Re: Newton's 2nd law Lab

[Rick Tarara <rtarara@SAINTMARYS.EDU>]

We do a 2nd law experiment fairly traditionally--that is, using air tracks,
air pulley, recording tape (as the massless cord) and falling mass in a
modified Atwood's configuration.  We DO keep the system mass constant in the
first set of measurements where the falling mass is varied by transferring
mass from cart to mass hanger.  Accelerations are determined using photogate
timers.  A series of second experiments are done, using a fixed falling mass
and changing the mass on the cart.  Each group of students does the fixed
system mass experiment and ONE of the fixed falling mass experiments
(several different falling masses are done).

Now the TWIST.  I let the students assume that the force acting on the
system is proportional to the falling mass, but that we don't know the
proportionality constant (taking a quasi-pre-Newtonian viewpoint).  The
fixed system mass data then gives a linear relationship but with an unknown
proportionality constant (so that units work).

After it is determined that the acceleration in the fixed falling mass
experiments is inversely proportional to the mass of the system, this is
plotted to give a linear relationship.  Each group has a different slope for
their work.

In group consultation, the students decide to do the only thing they know
how to do with data (at this point in the course) when one quantity (these
slopes) vary with another (the falling mass).  They graph it!  The
relationship is linear AND the slope (of slopes versus falling mass) has
units of cm/s^2 and a magnitude of about 1000!  This is then recognizable as
quite possibly the known (from Galileo) acceleration due to gravity--again
such recognition being based primarily on the fact that the data
manipulation produced a slope with physically meaningful UNITS.  Finally, it
is suggested that just possibly, this physical constant (g) which falls out
of the data could be the unknown proportionality constant still sitting
there from the constant system mass part of the experiment.  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)!
;-)

Rick

***********************
Richard W. Tarara
Associate Professor of Physics
Department of Chemistry & Physics
Saint Mary's College
Notre Dame, IN 46556
rtarara@saintmarys.edu

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-----Original Message-----
From: Mark Sylvester <msylvest@SPIN.IT>
To: PHYS-L@LISTS.NAU.EDU <PHYS-L@LISTS.NAU.EDU>
Date: Thursday, December 10, 1998 6:06 AM
Subject: Re: Newton's 2nd law Lab


> I have some reservations about the mbl experiments for Newton's second law,
> and wonder if they are shared.
>
> Minor reservation: I don't like using a force sensor already calibrated in
> newtons when we want to show the second law.
>
> Bigger reservation: I don't like using an accelerometer which works by
> inertia for this experiment. If we treat the sensors strictly as black
boxes
> this may be OK, but I like the students to have some idea of what the
sensor
> does.
>
> The force sensor is OK since it works by stretching, and the difficulty is
> with the unit only, but I much prefer getting the acceleration
> kinematically. Yes, the data can be messy if you "double difference" the
> position measurements, but it's easy and quick enough to do straight line
> fits to v-t graphs for a series of constant forces, and the graph is not
too
> bad for the experiment that John Gastineau describes below.
>
> Mark
>
> At 08:56 10-12-98 +0100, John Gastineau wrote:
>
> ...discussion of half-Atwood experiment deleted...
>
> > > A much cleaner experiment is possible using a force sensor and an
> > > accelerometer. Attach both devices to a cart; move the cart by hand using
> > only
> > > the force sensor. Record both the force vs. time and acceleration vs.
time
> > > data, then plot force vs. acceleration. The points should be on a line
with
> > > slope m, where m is the total mass of the cart, accelerometer and force
> > > sensor. Now change mass of the cart. New slope.
> > >
> > > This experiment is much, much cleaner than the old half-Atwood method for
> > > doing Newton II. The half-Atwood approach done with MBL is just a
> > computerized
> > > version of a non-computer method.
> > >
> > > You can also do this experiment with a motion detector and force sensor,
but
> > > the data quality suffers considerably since you must work with a second
> > > derivative to get the acceleration data, while the accelerometer gives it
to
> > > you directly.
> > >
> > > I can point you to more details if needed.
> > >
> > > JEG
>
>
>
> Mark Sylvester
> UWC of the Adriatic
> 34013 Duino TS
> Italy
> msylvest@spin.it