Module 02 - Physics PDF

Module 02 PHYSICS Pag.  Module 02 – Physics Copyright © 2020 by Aviotrace Swiss SA All rights reserved. No part of this publication may be reproduced, distributed, or tra...

Module 02 PHYSICS Pag.  Module 02 – Physics Copyright © 2020 by Aviotrace Swiss SA All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher. 01.04.2020 Ed2 Pag. 2  Module 02 – Physics Table of Contents 2.1 Matter 2.1 Mechanics 2.3 Thermodynamics 2.4 Optics 2.5 Wave motion and sound 01.04.2020 Ed2 Pag. 3  Module 02 – Physics Chapter 02.01 MATTER 01.04.2020 Ed2 Pag. 4  Module 02 – Physics Matter By definition, the matter is anything that takes up space and has a mass. The Law of Conservation of the matter says that the matter can’t be created, or destroyed. Only its characteristics can be changed. Whenever the matter changes its state there is an energy conversion, which is the matter ability to do a work. Rutherford noticed that the atom was kept together thanks to electrical fields generated by the nucleus, characterized by a positive charge, and by electrons which surrounded it, negative charged. The electrical charge, phenomenon studied in different ways, is bonded to atom‘s characteristics. In 1913, the physicist Bohr suggested some additions to the atomic model of Rutherford. 01.04.2020 Ed2 Pag. 5  Module 02 – Physics Matter Kept together, Rutherford and Bohr's theories speak of an atomic nucleus consisting of one or more corpuscles, positive charged, called proton. All around this nucleus rotate the electrons, at a precise distance, negative charged and equal in number to the protons of the nucleus. An electron is lighter than a proton, and its mass is approximately 1850 time less than the proton one. The negative charge of the electrons in the atom, balances the equal and opposite charge of the protons. The atom, kept alone, doesn't present outside any electrical charge. Neutrons = neutral charge, same mass of protons 01.04.2020 Ed2 Pag. 6  Module 02 – Physics Bohr’s atomic Model The path of every single electron around the nucleus is strictly determinate by the number of particles in the nucleus and by the energy level of each electron of the atom. Paths are organized in shells. 01.04.2020 Ed2 Pag. 7  Module 02 – Physics Bohr’s atomic Model Each shell contains a certain number of paths, called energetic levels. Each energetic shell can contain a maximum number of electrons, well defined. 𝑁𝑁 = 2 ∗ 𝑛𝑛2 With: N = number of electrons. n = number of the energy level in question. 01.04.2020 Ed2 Pag. 8  Module 02 – Physics Chemical compounds Nowadays it knows 109 different elements or atoms. Each of them has a precise number of protons, neutrons and electrons. Compound is defined as two elements in the same substance. Each of them is identified by a proper atomic number and has a proper atomic mass. 1. CHEMICAL ELEMENT: Pure chemical substance consisting of one type of atom. 2. ATOMIC NUMBER: The atomic number corresponds to the number of the protons in the nucleus. 3. ATOMIC MASS: The atomic mass is the mass of an atom of a single element; it corresponds to the sum of protons and neutrons. 01.04.2020 Ed2 Pag. 9  Module 02 – Physics States A solid is defined as a portion of the matter in a condensed state. In these conditions, the particles composing it, as to say atoms, molecules and ions, are strongly packed up among them, oscillating around fixed positions in the space and reacting to changes in shape and volume, with stresses depending on the function of the entity of the deformation suffered. Giving energy as heat to a solid material, the movement of the molecules increases. This energy forces molecules to go away from their fixed positions, which characterize the precise shape of the solid. When a material changes from solid to liquid, the volume of the material does not change so much. But the material adapts itself to the shape of the container. Liquids are considered incompressible. Going on giving energy to a liquid material, as heat, the molecular movement increases even more, until the liquid reaches the condition in which the surface voltage is no more able to hold the molecules of the material. At this point molecules go away as gas or steam. 01.04.2020 Ed2 Pag. 10  Module 02 – Physics States Gasses are very different from solids and liquids, because they have no definitive shape and volume. Chemically, gas molecules are identical to liquid and solid ones. But a gas, unlike liquid and solid, is compressible. 