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Re: [Phys-l] g...



On Nov 21, 2006, at 12:38 PM, Jack Uretsky wrote:

I dunno. Did you read the two sentences that state:
1 pound of force measure the deflection of a standard spring. 1 lb
accelerates a certain mass with an acceleration of 1 ft/s^2; we call
that amount of mass 1 slug.

Doesn't that specify "the standard spring and the defining
deflection"? So how is the situation "very different"?

My next sentence should have been "1 slug has a weight of ~32
slug-ft/s^2".



On Mon, 20 Nov 2006, Ludwik Kowalski wrote:

On Nov 20, 2006, at 5:54 PM, Jack Uretsky wrote:

But there is no "k" needed. In what my 1940 text calls the static
systim,
1 pound of force measure the deflection of a standard spring. 1 lb
accelerates a certain mass with an acceleration of 1 ft/s^2; we call
that
amount of mass 1 slug. 1 slug has a weight of ~32 ft/s^2. G has a
value
of about3.5x10^{-8}#(ft/slug)^2. F=ma in ordinary English units, no
"k"
needed.

This defines 1 lb in terms of acceleration in free fall. The situation
would be very different if the standard spring, and the defining
deflection, were specified instead of 32 ft/s^2.

Ludwik Kowalski
Let the perfect not be the enemy of the good.
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

Regards,
Jack
--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley



_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

It was a trick. It would be highly unlikely to produce an arbitrary spring (for defining one pound) that would make k=1. I am referring to k in F=k*m*a, not to the spring constant. The trick consisted of adjusting properties of a standard spring when k=1 and a=32 ft/s^2 are imposed. Motivation, I suppose, was to have F=m*a, as in the CGS system introduced by Maxwell. In that system, the unit of force, dyne, was defined in terms of acceleration a=980 cm/s^2. It is very unlikely that a pound defined by an arbitrary spring and a pound defined in terms of a=9.8 m/s^2 would be the same, unless by design.

My point is that F=k*m*a, when units for each of the three quantities are based on arbitrary selected standards (a chunk of gold for mass, a distance between two scratches on a stick, and an arbitrarily selected spring). "Why do we need three standards when two would be sufficient?" -- someone probably asked. And how do you make a spring which does not loose its properties? That was probably the motivation for defining F in terms of a. But that did not prevent me from introducing the F=k*m*a to students as if the unit of force was defined in terms of our classroom spring.

Here are logical steps of a lecture-demo shown each year. (The way of measuring F, in arbitrary units, has been described in a message I posted yesterday

Minimum hardware: Pasco cart (including the mounted force meter) plus iron blocks. Also a meter stick and a stopwatch.

a) Show that for a constant m the acceleration is directly proportional to F (a=k1*F)
b) Show that, for a constant F the acceleration is inversely proportional to the total mass. a=1/(k2*m )
c) Conclusion: a=(k1*F)*( 1(/k2*m) ) =(k1/k2)*(F/m), or F=k*m*a, where k=k2/k1.
b) But our textbook does not have any k! Why is it so? Because the unit of force was defined differently. Etc, etc. The numerical value of k depends on the units chosen to quantify m, a and F. It was convenient to have k=1 and the unit of F was chosen accordingly.

In a classroom demo the accelerated motion was obvious; we measured times needed to cover a distance between two chalk lines on the table and calculated average accelerations. An electronic range meter could be used to show that the measured a is nearly constant in each case. To save time one could simply say, during a lecture, that "by performing accurate measurements one finds a=k1/F and a=1/k2*m.

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