Re: Newton's 2nd law lab

[Rick Tarara <rtarara@SAINTMARYS.EDU>]

The experiment is normally done to confirm N2, in that the weight of the
falling mass is the applied force, the mass of the system is the mass of the
cart plus the falling mass, and the accelerations are calculated from
measurements of time and distance.  Plots of acceleration versus weight
produce linear graphs such that y=mx becomes F = ma (the slope is 'm').  The
variation on the experiment is to NOT let students know the numerical value
of the Force.

David objects to ignoring the Normal Force of the track or the pulley force.
The Ealing air tracks have an 'air pulley' that lets recording tape float on
a thin cushion of air--thus producing a nearly frictionless pulley.  The
Normal force of the track is perpendicular to the direction of motion and
therefore does not contribute to the acceleration of the cart.

This is a Lab for INTRODUCTORY PHYSICS STUDENTS.  As seems often the case, I
think David is too concerned with here with complicated details of 'real
world' physics.  However, this experiment, in many different, forms DOES
produce results quite consistent with the typical modified Atwood's machine
analysis WHICH relies on an application of Newton's Second law to analyze.
I really don't see the problem!

My twist on the typical experiment makes the analysis a little more
interesting than the typical "OK, we know F = ma, so let's measure F, m, and
a and see if indeed F = ma."  The assumption that the force of the falling
mass IS proportional to that mass does severely weaken the 'discovery' part
of the experiment, although the students don't realize that, but that's why
I included a ;-) at that point in the description.

Rick

-----Original Message-----
From: David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>
To: PHYS-L@LISTS.NAU.EDU <PHYS-L@LISTS.NAU.EDU>
Date: Thursday, December 10, 1998 11:43 AM
Subject: Re: Newton's 2nd law lab


> Regarding Rick Tarara's claim:
> >  ...                                                        We try it,
and
> > low and behold, the slope (when the data is plotted appropriately) ends up
> > to have units of grams and a magnitude pretty close to the actual system
> > mass.  We have 'discovered' the second law (rather than just verifying
it)!
> > ;-)
>
> I think I'm missing something and don't follow you here.  How does the
> experimental discovery/determination that the magnitude of the
> acceleration 'a' of the various parts of the apparatus is approximately
> related to the cart mass 'm_c' and the falling mass 'm_f' according to:
> (m_f + m_c)*a = g*m_f for some experimentally determined constant 'g'
> having a value of about 1000 cm/s^2 either 'discover' *or* verify Newton's
> second law?  This setup has the two masses going in two different
> directions and the resulting composite motion involves a messy
> entanglement of the motions of system's center mass and the relative
> internal positions of the system's constituent masses.  Some contributions
> to the total force on the system (e.g. the cart's weight, the normal force
> from the track, and the force from the pulley) seem to be ignored.  I
> don't see what this has to do with N2 for this composite system--which
> claims that the acceleration vector of the center of mass of a composite
> system is directly proportional to the total of all the (usually external)
> force vectors acting on the system with the proportionality constant being
> the total mass of the system.  If a particle (i.e. a single object which
> is negligibly extensive in space) rather than a composite system is used,
> then N2 claims that the acceleration vector of that particle is directly
> proportional to the total force vector acting on that particle with a
> proportionality constant which is the particle's mass.
>
> David Bowman
> dbowman@georgetowncollege.edu