big difference between replacing a vector with all sorts of combinations of component vectors, and working backwards from a net force to the actual forces that make it up. You can physically determine the magnitude and direction of applied forces that make up the net force--not components along a set of axes but the actual forces in a physical situation. You can also physically determine the magnitude and direction of the acceleration of an object. You can mathematically talk about component accelerations that are due to individual forces, but you cannot measure them physically. You can only measure the one acceleration of the object. There is an asymmetry in the physical forces acting on an object and the physical acceleration of the object. Those physical forces, providing they are the only ones acting, can lead to only one physical acceleration. There are, however, a myriad of possible combinations of physical forces that could have led to the one physically measurable acceleration.

Here I'm making a distinction between a certain level of reality and constructs from that reality. I stipulate that this argument falls apart if you look at all of these quantities as constructs that we place on the physical world.

Bill




On Nov 29, 2010, at 2:22 PM, John Denker wrote:

On 11/29/2010 12:38 PM, William Robertson wrote:
Regarding the symmetry argument..... There is a definite symmetry
between Fnet and ma. Knowing Fnet and m, you can predict a exactly.
Knowing a and m, you can predict Fnet exactly. However, we can remove
ourselves one step from the relationship Fnet=ma and discover an
asymmetry. There are many possible combinations of forces that can
make up Fnet. Given Fa, Fb, and Fc acting on a mass, there is only one
possible a. But given the acceleration of a mass, all we can infer
directly is Fnet. We don't know if Fa, Fb, and Fc made up Fnet or if
it was Fd and Fe. Therefore, it would seem a reasonable statement that
the combination of forces Fa, Fb, and Fc caused a given mass to have a
particular acceleration.

So while there is no causality implied in Fnet=ma, one can certainly
make a causality argument between a set of applied forces and a
resultant acceleration.

That asymmetry argument would be very interesting and important if
true. Alas it is not true.

This speaks to the question raised by Philip Keller: Here there is
no issue of confusion concerning language and grammar. This is a
wrong idea communicated with perfect clarity.

F is a vector. That is sufficient (indeed more than sufficient) to
guarantee that we can write it as the sum of three other forces
F1, F2, and F3.

I hate to belabor the obvious, but the acceleration a is also a
vector. That means we can write it as the sum of three other
accelerations a1, a2, and a3.

We can start with the obvious possibility a1=F1/m, a2=F2/m, and a3=F3/m
... but there is an infinitude of other ways of writing a as the sum
of three vectors ... not to mention an additional infinitude of ways of
writing a as the sum of four vectors, et cetera.

There are plenty of practical situations where I might control the various
contributions to the acceleration a1, a2, and a3 and wish to infer the force,
rather than trying to infer the accelerations from the force. The previous
examples of centrifuges and stepper motors should suffice to prove the
point. Three-axis translation stages are routinely used on optical tables,
and I assure you they do not work by applying a predetermined force and
inferring the acceleration from that.

I can go into a lot more detail on this if anybody is interested.

=========

Bottom line: There is no asymmetry in the equation F=ma, nor in the
physical law that we summarize by writing that equation.
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