01.04.2020 Ed2 Pag. 11  Module 02 – Physics Change between States In a solid, molecules are kept into fixed positions during a vibration. Increasing the solid temperature, increases also the actual vibration of molecules, and consequently increases the speed of vibration, as to say the kinetic or moving energy of molecules of the body. If the temperature continue to increase, bonds keeping together molecules become more weak, and so molecules can move from its fixed positions, which identified the solid state of the body. In these conditions the substance becomes a liquid. Increasing more the temperature, a bigger energy to molecules is provided, until a second point or energy level is reached, in which the attraction bond among molecules is no more able to keep them together and, at this point, the liquid becomes a gas. 01.04.2020 Ed2 Pag. 12  Module 02 – Physics Change between States The changes between states can be classified as: 1. Fusion: that is the transformation process between the solid state and the liquid state. 2. Consolidation: that is the transformation process between the liquid state and the solid state. 3. Evaporation: that is the transformation process between the liquid state and the gaseous state. 4. Condensation: that is the transformation process between the gaseous state and the liquid state. 5. Sublimation: that is the transformation process between the solid state and the gaseous state and vice versa. 01.04.2020 Ed2 Pag. 13  Module 02 – Physics Change between States The temperature at which we have the state change depends on the material and on the external pressure. During the state change, there are some moments in which both states coexist: when we melt ice we have both ice and water until the process is not complete. The triple point is a situation of temperature and pressure where the three states coexist in equilibrium. The triple point of water is the point where water, ice and vapor coexist in equilibrium. 01.04.2020 Ed2 Pag. 14  Module 02 – Physics Change between States State changes, whether from solid to liquid or from liquid to gas, happen at a definite and constant temperature. This phenomenon is due to the fact that the energy absorbed during the transformation phase, is used to break the attraction bonds. This energy is the latent heat. 01.04.2020 Ed2 Pag. 15  Module 02 – Physics Latent Heats When a substance changes states, require some energy. This energy is called latent heat. The necessary heat to reach the change from the substance solid state to the liquid one, is called "fusion latent heat", instead the one necessary to transform a liquid into a gas is called "evaporation latent heat". 01.04.2020 Ed2 Pag. 16  Module 02 – Physics Latent Heats The specific latent heat of fusion of a substance is the quantity of heat required to convert a unit mass of the substance from a solid to a liquid state without change of temperature. The specific latent heat of vaporisation of a substance is the quantity of heat required to change a unit mass of the substance from a liquid to a vapour state without a change of the temperature. The latent heat taken in is the same value as that given out, so the latent heat of vaporization is the same as the latent heat of condensation (except with opposite sign). 01.04.2020 Ed2 Pag. 17  Module 02 – Physics Chapter 02.02 MECHANICS 01.04.2020 Ed2 Pag. 18  Module 02 – Physics Fundamental Unit of Measurement Length Metre m Mass kilogram kg Time Second s Electric current Ampere A Temperature Kelvin K Luminous Intensity Candela cd Amount of substance Mole Mol 01.04.2020 Ed2 Pag. 19  Module 02 – Physics Unit of Measurement Secondary Density ρ kg/m3 Force F N Energy E J Pressure p Pa Power P W 01.04.2020 Ed2 Pag. 20  Module 02 – Physics Prefix Multiples Deci d 10^-1 Centi c 10^-2 Milli m 10^-3 Micro μ 10^-6 Nano n 10^-9 Pico p 10^-12 01.04.2020 Ed2 Pag. 21  Module 02 – Physics Forces, moments and couples Force is defined as "what changes or tries to change the state of rest of a body or its state of uniform motion on a straight line". The unit of measurement of the force, in all its aspects, is the Newton [N]. The Newton is the unit of the force in the International System, adopted in honor of Sir Isaac Newton. 