School of Biotechnology

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1 Physics reference slides Donatello Dolce Università di Camerino a.y. 2014/2015 mail: School of Biotechnology

2 Program and Aim Introduction to Physics Kinematics and Dynamics; Position and reference frame. Average and Instant velocity Acceleration. Motion in two and three dimensions. Uniform circular motion Netwon s laws: classic mechanics Work and Kinetic energy Integrals: geometrical and analytical definitions. Kinetic energy theorem Conservative forces Conservative forces and conservation of mechanical energy Equilibrium positions Introduction to Thermodynamics Equlibrium and Zeroth principle of thermodynamics. Heat. Specific heat and thermodynamical transformations Notions of Quantum Mechanics Notions of Atomic physics Cultural skills: Methodology skills: Experimental data analysis Build models to describe physical systems Fundamentals of modern physics Laboratory experiences (?) Lab 1: harmonic oscillator Lab 2: ideal gas law Lab 3: magnetic induction Knowledge of fundamental of physics necessary to understand natural phenomena, including biological dynamics of living organisms and the working principles of instrumentations in biology laboratories.

3 Detailed program (for your reference) Introduction to mechanics Kinematics and Dynamics; Relevant physical quantities for kinematics: position and distance; time; velocity; acceleration. Instruments and units of measure. Errors in measurement: precision and sensitivity of an instrument. Systematic errors and random errors with examples for the measure of length. Position and reference frame. Reference frame and position in one dimension. Reference frame and position in 2 and 3 dimensions. Algebraic and geometric definition of a vector. The position vector. Average and Instant velocity Concept of mass point or particle with examples in 2 and 3 dimensions. Dimensional analysis. Average velocity. Instant velocity. Incremental ratio and derivative and its geometrical meaning. The case of uniform motion. Acceleration. Motion in two and three dimensions. Average acceleration. Instant acceleration. Uniform acceleration along a line. Motion in 2 and 3 dimensions. From equation of motion to equation for trajectory. Uniform circular motion Circular motion. From Cartesian coordinates to Polar coordinates. Angular frequency and units. Equations of motion for position, velocity and acceleration for uniform circular motion. First principle of dynamics. Tangent and centripetal acceleration. Introduction to dynamics. First principle of dynamics. Inertia. Relativity principle. Non uniform circular motion: tangential and centripetal acceleration. Second principle of Dynamics Sum and differences of vectors: algebraic and geometrical methods. Second principle of dynamics: inertial mass and force. Units of force. Systems with variable mass. Third principle of dynamics Internal and external forces: action and reaction. Conservation of total momentum and motion of centre of mass. Elastic and inelastic collisions. Binary elastic collisions. Universal Law of Gravitation Newton's law of gravitation. The meaning of a physical law: universality and predicting power. From Newton's law to the law of the weight force. Acceleration due to gravity on planets in the Solar system. Relation between Kepler's laws and Newton's law. The Cavendish experiment to measure the Gravitational constant. Weight force and free fall The weight force. Acceleration due to gravity. Calculation of equation of motion for free fall. Parabolic motion Equation of motion for parabolic motion. Parabolic trajectory and range. Elastic force Ideal spring. Law of elastic force. Harmonic oscillator Ideal harmonic oscillator. Calculation of equation of motion of harmonic oscillator. Plots of position, velocity and acceleration. Angular frequency, frequency and period of oscillations. Work and Kinetic energy Operational definition of work. Unit of work. Example of uniform force for one dimensional motion. Operational definition of kinetic energy. Unit of kinetic energy. Integrals: geometrical and analytical definitions. Definition of the integral. Geometrical interpretation. Examples of calculation of indefinite and definite integrals of simple functions.. Kinetic energy theorem General definition of work. Definition of scalar product for two vectors. Kinetic energy Theorem and its demonstration in one dimension. Applications of kinetic energy theorem to inclined plane and free fall. Meaning of the sign of the work. Conservative forces Operational definition of a conservative field of forces. Work done by a conservative force along different trajectories. Conservative forces and conservation of mechanical energy Definition of conservative force in terms of potential energy. Work and potential energy. Definition of mechanical energy. Theorem of conservation of total mechanical energy. Examples for free fall and harmonic oscillator. Dissipation of energy due to friction. Equilibrium positions Definition of positions of equilibrium in a field of forces. Characterization of stable and unstable equilibrium positions. Introduction to Thermodynamics The states of matter: solid, liquid and gaseous. Phase transitions. Characterisation of an ideal gas. Kinetic energy and thermal energy. Temperature: operational definition and the thermometer. Linear thermal expansion of a metal. The Celsius and Kelvin temperature scales. Boiling points of elements. Equlibrium and Zeroth principle of thermodynamics. Heat. Definition of thermal equilibrium. The Zeroth principle of thermodynamics and temperature measurements. Transfer of thermal energy and heat. Mechanical equivalence of the calorie: the Joule experiment. Positive and negative heat: transfer of thermal energy between a system and its environment. Specific heat and thermodynamical transformations Heat Capacity, specific heat at constant volume and constant pressure.

