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From: carlc@tektronix.UUCP (Carl Clawson)
Newsgroups: net.physics
Subject: Newton's second law
Message-ID: <5474@tektronix.UUCP>
Date: Mon, 8-Jul-85 11:58:20 EDT
Article-I.D.: tektroni.5474
Posted: Mon Jul  8 11:58:20 1985
Date-Received: Thu, 11-Jul-85 00:26:24 EDT
References: <9255@Glacier.ARPA>
Reply-To: carlc@tektronix.UUCP (Carl Clawson)
Organization: Tektronix, Beaverton OR
Lines: 49
Summary: Thought experiment to discover Newton's 2nd law.

In article <9255@Glacier.ARPA> wong@Glacier.ARPA (Man Wong) writes:
> What is mass? ...  What is force?
>> (several followups, which don't answer the questions, follow).

This is a serious question that most students probably don't bother
to think about.  I'll give my favorite thought experiment for answering
it.

Let's play Newton.  Take some objects of different weights to experiment
with, and get a spring scale to measure how hard we pull on an object.
We will call the reading of the spring scale "force."  For starters, we
put two marks on our scale, which correspond to forces F1 and F2.  This
is the definition of forces F1 and F2.  We have not yet assigned a NUMBER
to either F1 or F2, just marks on a scale.

Now we pull on some objects and measure the accelerations.  (I'm assuming
that time and distance have already been suitably defined.)  The first
thing we notice is that the acceleration is determined by the force,
i.e., it is constant as long as the force is constant.  We're on to something!

Two objects are pulled with the same force when the spring scale gives
the same reading.  By pulling with the same force F1 on a number of
objects we get different accelerations for different objects.  Now pull
with force F2 on the same objects.  Being clever scientists, we notice
that although each object is accelerated at a different rate than when
we pulled with F1, the ratios between the different objects are the same.
If object A has twice the acceleration of object B under force F1, then
it will also have twice the acceleration of B under F2.  Thus there is
a property of objects that governs this proportionality.  We call this
property "mass," and we can define ratios of masses by pulling different
objects with the same force and taking the inverse ratio of the accelerations.
To define mass absolutely, you need a standard from which other masses can
be measured by taking ratios.  A hunk of metal in France will do for now.

Now we want to calibrate our force scale.  We have so far not assigned numbers
to forces, we've just put marks on our scale so we can reproduce them.
Let's do the simplest thing and make force proportional to acceleration.
Now we can sit back, have a beer, and declare Newton's Second Law,
F=ma.  (We could just as well have calibrated our scale differently,
in which case the second law would be f(F)=ma where f is some calibration
function.)

Summary:  Mass is defined by ratios of accelerations under a given force.
The essence of Newton's second law is that these ratios are independent
of the force used.  Force is defined operationally as the reading of a scale,
and calibrated to give the simplest proportionality.

-- Carl,
who is not a historian and doesn't claim that this is what Newton actually did.