𝑚𝑚 FORCE = 𝑁𝑁 = 𝑘𝑘𝑘𝑘 𝑠𝑠 2 A force can be used to produce a rotation, for example as happens when you open a door. This movement requires that the door rotates, hinged in a certain position and that the force is applied at a certain distance from the point of rotation. 01.04.2020 Ed2 Pag. 22  Module 02 – Physics Change between States A force can be represented by a straight line of the action, a length indicating its magnitude, and by a symbol of an arrow, showing the direction. Vectorial magnitudes have a quality compared to scalar ones in fact, vectors can be added graphically, and this characteristic simplifies problems. Magnitudes expressed only by a number are called scalars. Some scalar magnitudes are time, temperature and mass. A scalar magnitude can be represented by a marked length on an opportune scale. A scalar quantity is characterized by its magnitude, and to define it nothing else is necessary. It can be represented by a length drawn on a straight line quoting a scale. 01.04.2020 Ed2 Pag. 23  Module 02 – Physics Stress Each time an external force acts on a body, it is contrasted by an internal force of the body, called stress: 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 The English measurement unit is pound per square foot [lb/ft2] or pound per square inches [lb/in2], while in the I.S. it’s measured by Pascal [Pa]. Mechanics distinguishes between five different types of stress applied to bodies: tension, compression, torsion, flexion and shear. 01.04.2020 Ed2 Pag. 24  Module 02 – Physics Stress The tension indicates the force tending to separate an object. A steel flexible hose, used to control an airplane system, is an example of an element designed to bear tension loads. The compression is the characteristic to resist to an external force that tends to push the object inside. Aeronautical rivets are inserted using a force of compression. The torsion stress is applied to a material when it is twisted. The crankshaft of an engine is a piece, whose principal stress is the torsion. The flexion stress is applied to a material, when it is subjected to two simultaneous stresses, tension and compression. The stress of shear tends to divide the body into slices. A bolt subjected to shear inserted in an airplane control system, is designed to bear stresses to cut. 01.04.2020 Ed2 Pag. 25  Module 02 – Physics Hooke’s Law Subjected to a stress load, lots of materials behave initially as they were elastic, but increasing the load they acquire at the end a permanent deformation. The first connection between load and extension was made by Robert Hooke in 1676. Hooke's law states that "the extension produced by an elastic material is directly proportional to the load which has produced it. Hooke’s law establishes that: if the strain or deformation (ε) doesn't overcome the elasticity limit of the body, there is direct proportionality to the stress applied (σ). The constant of proportionality is E and it is defined as Young’s Module. 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝑒𝑒 ′ 𝑠𝑠 𝐿𝐿𝐿𝐿𝐿𝐿 → 𝜎𝜎 = 𝐸𝐸𝐸𝐸 01.04.2020 Ed2 Pag. 26  Module 02 – Physics Pressure The pressure is defined as a force per unit of surface, and is expressed in Newton per square meter [N/m2] or in Pascal [Pa]. Other units are: bar and atm (1013.2 millibar= 1 atm) Properties of the pressure in fluids: The pressure applied on a point, inside a fluid, is the same in all directions. The pressure applied by a fluid is always directed perpendicularly to the container sides, containing the fluid A fluid in pressure exerts the same pressure in all fluid points, without important losses. 01.04.2020 Ed2 Pag. 27  Module 02 – Physics Pressure INDICATED PRESSURE: it is the pressure shown directly on instrument dial, and represents pressure which overpasses the atmospheric one. ABSOLUTE PRESSURE: it is the pressure referred to the vacuum and it is equivalent to the sum of pressure indicated and the atmospheric one. DIFFERENTIAL PRESSURE: it is the pressure equivalent to the difference between two pressures. 