4 Some founding fathers a Science Pythagoras b.c. Study of harmonics systems (physics, mathematics, music, harmony in architecture and art) Archimedes b.c. Nature and its phenomena can be represented by numbers and mathematical laws Galileo Indeed it moves! Defined the scientific method to certify objective truths.

5 Physics Units (Internat. System [SI] [MKS]) Science concerns aspects of nature that can be measured The measurement act consists in the comparisons of a physical quantity w.r.t. a standard. The measure is how many times the standard quantity stays in the measured quantity The Meter and Kilogram historical standards are preserved in Paris. They are composed of very stable material and in an isolated environment second corresponds to the duration of periods of the characteristic radiation of Cesium 133 atom (about 1 / of a solar day) To define time it is necessary to count the number of period of a phenomenon which is supposed to be periodic (we suppose that the unit of time doesn t change, we can not travel in time)

6 Physics Units (Internat. System [SI] [MKS]) Science concerns aspects of nature that can be measured The measurement act consists in the comparisons of a physical quantity w.r.t. a standard. The measure is how many times the standard quantity stays in the measured quantity

7 Derived Units A physical quantity A can be always expressed as combination of fundamental IS unit [MKS] [A] =[m α Kg β s γ ] with α, β, γ integer numbers..., 3, 2, 1, 0, 1, 2, 3,...

8 Derived Units A physical quantity A can be always expressed as combination of fundamental IS unit [MKS] [A] =[m α Kg β s γ ] with α, β, γ integer numbers..., 3, 2, 1, 0, 1, 2, 3,... The Dimensional Analysis is very important to check your problems and to remember physics laws [N] = Kg m s 2 = Kg m s 2 F = Ma where the mass M =[Kg] and the acceleration a = m s 2

9 Conversion factors and scale factors These are dimensionless factors and they allows for the conversion of physical units among different dimensional systems

10 Conversion factors and scale factors These are dimensionless factors and they allows for the conversion of physical units among different dimensional systems Time scales

11 Elementi di Statistica Statistic error: consequence of aleatoric causes (ability of the operator, variations of physical conditions, etc) Systematic error: consequence of a non accurate off-set of the experimental equipment Given a set of N measures {x 1,x 2,...x N } of a given physical quantity X, we define mean value x e stadard devation σ x (quadratic deviation), respectively, x = x 1 + x x N N 2 1 σ x = N N 1 The magnitude of the standard deviation determines the number of significative figures of the results. = = N i=1 x i N N i=1 2 i N 1 where the deviations are defined as i = x i x. The outcome of a measure is expressed by the mean value and by the standard deviation denoting the error in the measure itself x ± σ x

12 Gaussian distribution For a large set of measurements the probability of an outcome is typically given by the Gaussian distribution (normalised to 1). The probability f(x) to measure x is f(x) = 1 e (x x) 2σ x 2 2πσ 2 x 2

13 Propagation of the errors if x = x ± x: relative error x x, where the absolute error is x. We want to test the generic physical law F = f(x, y) for two (non independent) physical quantities x = x ± x and y =ȳ ± y. TheresultisF = f( x, ȳ) ± F where F is given by (α is a known coefficient): if f(x, y) =α(x + y) or f(x, y) =α(x y): sum of absolute errors F = α( x + y) 1 if f(x, y) =α(x y) or f(x, y) =α x y : sum of relative errors F F x = α( x + y y ) 1 1 Notice: if the errors are independent f = α x 2 + y 2.