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Physics
reference slides
Donatello Dolce
Università di Camerino
a.y. 2014/2015
mail: [email protected]
School of Biotechnology
Program and Aim
Methodology skills:
• Experimental data analysis
• Build models to describe physical systems
• Fundamentals of modern physics
Introduction to Physics
Kinematics and Dynamics;
Position and reference frame.
Average and Instant velocity
Acceleration. Motion in two and three dimensions.
Laboratory experiences (?)
Uniform circular motion
Lab 1: harmonic oscillator
Netwon’s laws: classic mechanics
Lab 2: ideal gas law
Work and Kinetic energy
Lab 3: magnetic induction
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:
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.
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.
Some founding fathers a Science
Pythagoras 560-495 b.c.
Study of harmonics systems (physics,
mathematics, music, harmony in architecture
and art)
Archimedes 287-214 b.c.
Nature and its phenomena can be represented
by numbers and mathematical laws
Galileo 1564-1642
“Indeed it moves!” Defined the scientific
method to certify objective truths.
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
A “second” corresponds to the duration of 9.192.631.770 periods of the characteristic
radiation of Cesium 133 atom (about 1 / 86400 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)
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
Derived Units
A physical quantity A can be always expressed as combination of fundamental IS unit [MKS] [A] = [mα Kg β sγ ]
with α, β, γ integer numbers . . . , −3, −2, 1, 0, 1, 2, 3, . . .
Derived Units
A physical quantity A can be always expressed as combination of fundamental IS unit [MKS] [A] = [mα Kg β sγ ]
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
s2
�
=
�
Kg sm2
�
→ F = Ma
where the mass M = [Kg] and the acceleration a =
�m�
s2
Conversion factors and scale factors
These are dimensionless factors and they allows for the
conversion of physical units among different dimensional
systems
Conversion factors and scale factors
These are dimensionless factors and they allows for the
conversion of physical units among different dimensional
systems
Time scales
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 {x1 , x2 , . . . xN } of a given
physical quantity X, we define mean value x̄ e stadard devation σx (quadratic deviation), respectively,
�N
xi
x1 + x2 + · · · + xN
= i=1
N
N
�
�
�N 2
2
2
2
�1 + �2 + · · · + �N
i=1 �i
σx =
=
N −1
N −1
x̄ =
where the deviations are defined as �i = xi − x̄.
The outcome of a measure is expressed by the mean
value and by the standard deviation denoting the error in
the measure itself
x̄ ± σx
The magnitude of the standard deviation determines the number of significative figures of the results.
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
(x−x̄)
1
− 2σ2
x
f (x) = �
e
2
2πσx
2
Propagation of the errors
if x = x̄ ± ∆x: relative error
∆x
x̄ ,
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 = x̄ ± ∆x
and y = ȳ ± ∆y. The result is F = f (x̄, 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 xy :
sum of relative errors ⇒
1
∆F
F
= α( ∆x
x +
∆y
y )
�
Notice: if the errors are independent ∆f = α ∆x2 + ∆y 2 .
1