# 22455 - Lab-based Course on Mechanics and Thermodynamics (M-Z)

• Moduli: Sara Valentinetti (Modulo 1) Nicolò Jacazio (Modulo 2) Silvia Arcelli (Modulo 3) Silvia Arcelli (Modulo 4)
• Campus: Bologna
• Corso: First cycle degree programme (L) in Physics (cod. 9244)
• from Sep 16, 2024 to Dec 19, 2024

## Learning outcomes

At the end of the course, the student possesses the basic skills to carry out measurements of physical quantities and the knowledge of metrology and statistics that allow him to analyze the data collected in the laboratory, correctly expressing the experimental results. In particular, the student is able to: use some of the most common measuring instruments and carry out measurements using sensors and a data acquisition chain via PC; perform the dimensional analysis of a physical quantity and express the measurements in the SI; evaluate instrumental, random and systematic uncertainties; use random error statistics and calculate the propagation of uncertainties in indirect measurements; compare the outcome of an experiment with other experimental results and with theoretical predictions through appropriate tests; apply some of the statistical and graphical functions of a spreadsheet and the ROOT software package for data analysis on a PC; write a clear and concise experimental report.

## Course contents

Module 1

The measurement of physical quantities

the experimental method; the measurement procedure; the international system of units of measurement; the length, mass, time and temperature standards; main characteristics of measuring instruments; calibration of an instrument; measurement errors; random fluctuations and systematic effects; precision and accuracy; evaluation of the uncertainty of a result; the Gaussian distribution; linear and quadratic combination of uncertainties in indirect measurements; representation of the result of a measurement.

Introduction to data acquisition and measurement methods based on electronic devices and personal computers

sensor/transducer concept and examples; analog and digital signals and information contained therein; amplification resolution, code width of a measurement chain.

Elements of probability and statistics

basic elements of probability; random variables; probability functions; binomial, Poisson, uniform, normal distribution; mean and variance; joint probability functions; covariance and correlation coefficient; statistics of random uncertainties; confidence interval for the mean of a sample of measurements; criteria for rejecting spurious data; small samples and Student statistics; maximum likelihood criterion and least squares method; weighted averages; linear regression; chi-square statistic; "best fit" methods; hypothesis testing; confidence level of a test; the null hypothesis; test of fit of a series of measures of a given distribution; test of fit of measures coupled to a function.

Laboratory experiments on mechanics and thermodynamics topics

1) measurement of the moment of inertia of a solid;

2) calibration of a thermocouple.

3) conservation of momentum; conservation of angular momentum; 4) Ruchardt experiment; Perrin experiment;

Experiments 3) and 4) are the subject of Modules 2, 4 and 5.

The analysis of the collected data is also carried out through some statistical functions of the ROOT software package.

Module 3

The ROOT framework for data analysis

- General structure

- the user interface (command line, use of macros, graphical interface).

-Representation of experimental data with ROOT: histograms and classes charts (basic functionality). Main commands for presentation of results in graphs and histograms (axes, legends, divisions etc) with ROOT .

-Monte Carlo generation: Basics (Number generators pseudorandom, rejection method, transformation method inverse) ROOT functionality for Monte Carlo generation.

-Concrete examples on uniform, Gaussian distribution, exponential, binomial. Verification of results derivable a priori (Poissonian and Gaussian distribution as limit of the distribution Binomial, etc.).

-Examples of ROOT macros for the analysis of experimental data (with reference to the laboratory tests proposed as part of the Course).

P. Fornasini "The uncertainty in physical measurements" Springer.

J. R. Tayor "Introduction to the analysis of errors" Zanichelli.

The ROOT Data Analysis Framework: https://root.cern.ch/
The ROOt Primer:
https://root.cern.ch/root/htmldoc/guides/primer/ROOTPrimer.html

## Teaching methods

Lectures on the blackboard, also with the aid of slides (made available in advance on the virtual platform) - Classroom exercises; - Four laboratory sessions (attendance is mandatory), with written reports. In consideration of the types of activities and teaching methods adopted, attendance of this training activity requires all students to carry out modules 1 and 2 in e-learning mode [https://www.unibo.it/it/servizi -e-opportunita/health-and-assistance/health-and-safety/safety-and-health-in-places-of-study-and-internship] and participation in module 3 of specific training on safety and health in places of study. Information on the dates and methods of attendance of module 3 can be consulted in the specific section of the study course website.

## Assessment methods

Written exam and oral exam. The written test consists of three problems on different topics of probability and statistics plus a problem relating to ROOT. The written test is evaluated with a score out of 30. Each of the four problems is assigned a score, indicated in the text of the written test; the sum of the four scores is equal to 30. During the written test, which lasts 120 minutes, the use of books and notes is permitted. The oral test follows the written test and can only be taken if a minimum score of 18/30 is obtained in the written test. The validity of each written test passed is limited to the session. During the oral test, which lasts approximately 45-50 minutes, the student is asked questions that may concern all the topics on the program. In particular, the questions may also concern the topics covered in the various laboratory experiences, the methods of carrying them out and the results obtained. The oral test is evaluated with a score out of 30. The grade of the oral exam is established based on the following criteria: - if the preparation is limited to a subset of topics that are part of the course program and the critical capacity emerges only with the help of the teacher, then the grade will be in the range 18-21; - if the preparation is on a large number of topics covered in the course but the analytical ability proves to be autonomous only in a limited way, then the vote will be in the range 22-25; - if the preparation is satisfactory on all the topics covered in the course, demonstrating good autonomy of critical analysis and good command of specific terminology, then the grade will be in the range 26-29; - if the preparation is complete and you demonstrate excellent ability to independently carry out critical and liaison analyses among the various topics covered in the course, with full mastery of the terminology and argumentation skills, then the grade will be 30 or 30 with honors. The final score represents the average of the scores of the written test and the oral test.

## Teaching tools

Use of slides available to the student in advance on the virtual platform. Physics laboratory (viale Berti-Pichat 6/2, floor -1) for the experiences proposed during the academic year.

## Office hours

See the website of Sara Valentinetti

See the website of Nicolò Jacazio

See the website of Silvia Arcelli

See the website of Silvia Arcelli

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.