01.04.2020 Ed2 Pag. 28  Module 02 – Physics Velocity The motion of an object is never absolute, but relative. To study the motion of an object is necessary to establish a system of reference for example, the system of Cartesian coordinates, in order to specify positions comparing to it. If S is the measure of the displacement of a body and t is the time spent to do it, average velocity can be defined as the ratio of displacement and time: 𝑆𝑆 𝑉𝑉 = 𝑡𝑡 In the IS the unit of measurement is the meter per second [m/s]. Considering that usually velocity is expressed in kilometers per hour [km/h], learning now this conversion is necessary. How to transform from km/h into m/s? 01.04.2020 Ed2 Pag. 29  Module 02 – Physics Acceleration When instant velocity isn't constant but varies in time, there is an acceleration. Average acceleration can be defined as the variation of the average velocity in a time interval: 𝑉𝑉 𝑎𝑎 = 𝑡𝑡 In the International System, the unit of measurement of acceleration is the meter per square second [m/s2]. As for instant velocity, there is also an instant acceleration. Obviously, if a body is slowing down, as to say decelerates, we obtain a negative value of acceleration. 01.04.2020 Ed2 Pag. 30  Module 02 – Physics Velocity: uniform linear motion If the velocity vector keeps constant module, direction and verse, there is a uniform linear motion. 𝑆𝑆 = 𝑉𝑉𝑉𝑉 Exercise: Distance = 2km ; t = 90 sec; v? 01.04.2020 Ed2 Pag. 31  Module 02 – Physics Velocity: uniformly accelerated motion When the acceleration in a motion is constant, there is a uniformly accelerated motion. Using the definition of acceleration, it is possible to find out the velocity law: 𝑉𝑉 = 𝑎𝑎𝑎𝑎 The graphic representation of velocity law in a velocity-time graph is a straight line 01.04.2020 Ed2 Pag. 32  Module 02 – Physics Free Falling Object A particular case of uniformly accelerated motion is a free falling object. In this case the acceleration of the motion is given by the gravity acceleration (g), which corresponds approximately to 9.81 m/s2. 1 2 𝑠𝑠 = 𝑔𝑔𝑡𝑡 2 𝑉𝑉 = 𝑔𝑔𝑔𝑔 2ℎ 𝑉𝑉 = 𝑔𝑔 = 2𝑔𝑔𝑔 𝑔𝑔 Ex.1: t=3sec, h=? Ex.2: t=5sec, V=? Ex.3: h=180m, V=? 01.04.2020 Ed2 Pag. 33  Module 02 – Physics Uniform Circular Motion An object moving throughout a circumference makes a circular motion. If that movement has a constant module velocity, it is a uniform circular motion. In uniform circular motion we define some magnitudes. The time spent by the object to make a whole revolution on the circumference, is called period T. The number of revolutions that the object makes in a second is called frequency (f). The frequency is equal to the multiplicative inverse of the period. In the International System the unit of the frequency is Hertz [Hz]. 01.04.2020 Ed2 Pag. 34  Module 02 – Physics Uniform Circular Motion The time spent by the object to make a whole revolution on the circumference, is called period T. The number of revolutions that the object makes in a second is called frequency (f). 2𝜋𝜋𝜋𝜋 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 → 𝑉𝑉 = 𝑇𝑇 As tangential vector changes continuously direction, that variation determines an acceleration, called CENTRIPETAL ACCELERATION. 𝑉𝑉 2 𝑎𝑎𝑐𝑐 = 𝑟𝑟 01.04.2020 Ed2 Pag. 35  Module 02 – Physics Angular Velocity The angular velocity is the ratio between the angle described and the time spent to do it: 2𝜋𝜋 𝜔𝜔 = 𝑇𝑇 In the International System, the unit of the angular velocity is radiant per second [rad/s]. Comparing angular velocity value to tangential velocity one, we can deduce a relation connecting the two magnitudes: 2𝜋𝜋𝜋𝜋 𝑉𝑉 = = 𝜔𝜔𝜔𝜔 𝑇𝑇 01.04.2020 Ed2 Pag. 36  Module 02 – Physics Vibration The term “vibration” indicates a particular mechanical oscillation around an equilibrium point. The oscillation can be periodic, as the motion of the pendulum (harmonic), or random as the movement of a tire on a paved road. In some case the vibrations are a “wanted phenomenon”: for example musical instruments. However the vibrations are more often undesired: in fact they can disperse energy and create tiresome sounds and noises. An example is the engine of a vehicle when it is working. The vibrations are more often undesired: in fact they can disperse energy and create tiresome sounds and noises. 01.04.2020 Ed2 Pag. 37  Module 02 – Physics Spring Springs obey the Hook’s law, which is concerned with the elasticity in materials. The extension of the spring is proportional to the applied force. If you suspended a mass to the free end of a vertical spring and then pull it down and release it the mass would oscillate up and down. The force causing the mass to accelerate back through its rest position. Springs have different values of stiffness. Each spring has a stiffness value that is expressed as its spring constant k. The spring constant will affect the amplitude, the frequency and periodic time of the oscillation of the spring. 