Another Look at the Wine Butler

Abstract

In a recent article, Iain MacInnes analyzed the static equilibrium of a
system consisting of a wine bottle and a wine butler.1 After discussing
that composite system, students can be asked to consider only the bottle
(and its contents) as the system. An interesting challenge for them is
to describe the forces on the bottle in static equilibrium.

Full text

Another Look at the Wine
Butler
Alan J. DeWeerd, University of Redlands, Redlands, CA
In a recent article, Iain MacInnes analyzed the
static equilibrium of a system consisting of a
wine bottle and a wine butler.1 After discussing
that composite system, students can be asked to con-
sider only the bottle (and its contents) as the system.
An interesting challenge for
them is to describe the forces
on the bottle in static equilib-
rium.
At first glance, it may ap-
pear that there are only two
forces acting on the bottle as
shown in Fig. 1: the down-
ward gravitational force and
an upward force exerted by
the wine butler. If the two
forces have equal magnitudes,
they satisfy the condition that
the net force bottle is zero.
However, those two forces
would result in a net clock-
wise torque with respect to
any point, so something is
wrong with this analysis.
A closer inspection reveals
that the wine butler touches
the neck of the bottle in two
places: on the top closer to the
lip and on the bottom closer
to the shoulder. The correct
free-body diagram with a
downward force Fd near the top of the neck and an
upward force Fu farther down the neck is shown in
Fig. 2. If the distances between the forces are s and c as
shown, the conditions for static equilibrium are
no net force:
Fu = Mg + Fd,
no net torque:
Fus = Mg c.
The torques in the second
equation are calculated about
the point (O) where the
downward force acts. Both
equations imply that the
upward force must be larger
than the weight of the bottle.
The relative size of the
forces can be estimated using
the data from Ref. 1:
c = 12 cm
and
a = 36o,
and the neck’s diameter, which
is D = 2.5 cm for a typical
bottle. Ignoring the thickness
of the wine butler, we have ap-
proximately:
s < D/tan a = 3.4 cm.
N
Mg
Mg
Fu
c
s
O
D
Fdα
Fig. 1. An incorrect free-body diagram for the
bottle.
Fig. 2. The correct free-body diagram for the
bottle.
438 DOI: 10.1119/1.2783154 THE PHYSICS TEACHER ◆ Vol. 45, October 2007

THE PHYSICS TEACHER ◆ Vol. 45, October 2007 439
The upward force is predicted to be c/s < 3.5 times
as large as the bottle’s weight and the downward force
about 2.5 times as large as the weight.
The predictions above were tested using a bottle
with a weight of Mg = 12 N. Using a Dual-Range
Force Sensor,2 I measured the forces on the bottle
while it was held in the orientation shown in Fig. 2. To
determine the upward and downward forces, a metal
beam was positioned to apply one of them while a
loop of string attached to the sensor applied the other.
The measured forces were Fu = 40  2 N and Fd =
27  2 N, where the uncertainties were due to the
difficulty in placing the string exactly where the wine
butler contacted the bottle. The ratios between the
contact forces and the weight, Fu/Mg = 3.3  0.2 and
Fd/Mg = 2.3  0.2, agree well with the predictions
above.
Students who have difficulty picturing the two
contact forces could experiment with holding a pencil
or a pen horizontally near one end between horizontal
index and middle fingers. If they don’t squeeze their
fingers together too hard, the offset between places
where they apply forces should be obvious. Students
can also confirm that bringing the fingers closer to-
gether (reducing s) requires squeezing harder (increas-
ing Fu and Fd).
The wine bottle is similar to the match in a balanc-
ing spoon-fork-match system discussed in an earlier
article.3 The correct analysis of that problem requires
the same care in identifying all of the forces.4
References
1. Iain MacInnes, “The rod and bottle system: A problem
in statics,” Phys. Teach. 43, 538–539 (Nov. 2005).
2. Vernier Software & Technology, Model DFS-BTA.
3. Robert G. Kirkham, “Choosing the right system for
analysis of forces,” Phys. Teach. 34, 402–403 (Oct.
1996).
4. A. John Mallinckrodt, “On ‘choosing the right system
for analysis of forces,’” Phys. Teach. 34, 534 (Dec. 1996).
PACS codes: 01.50.My, 45.00.00
Alan J. DeWeerd received his BS from the University of
California-Irvine and his MS and PhD from the University
of Wisconsin–Madison. He is an associate professor of
physics and an oenophile.
Department of Physics, University of Redlands,
Redlands, CA 92373; Alan_DeWeerd@redlands.edu