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Re: [Phys-l] g...



On Nov 20, 2006, at 12:19 PM, Jack Uretsky wrote:

. . . Defining a system of units where a constant is equal to unit, does
not make it non-arbitrary. The "arbitrary constants" are buried in the
choice of units. There are consistent sets of English units, which used
to be taught, where the arbitrary constant in N2 is also unity. Ludwik's
argument is, I think, circular, because the SI (and many other systems of
units) aredefined so that there is no "k" in N2. The K_g (along with K-e
and K-m) is incorporated into the Newtonian constant G.

The SI and CGS define their force units in terms of units of mass and acceleration. One dyne, for example, was assigned to a net force producing the acceleration of 1 cm/s^2 when m=1 gram. Likewise, F=1 N is defined in terms of 1 m/s^2 and 1 kg. This "artificial trick" makes k=1 dimensionless. Was a minor computational convenience responsible for conceptual difficulties of students?

I was thinking about a situation in which units of m, a and F are defined independently of each other, for example, 1 lb is a force needed to deform a standard spring by a specified distance. (Our kilogram is still defined in terms of an arbitrary-chosen standard reference.) Then the N2 law would have to be F=k*m*a, as I described in the message posted last night. I was not thinking about lb defined in terms ft/s2, etc. Shortcuts can be costly; taking a shortcut one might be lost. There is a Polish proverb about this.

Ludwik Kowalski
Let the perfect not be the enemy of the good.