The acceleration of a light buoyant object in a fluid is analyzed. Misconceptions about the magnitude of that acceleration are briefly described and refuted. The notion of the added mass is explained and the added mass is computed for an ellipsoid of revolution. A simple approximation scheme is employed to derive the added mass of a slender body. The slender-body limit is non-analytic, indicating a singular character of the perturbation due to the thickness of the body. An experimental determination of the acceleration is presented and found to agree well with the theoretical prediction. The added mass illustrates the concept of mass renormalization in an accessible manner.

1.
Leonard
Meirovitch
,
Fundamentals of Vibrations
(
Waveland Press
,
Long Grove, IL
,
2010
).
2.
H. D.
Young
,
R. A.
Freedman
, and
A. L.
Ford
,
Sears' and Zemansky's University Physics
, 14th ed. (
Pearson
,
New York
,
2014
).
3.
Thomas
Smid
, “
Beyond Archimedes' principle of buoyancy
,” <https://www.physicsmyths.org.uk/buoyancy.htm>.
4.
George
Green
,
Mathematical Papers of the Late George Green
(
Macmillan
,
London
,
1871
).
5.
A.
Connes
and
M.
Marcolli
,
Noncommutative Geometry, Quantum Fields and Motives
(
American Mathematical Society
,
Providence, RI
,
2007
).
6.
J.
Messer
and
J.
Pantaleone
, “
The effective mass of a ball in the air
,”
Phys. Teach.
48
,
52
54
(
2010
).
7.
J.
Pantaleone
and
J.
Messer
, “
The added mass of a spherical projectile
,”
Am. J. Phys.
79
(
12
),
1202
1210
(
2011
).
8.
Robert E.
O'Malley
,
Historical Developments in Singular Perturbations
(
Springer International Publishing
,
Cham, Switzerland
,
2014
).
9.
Max M.
Munk
, “
The aerodynamic forces on airship hulls
,” Technical Report NACA-TR-184, National Advisory Committee for Aeronautics, Washington, DC,
1924
.
10.
R. A.
Handlesman
and
J. B.
Keller
, “
Axially symmetric potential flow around a slender body
,”
J. Fluid Mech.
28
(
1
),
131
147
(
1967
).
11.
Tracker: free video analysis and modeling tool for physics education, <https://physlets.org/tracker/>.
12.
C. M.
Bender
and
S. A.
Orszag
,
Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory
(
Springer
,
New York
,
1999
).
13.
L. M.
Milne-Thomson
,
Theoretical Hydrodynamics
, 4th ed. (
Macmillan
,
London
,
1962
).
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