30/04/18 fred 0 0
![](http://opentp.fr/en/app/wp-content/themes/darfuino/includes/pics/logo-opentp-2.jpg)
Measuring the elasticity of a ruler
Developed by Margaux Khalil (École Estienne), Julien Bobroff and Frédéric Bouquet (Laboratoire de Physique des solides, Université Paris-Sud and CNRS). More information and other projects on opentp.fr/en
![](http://opentp.fr/en/app/wp-content/themes/darfuino/includes/pics/pictos_pitch.jpg)
Level : Medium
1 day
The goal of this project is to measure the Young modulus of a plastic ruler, by measuring its deformation when one presses in its middle.
![](http://opentp.fr/en/app/wp-content/uploads/2018/02/openTP_principles_solide.png)
The physic in action
The Young’s modulus, (E), characterizes the ability of a material to deform in a reversible manner when a force is applied. In the case of a beam with a quadratic moment beam I, on two supports distant from the distance L, when a force F is applied in the middle, the deformation \( \delta z \) is given by the following formula :
\[ \delta z = \frac{F L^3}{48 E I} \]
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Arduino
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Hall sensor
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Ruler, set square, protractor
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Magnets
Material
You will also need:
- tinkering hardware;
- screw nuts (to apply a force on the middle of the ruler).
![](http://opentp.fr/en/app/wp-content/uploads/2017/12/openTP_student1_mesure5.jpg)
Calibrating the distance measurement
Measure the value of the magnetic field created by the magnet as a function of the distance between the sensor and the magnet.
![](http://opentp.fr/en/app/wp-content/themes/darfuino/includes/pics/question_3.png)
Is the orientation of the Hall sensor important?
![](http://opentp.fr/en/app/wp-content/uploads/2018/01/openTP_student1_analyse1-1.jpg)
Calibrating the distance measurement - part 2
With your measurements, determine an equation that converts the value of the measured magnetic field into the value of the distance between the sensor and the magnet.
![](http://opentp.fr/en/app/wp-content/uploads/2018/01/openTP_student1_brico5.jpg)
Experimental setup
![](http://opentp.fr/en/app/wp-content/uploads/2018/01/openTP_student1_mesure4.jpg)
Measurements!
Use your device on your plastic ruler to obtain its deformation with the applied force. To apply a force, you can place objects of known mass in the middle of the ruler (screw nuts for example).
![](http://opentp.fr/en/app/wp-content/uploads/2018/04/resultat_young-1.png)
Analyze
Analyze your results, and determine the value of plastic Young modulus.
![](http://opentp.fr/en/app/wp-content/themes/darfuino/includes/pics/question_3.png)
How accurate is your result?
How does it compare with the data in the literature?
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