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

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.

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 :

\[ \delta z = \frac{F L^3}{48 E I} \]

Arduino
Hall sensor
Ruler, set square, protractor
Magnets

Material

You will also need:

tinkering hardware;
screw nuts (to apply a force on the middle of the ruler).

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.

Is the orientation of the Hall sensor important?

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.

Experimental setup

Build an experimental setup to measure the deformation of the plastic ruler when a force is applied in its middle. For this, you can glue a magnet under the ruler.

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).

Analyze

Analyze your results, and determine the value of plastic Young modulus.

How accurate is your result?

How does it compare with the data in the literature?