Re: Newton's 2nd Law Lab

[Rick Tarara <rtarara@SAINTMARYS.EDU>]

One last comment on this thread--then I'll grade my exams and head to
Florida.

I have no doubt that David is technically correct about all of this--he
generally is.  However, this kind of lab is used with intro students (often
stressing measurement and analysis techniques as much as the physical
concepts) and in that situation, analyzing the horizontal motion of the cart
(measuring _horizontal_ accelerations as functions of either the falling
mass or the mass of the system), the results are:

1)  If one plots the weight on the hanger versus the acceleration (yes this
is backwards, but conveniently so) then one gets a linear (yes y-intcpt = 0)
with a slope IN MASS UNITS that reasonably matches the total mass of the
system--assuming one keeps the system mass constant.

2)  If one plots the acceleration versus the mass (for a fixed falling
weight) one gets an inverse relationship--which for these students then
usually involves replotting the acceleration versus 1/mass to get a linear
relationship--and these have slopes that match the weight of the falling
hanger.

Put together these results certainly seem to confirm the intro statement of
N2 -- F = ma. (one dimensional)

The modifications I've outlined previously complicate the analysis by
removing the fore-knowledge of how to calculate weight and then tries to
massage the proportionality constant (g) out of the data.


Rick

-----Original Message-----
From: David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>


stuff deleted
> There is, however, an analog of N2 in Lagrangian mechanics, it's the
> Euler-Lagrange equations of motion.  But these equations do not actually
> explicitly describe N2 *unless* the generalized coordinates appearing
> in those equations happen to be the components of position vectors in
> ordinary spatial 3-space for the individual constituent particles or are
> the components of the center of mass vector of a composite assembly of
> particles, *and* there are no forces of constraint acting on the system
> which are explicitly suppressed by using the constraints to eliminate
> the redundant generalized coordinates (which are redundant by virtue of
> those constraints).  When the generalized coordinates of the Lagrangian
> are all components of position vectors (in ordinary space) *and* there
> are no suppressed coordinates due to constraints, then the E-L equations
> *do* explicitly represent N2 for a dissipationless system.  Unfortunately,
> in the case of the half-Atwood problem (as described by Rick) the tape
> tension and the pulley forces are intentionally suppressed so that when
> the single E/L equation is solved, the motion is described without
> reference to some of the crucial force contributions needed to show N2 for
> either the individual masses or for the composite system.>

> David Bowman
> dbowman@georgetowncollege.edu