Goniobarimeter
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Publicado: 18 de noviembre de 2012
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The Darío Bacas goniobarimeter: building a balance based on properties of the cycloid
This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2010 Phys. Educ. 45 475 (http://iopscience.iop.org/0031-9120/45/5/003) View the table of contents for this issue, or go to thejournal homepage for more
Download details: IP Address: 147.96.27.71 The article was downloaded on 01/09/2010 at 11:13
Please note that terms and conditions apply.
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www.iop.org/journals/physed
The Dar´o Bacas goniobarimeter: ı building a balance based on properties of the cycloid
Javier del Rey Pant´n1 and Jos´ M Ortiz de Z´ rate2 ı e a
1 2
IES Do˜ a Jimena, Gij´ n,Spain n o Departamento de F´sica Aplicada I, Universidad Complutense, Madrid, Spain ı
E-mail: JDELREY@terra.es and jmortizz@fis.ucm.es
Abstract In this article we describe and build a model of a historical weighing device proposed by the Spanish engineer Dar´o Bacas in the second half of the 19th ı century. The balance was named ‘goniobarimeter’ by its inventor, and the weighing principle isbased on a curious, and not very well known, property of the cycloid. The simplicity of the design makes it especially suitable for a hands-on educational project with pre-university physics students.
Historical introduction
Nowadays, the ready availability of modern electronic weighing apparatus has in most cases replaced the old balances in stores and laboratories. However, weighing devicesbased on mechanical equilibrium undoubtedly still have a historical, educational and scientific interest. In this short article we describe the operation and building of a model of one of these historical balances. Our present work could be interesting for educational purposes, as a hands-on project for pre-university physics students, as well as for science museums. The original design of this devicewas due to the Spanish engineer Dar´o Bacas Montero ı (1845–1913) who named it the ‘Goniobar´metro’ ı (goniobarimeter) [1]. With this name he meant (gonio-bari-metro: angle-weight-meter) a balance that indicated on a graduated disk a lean angle proportional to the weight under measurement. This feature is common to several weighing devices; the peculiarity of the Bacas design is
that it isbased on the pure geometrical properties of the cycloid. In this article we summarize the working principle, and describe succinctly how to build the apparatus. Historical details on the life of the engineer Bacas can be found in [2], while a more exhaustive account of the physics behind the goniobarimeter, as well as a more detailed step-bystep building guide, can be found in [3, 4] (all inSpanish).
The physics of the goniobarimeter
Figure 1, which is an adaptation of the original Bacas illustration [1], shows a schematic representation of the goniobarimeter. The main part is a seesaw AB that is free to rotate around a fixed point O. From the point B hangs the weight P under measurement. At the other end of the seesaw beam a counterweight guiding part ATH is rigidly fixed. This partguides the counterweight Q by means of a string that gradually unfolds as the seesaw leans due to the weight P . E
PHYSICS EDUCATION 45 (5)
0031-9120/10/050475+06$30.00 © 2010 IOP Publishing Ltd
475
J del Rey Pant´n and J M Ortiz de Z´ rate ı a
T = {x, y} and intercepts the x -axis with angle α is given by:
A
d(α) = x sin α − y cos α,
X Y C O R
(3)
E′
T{x, y} B
where we areimplicitly assuming x > 0, y < 0, α > 0. Combining equations (2) and (3), and taking into account that the slope of the tangent line to a curve is given by the derivative, one obtains the following nonlinear differential equation for the curve y = y(x)
E
y=
dy dy π x − k + k arctan dx 2 dx
.
(4)
H Q P
Figure 1. Schematic representation of the Bacas goniobarimeter. P is the...
Search
Collections
Journals
About
Contact us
My IOPscience
The Darío Bacas goniobarimeter: building a balance based on properties of the cycloid
This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2010 Phys. Educ. 45 475 (http://iopscience.iop.org/0031-9120/45/5/003) View the table of contents for this issue, or go to thejournal homepage for more
Download details: IP Address: 147.96.27.71 The article was downloaded on 01/09/2010 at 11:13
Please note that terms and conditions apply.
FEATURES
www.iop.org/journals/physed
The Dar´o Bacas goniobarimeter: ı building a balance based on properties of the cycloid
Javier del Rey Pant´n1 and Jos´ M Ortiz de Z´ rate2 ı e a
1 2
IES Do˜ a Jimena, Gij´ n,Spain n o Departamento de F´sica Aplicada I, Universidad Complutense, Madrid, Spain ı
E-mail: JDELREY@terra.es and jmortizz@fis.ucm.es
Abstract In this article we describe and build a model of a historical weighing device proposed by the Spanish engineer Dar´o Bacas in the second half of the 19th ı century. The balance was named ‘goniobarimeter’ by its inventor, and the weighing principle isbased on a curious, and not very well known, property of the cycloid. The simplicity of the design makes it especially suitable for a hands-on educational project with pre-university physics students.
Historical introduction
Nowadays, the ready availability of modern electronic weighing apparatus has in most cases replaced the old balances in stores and laboratories. However, weighing devicesbased on mechanical equilibrium undoubtedly still have a historical, educational and scientific interest. In this short article we describe the operation and building of a model of one of these historical balances. Our present work could be interesting for educational purposes, as a hands-on project for pre-university physics students, as well as for science museums. The original design of this devicewas due to the Spanish engineer Dar´o Bacas Montero ı (1845–1913) who named it the ‘Goniobar´metro’ ı (goniobarimeter) [1]. With this name he meant (gonio-bari-metro: angle-weight-meter) a balance that indicated on a graduated disk a lean angle proportional to the weight under measurement. This feature is common to several weighing devices; the peculiarity of the Bacas design is
that it isbased on the pure geometrical properties of the cycloid. In this article we summarize the working principle, and describe succinctly how to build the apparatus. Historical details on the life of the engineer Bacas can be found in [2], while a more exhaustive account of the physics behind the goniobarimeter, as well as a more detailed step-bystep building guide, can be found in [3, 4] (all inSpanish).
The physics of the goniobarimeter
Figure 1, which is an adaptation of the original Bacas illustration [1], shows a schematic representation of the goniobarimeter. The main part is a seesaw AB that is free to rotate around a fixed point O. From the point B hangs the weight P under measurement. At the other end of the seesaw beam a counterweight guiding part ATH is rigidly fixed. This partguides the counterweight Q by means of a string that gradually unfolds as the seesaw leans due to the weight P . E
PHYSICS EDUCATION 45 (5)
0031-9120/10/050475+06$30.00 © 2010 IOP Publishing Ltd
475
J del Rey Pant´n and J M Ortiz de Z´ rate ı a
T = {x, y} and intercepts the x -axis with angle α is given by:
A
d(α) = x sin α − y cos α,
X Y C O R
(3)
E′
T{x, y} B
where we areimplicitly assuming x > 0, y < 0, α > 0. Combining equations (2) and (3), and taking into account that the slope of the tangent line to a curve is given by the derivative, one obtains the following nonlinear differential equation for the curve y = y(x)
E
y=
dy dy π x − k + k arctan dx 2 dx
.
(4)
H Q P
Figure 1. Schematic representation of the Bacas goniobarimeter. P is the...
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