# PHYSICAL METHODS

## LEARNING OUTCOMES OF THE COURSE UNIT

The course has been designed to provide fundamental concepts indispensable for understanding the mechanisms and the laws that rule the nature and that underlie the properties of matter, with special emphasis on those aspects useful in the comprehension of chemical and biological processes.

The experiments in the laboratory will show some practical applications.

## PREREQUISITES

Basic concepts of algebra and calculus.

## COURSE CONTENTS SUMMARY

Physical quantities and units. Frames of reference and coordinate axes. Vectors. MECHANICS. Force. Displacement. Velocity. Acceleration. Particular motions. Newton’s laws. Gravity. Relative velocity. Normal force. Friction. Restoring force of a spring. Centripetal force. Uniform and non-uniform circular motion. Periodic motions. Law of universal gravitation. Work. Kinetic energy. Potential energy. Conservation of mechanical energy. Generalized principle of energy conservation. Power. Linear momentum and its conservation. Impulse. Collisions. FLUIDS. Pressure. Stevino’s law. Pascal’s principle. Archimede’s principle. Laminar and turbulent flow. Equation of continuity. Bernoulli’s equation. Torricelli’s theorem. Venturi tube. Poiseuille’s equation. Surface tension. THERMODYNAMICS. Temperature and thermometric scales. Zeroth law of thermodynamics. Thermal expansion. The ideal and real gas law. Kinetic theory of gases. Real gas. Diffusion and Fick’s law. Heat. Thermal capacity and specific heat. Latent heat and change of phase. Conduction, convection and radiation. The first law of thermodynamics. Isobaric, isochoric, isothermal and adiabatic processes. Cycles. Specific heat at constant P or V for an ideal gas. The second law of thermodynamics. Heat engines and efficiency. Carnot cycle. Entropy. ELECTROMAGNETISM. Electric charge. Conductors and insulators. Conduction and induction. Coulomb’s law. Electric field. Different kinds of charge distributions and their Electric field. Electric field flow. Gauss law. Electric potential energy. Electric potential. Circuits. Capacitors. Electric current. Resistance. Ohm’s law. Electric power. Joule effect. Magnetic field. Magnetic force. Motion of a charge in a uniform magnetic field. Lorentz’s force. Wires and loops. Ampere’s law. Solenoid. Magnetism in the matter. Magnetic field flow. Faraday’s law of induction. Lenz’s law. Conductor in motion in an uniform magnetic field. Generalization of Ampere’s theorem. Maxwell’s equations in vacuum. OPTICS. Electromagnetic waves. Electromagnetic spectrum. Reflection and refraction. Snell’s law. Total reflection. Lens and images forming. Relationship between conjugate points. Lenses’ builders equation. Diffraction. Interference. INTRODUCTION TO ERROR ANALYSIS. Kind of error. Error distribution: standard deviation and normal distribution. Error propagation. Linear least square fitting and non-linear approximations. Chi-square test. PRACTICAL EXPERIMENTS. Verification of the Ohm’s law. Geometric optics: measurement of the rifraction index.

## RECOMMENDED READINGS

R.A. Serway e J.W. Jewett, Principi di Fisica, EdiSES.

J.S. Walker, Fondamenti di Fisica, Pearson.

J.R. Taylor, Introduzione all'analisi degli errori, Zanichelli.

## ASSESSMENT METHODS AND CRITERIA

Written exam concerning both problem solving and question about the contents of the lessons and the experiments in the lab.

## TEACHING METHODS

Oral lessons and practical experiments in the lab.

## COURSE CONTENTS

ORAL LESSONS:

Physical quantities and units. Dimensional analysis. Frames of reference and coordinate axes. Vectors: components, addition, subtraction, multiplication by a scalar, dot product, cross product, versors. MECHANICS. Force. Displacement. Average and instantaneous velocity. Uniform motion, motion laws. First Newton’s law. Average and instantaneous acceleration. Uniformly accelerated motion, motion laws. Graphical analysis. Second and third Newton’s laws. Motions in two/three dimensions. Gravity. Falling objects. Projectile motion. Relative velocity. Normal force. Static and dynamic friction. Fluid friction and viscosity. Restoring force of a spring and Hook’s law. Uniform circular motion and centripetal force. Conic pendulum. Non-uniform circular motion. Periodic motions. Simple harmonic motion. Law of universal gravitation. Work. Kinetic energy theorem. Potential energy. Gravitational and elastic potential energy. Conservation of mechanical energy. Conservative forces and dissipative forces. Generalized principle of energy conservation. Power. Linear momentum and its conservation. Impulse. Collisions. FLUIDS. Pressure. Stevino’s law. Pascal’s principle. Archimede’s principle. Laminar and turbulent flow. Rate of flow. Equation of continuity. Bernoulli’s equation. Torricelli’s theorem. Venturi tube. Dynamic lift. Poiseuille’s equation. Surface tension. THERMODYNAMICS. Temperature and thermometric scales. Zeroth law of thermodynamics. Thermal expansion of solids and liquids. Water’s behavior. The ideal gas law. Kinetic theory of gases. Real gas. Diffusion and Fick’s law. Heat. Thermal capacity and specific heat. Latent heat and change of phase. Energy transfer mechanisms in thermal processes: conduction, convection and radiation. The first law of thermodynamics. Reversible and irreversible processes. Isobaric, isochoric, isothermal and adiabatic processes. Cycles. Specific heat at constant P or V for an ideal gas. The second law of thermodynamics. Heat engines and efficiency. Carnot cycle. Refrigerators. Entropy and the second law. Entropy-work relationship. ELECTROMAGNETISM. Electric charge. Conductors and insulators. Charge transfer by conduction and induction. Coulomb’s law. Electric field and field lines. Electric field of different kinds of charge distributions. Charge distribution in a conductor. Electric field flow. Gauss law. Electric field from the Gauss law. Electric potential energy. Electric potential. Energy conservation. Electric potential of a point charge. Electric potential energy of a charges system. Electric potential of a charged conductor. Equipotential surfaces. Circuits. Capacitors and capacitance. Capacitors in series and in parallel. Energy stored in a capacitor. Dielectrics. Electric current. Resistance. Ohm’s law. Resistivity. Electric power. Joule effect. Resistors in series and in parallel. Magnetism. Magnetic dipole. Magnetic field. Magnetic force. Motion of a charge in a uniform magnetic field. Lorentz’s force. Current straight wires and loops into a magnetic field. Magnetic field due to an electric current. Ampere’s law. Forces between two current straight wires and loops. Solenoid. Magnetism in the matter. Magnetic field flow. Faraday’s law of induction. Lenz’s law. Conductor in motion in an uniform magnetic field. Generalization of Ampere’s theorem. Maxwell’s equations in vacuum. OPTICS. Relationship between harmonic motion and waves. Wave’s parameters. Wave-particle duality. Electromagnetic waves. Electromagnetic spectrum. Reflection and refraction. Snell’s law. Total reflection. Lens and images forming. Relationship between conjugate points. Lenses’ builders equation. Diffraction. Interference.

LABORATORY:

INTRODUCTION TO ERROR ANALYSIS. Kind of error. Error distribution: standard deviation and normal distribution. Error propagation. Linear least square fitting and non-linear approximations. Chi-square test.Use of the program “Origin” for data analysis. PRACTICAL EXPERIMENTS. Ver