PHYSICS I WITH EXERCISES
Basic elements of mathematics and geometry at the secondary school level.
The final exam is split in two separate parts: the first concerns kinematics and mechanics and the second, only for students in Mathematics, thermodynamics. The first part consists in a written test including:
1) two exercises (12 points each) where the student will be able to show his/her understanding of the problem, his/her ability to identify the physical laws governing the phenomena and his/her capacity to carry out the necessary calculations;
2) two questions concerning topics discussed in class (5 points each) where the student will be able to show his/her comprehension of the nature of the physical laws and their domain of validity.
The final mark is given by the sum of the marks earned in the test. Laude is granted to the student whose final mark exceeds 30.
The second part of the final exam, also consists in a written test. The written test, which last 2 hours, consists in two exercises of thermodynamics similar to those seen during the lectures. The written test also includes two or more questions related to the program of the course. The student will be able to show its understanding of the different topics seen during the lectures.
The final mark will be obtained as the average, weighted by the credits, of the separate marks of the two parts (mechanics and thermodynamics).
This course represents the first chance a freshman has to come into contact with the physical laws. Although the main topics addressed in this course, kinematics, dynamics of a point mass, gravitating systems and thermodynamics, were already addressed in the secondary school, it is important to give a rigorous, complete and detailed introduction at a professional level, in order to provide a solid methodological basis. The concepts of geometry and calculus required for the mathematical formulation of the physical laws will be introduced by the teacher. The experimental facts supporting the fundamental physical laws will be critically discussed.
At the end of the course the successful student will be able
1) to use in an appropriate way the physical laws to frame physical problems;
2) to use the correct mathematical techniques to solve the equations previously obtained;
3) moreover the student will acquire critical sensibility and scientific method.
The last 6 points of the course program are specifically devoted to the students in Mathematics.
STUDENTS IN PHYSICS AND IN MATHEMATICS:
1) Introduction. Measuring physical quantities. (2 h)
2) Vectors: sum, scalar product, vector (cross) product. Coordinate systems: Cartesian and polar. Elementary introduction to differential calculus (6 h).
3) Kinematics. Trajectory and the description of motion. Velocity and acceleration. Uniform motion, uniformly accelerated motion, harmonic motion. Uniform circular motion, centripetal acceleration. Tangential and normal acceleration. Reference systems: principle of relativity. Relationship between different reference systems (10 h).
4) Dynamics. First and second laws of dynamics. Third law and momentum conservation. Weight. Rheonomic constraints: inclined plane. Elastic forces: Hooke's law.The pendulum. Tensions. Atwood machine (10 h).
5) Frictional laws and viscous forces. Some example of motion in the presence of friction and viscosity. Fictitious forces (4 h).
6) Impulse-momentum theorem.Variable masses. Kinetic energy, work: work-energy theorem. Conservative forces, potential energy. Conservation of mechanical energy. Angular momentum. Central forces and conservation of angular momentum (10 h).
7) Gravitation. Equivalence principle. Newton's law of gravitation. Measuring G: the Cavendish experiment. Gravitational potential energy.Kepler laws. Center of mass and reduced mass. Gauss theorem. Motion of a point in a gravitational field (10 h).
8) Elastic and inelastic collisions. Dynamics of systems of points: Newton's equations and the definition of torque (4 h).
STUDENTS IN MATHEMATICS:
9) Introduction - state variables of a thermodynamics system. Pressure and temperature of a system at equilibrium – units.
10) The ideal gases Determination of the state equations of an ideal gas. Measurement of the temperatures and thermometers.
11) Heat and work – the first principle of thermodynamics. Formulation of the first principle of thermodynamics – definition of the internal energy of a system as a state variable.
12) Kinetic theory of gases – a classical microscopic model for the ideal gas. Relations between thermodynamics macroscopic variables and the microscopic physical quantities.The Clausius Joule formula. Interpretation of the temperature as a measure of the mean kinetic energy of the gas molecules. Internal energy of a monoatomic gas – relation to the principle of equipartition of energy. The Maxwell distribution of the molecular velocities.
13) the 2° principle of thermodynamics The Kelvin and Clausius postulate of the 2° principle of thermodynamics – proof of their equivalence. The performance coefficient of the Carnot cycle of an ideal gas. The Carnot theorem for the heat engine performance. Introduction of the system entropy S as state variable. The principle of entropy increase for an isolated system – relation between entropy and irreversibility,
14) Applications of the 1° and 2° principle to a pure substance (pVT systems) – phase transition. Real gasses – the Van der Waals state equations
The course is essentially based on lectures, during which the teacher presents the contents of the course in full detail, including mathematical derivations. The final chapter about thermodynamics will be mainly covered in the exercise sessions (36 h) specifically devoted to the students in Mathematics. At the end of each section, as previously detailed, a tutor will solve and discuss with the students few exercises taken from past exams (20h). An open source software for the numerical solution of differential equations (OdeFactory) will be presented and used during the lessons, in order to get the students used to this kind of techniques.
The teachers are available for questions by appointment. The e-mail of the teacher of the first part of the course is:
alberto.parola@uninsubria.it
The e-mail of the teacher of the second part (for students in mathematics only) is
enrico.brambilla@uninsubria.it
Professors
Borrowers
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Degree course in: Physics