30/04/18 fred 0 0

# 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

## 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?

## comments