A 10 kg transportable flexure-strip beam balance
Gary H. N. Shoemaker,
a)
Robb Robel,
b)
Charles Lewis, and Tom Ramonda
c)
Department of Physics and Astronomy, California State University, Sacramento, California 95819-6041
͑Received 15 August 1996; accepted for publication 13 June 1997͒
The design and construction of a 10 kg transportable flexure-strip beam balance to be used in
searches of composition-dependent forces and/or tests of the weak equivalence principle is
discussed. The results of the instrument performance presented herein are based upon operation of
the balance under simulated experimental conditions that require our balance maintains a high level
of sensitivity ͑i.e., resolution associated with the standard deviation of our data sample͒ during a
continuous measurement process which alternates between two different elevations, a unique
application for a beam-balance measuring device. Our results indicate that this balance is the most
sensitive transportable balance used in measurement in the 10 kg load capacity range, obtaining a
measurement sensitivity of about 15–20
Gal. Also, we have established that our method of
balance transport affects the sensitivity less than 15
Gal at the 95% confidence level. An increase
in sensitivity of approximately 30 would be required to establish new upper limits on
composition-dependent forces in the interaction range of most interest. © 1997 American Institute
of Physics. ͓S0034-6748͑97͒02910-9͔
I. INTRODUCTION
A 10 kg flexure-strip supported, transportable beam bal-
ance can be employed to test the weak equivalence principle
͑WEP͒ by searching for new macroscopic forces; specifi-
cally, forces which depend upon the composition of the ma-
terials. Our balance was designed to allow the comparison, at
two distinct geographical locations, of the differential accel-
eration on two compositionally distinct proof masses at-
tached to a balance beam. This is, in fact, the distinguishing
feature of our use of a beam balance; normally the balance is
fixed in position and the source mass is moved.
1
To our
knowledge, this balance is the first of its kind to achieve
successful transport without disturbing the masses being
measured and achieve a reproducible signal at the level of
sensitivity that we report here and competitive with recent
Galilean experiments for interaction ranges of less than 1
km, but over one order of magnitude less than what would be
necessary in the interaction range of 10–1000 km, where the
experimental results are most needed. It appears that the fac-
tors responsible for limiting our sensitivity presently have to
do with anelastic after-effects of the flexure-strip and a long-
term temperature drift, but probably not from the moving of
the balance.
Over the last two decades, a number of experiments have
been performed to search for new interactions and their as-
sociated bosons since there has been a growing consensus
that new mediating particles are required to complete the
Standard Model.
2
One relatively unexplored window on pos-
sible new interactions is the low-mass boson, which could
generate macroscopic forces, dependent upon the composi-
tion of the material. Composition-dependent forces can ac-
count for the violation of the inverse-square law of gravita-
tion and the universality of free fall. These forces add an
additional Yukawa term to the Newtonian potential and will
cause a test body T, placed in the field of a source S,to
accelerate with
͉
a
͉
ϭ
g
5
2
4
ͩ
q
m
ͪ
T
ͩ
q
m
ͪ
s
͵
ͩ
1
r
2
ϩ
1
r
ͪ
exp
͑
Ϫr/
͒
͑
r
͒
d
3
r,
͑1͒
where
(r) represents the mass density of the source.
A recent reanalysis of the Eo
¨
tvo
¨
s, Peka
´
r, Fekete ͑EPF͒
experiment
3
had suggested the possible existence of a short-
ranged non-Newtonian force coupling to the number of
nucleons ͑or baryon number͒ in the material, directly contra-
dicting the WEP. Although this article generated much re-
newed interest in this subject, subsequent investigations
found no evidence of such coupling and have set upper limits
on
␣
several orders of magnitude more sensitive than the
EPF results.
4
For the most part, experiments searching specifically for
composition-dependent forces have employed torsion bal-
ances or other similar devices in which the action takes place
in the tangent plane to the surface of the earth and the
sources investigated are objects on the earth’s surface ͑these
‘‘objects’’ could be mountains or other large geographical
features͒. These tangential-field measurements involve
source masses which are generally Ͻ10–100 km in size, ir-
regular in shape and hence often difficult to model precisely,
and variable in composition. Two important exceptions
5
measured the radial field of the earth ͑used here as a source
mass͒ and hence are known as Galilean ͑or WEP͒ experi-
ments. Such experiments are generally much more sensitive
than corresponding tests for violation of the inverse-square
law since the WEP experiments are ‘‘inherently precise be-
cause they can be conducted as differential null
experiments.’’
6
Also, composition-dependent radial accel-
erations can be reliably calculated for all ӷa ͑where a is
the length scale of the apparatus͒ and thus avoid the diffi-
culty often associated with interpreting the results of the
tangential-field tests. Clearly then, WEP measurements oc-
a͒
Electronic mail: SHOEMAKR@SACLINK.CSUS.EDU
b͒
Current address: H Power Corporation, 8008 Sacramento St., Fair Oaks,
CA 95826.
c͒
Current address: Rio Vista High School, Rio Vista, CA 94571.
3777Rev. Sci. Instrum. 68 (10), October 1997 0034-6748/97/68(10)/3777/8/$10.00 © 1997 American Institute of Physics