In a Phys-L posting of 11/29/97 of the above title, Donald Simanek
reviews unconvincing (to him) arguments for the educational value of
=93inertia demos.=94 One of them is:
=09
=93(3) It demonstrates F=3Dma. (Huh? Exactly how?)=94
The way in which the =93tablecloth slip-out=94 demonstrates F=3Dma was sh=
own
by Haber-Schaim and Dodge (HD) (1). HD consider two phases of the
motion of a dish of mass m:=20
(a) As the cloth is pulled out from under the dish, the dish slips on
the cloth and accelerates due to the frictional force f =3D u(c)mg in the
direction of the dish velocity, where u(c) is the kinetic coefficient of
friction between the cloth and the dish.
(b) After the cloth has slipped out from under the dish, the dish slides
on the table and accelerates due to the frictional force f =3D u(t)mg
opposite the direction of the dish velocity, where u(t) is the kinetic
coefficient of friction between the table and the dish.=20
Using f =3D ma to obtain the acceleration a =3D u(c)g for the first phase
and a =3D u(t)g for the second phase, HD derive
D =3D (1/2) u(c)g TT [1 + u(c)/u(t)] ....................(1)
where D =3D total displacement of the dish, TT =3D square of T, the time
that the dish slides on the cloth. Note that D is independent of m, as
is commonly observed. Thus the tablecloth slip-out is NOT a
demonstration of inertia. =09
=09
HD measured D=92s for various measured T=92s and showed that D was
proportional to TT in accord with Eq. (1). The slope of D vs TT was in
agreement with Eq. (1) to within the rather large experimental errors
[about 13% in the slope, 13% in u(c), and 20% in u(t)].
HD ignored the initial phase of the motion in which the acceleration of
the cloth is less than u=92(c)g, the dish is stationary with respect to
the cloth, and the dish is accelerated by the static frictional force f
< u=92(c)mg in the direction of the dish velocity. Here u=92(c) is the
static coefficient of friction between the cloth and the dish. If the
cloth is accelerated to u=92(c)g over a very short time interval then the
initial phase of the motion would presumably have negligible effect on
D.
I agree that the tablecloth slip-out as usually demonstrated is
virtually worthless. When I did this stunt for a class which included a
psychology professor, he wrote =93Hake didn=92t teach me what I needed to
know to do well on the exams. Who needs a showy demonstration on
pulling a tablecloth? I need a review on how to calculate vector
forces.=94(2) =20
However, the tablecloth slip-out can be a worthwhile lab activity (3):
students (a) slip the tablecloth out from under dishes, (b) measure D
for a plate 30 cm from the edge of the tablecloth (awards are given to
students achieving low D=92s), (c) draw =93snapshot sketches=94 of all th=
e
forces on the dish and the acceleration and velocity vectors for the
dish during the three phases of the motion, (d) derive Eq. (1) and show
that the equation is dimensionally ok and physically reasonable.
Toppling of objects on the tablecloth due to frictional torque has been
studied by Noovo-Gradac and Hubbard (4).
REFERENCES
1. U. Haber-Schaim and J.H. Dodge, =93There=92s More to It than Friction=
,=94
Phys. Teach. 29, 56 (1991).
2. S. Tobias and R.R. Hake, =93Professors as physics students: What can
they teach us?=94, Am. J. Phys. 56, 786 (1988).