01.04.2020 Ed2 Pag. 38  Module 02 – Physics Spring: free vibration without damping The mass of the system is called m and the stiffness of the spring is indicated by k. The number fn is one of the most important quantities in vibration analysis and is called the “UNDAMPED NATURAL FREQUENCY”. 1 𝑘𝑘 𝑓𝑓𝑛𝑛 = 2𝜋𝜋 𝑚𝑚 01.04.2020 Ed2 Pag. 39  Module 02 – Physics Spring: free vibration with damping The proportionality constant c is called the damping coefficient. The frequency in this case is called the "DAMPED NATURAL FREQUENCY", and it is lower than the undamped natural frequency. 01.04.2020 Ed2 Pag. 40  Module 02 – Physics Mechanical Advantage Lots of machines, realizable in practice, use the so-called "mechanical advantage", to modify the force necessary to move an object. The lever, the inclined plane, pulley, and gears allows to move a great load Weight with a low stress. The ratio between the Weight moved and the Stress required is the mechanical advantage (MA). 𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊 𝑀𝑀𝑀𝑀 = 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 A mechanical advantage of 4 indicates that for each pound of applied force, 4 pounds of resistance can be contrasted. 01.04.2020 Ed2 Pag. 41  Module 02 – Physics Levers Three classes of levers exist: LEVER OF FIRST CLASS: In order to deduce the required stress to lift the load is necessary to calculate, the moments at the two opposite sides of the fulcrum. LEVER OF SECOND CLASS: Unlike lever of first class, a second class lever has the fulcrum at one extreme of the lever, and the force is applied on the other extreme. The resistance, as to say the load to lift, is applied on the lever near the fulcrum. LEVER OF THIRD CLASS: A third class lever is mainly used to move a resistance to an exceeding distance, compared to the one of the force applied. This is obtained applying a force between the fulcrum and the resistance. 01.04.2020 Ed2 Pag. 42  Module 02 – Physics Pulley Pulleys or sheaves are another type of simple machine which allow obtaining a mechanical advantage. A single pulley joint to a fix point, is equivalent to a lever of first class and has a mechanical advantage of one: there is no reduction in the required force. 01.04.2020 Ed2 Pag. 43  Module 02 – Physics Pulley If the pulley is not franked or is a mobile pulley, it works as a second class lever, as to say that both force and weight are in the same direction. In the pulley, the more one gains in a mechanical advantage, the more the distance to which apply the force increases. In other words if a mechanical advantage of 2 is obtained, for each foot of resistance shift, a force of 2 feet of rope must be applied. 01.04.2020 Ed2 Pag. 44  Module 02 – Physics Force and Heat The force is the magnitude that measures the interaction among physical systems. The force can be defined as the cause that produces or modifies the movement of a body: that is the cause that generates changes of velocity. If an object is steady and it remains steady, the total force that the body is suffering is null. Instead, if an object is steady and then it gets a move on and gains velocity, there is a force that produces the movement. The force is a vector. The heat is a transfer of energy (at macroscopic level) between two bodies, initially at different temperatures. The heat is energy in transit. It is measured in Joule, but it can also expressed by the calorie: 1 𝑐𝑐𝑐𝑐𝑐𝑐 = 4,186 𝐽𝐽 1 𝐽𝐽 = 0,239 𝑐𝑐𝑐𝑐𝑐𝑐 01.04.2020 Ed2 Pag. 45  Module 02 – Physics Efficiency The energetic efficiency is a dimensionless number with a value between 0 and 1. This value can be multiplied by 100 and so we can speak about percentages. The efficiency of a process is defined as: 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑜𝑜𝑜𝑜𝑜𝑜 𝜂𝜂 = 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑖𝑖𝑖𝑖 The work done by a force F is the product of the intensity of the component of the parallel force, at displacing, to the displacement. In the International System, the work is measured in Newton meter [N·m]. This unit is the Joule [J], which is defined as the work done by a force of one Newton, acting on a distance of one meter. 01.04.2020 Ed2 Pag. 46  Module 02 – Physics Power The power is the work done in the unit quantity of time. Knowing that the work is the product of the force to the displacement, it is possible to give another definition to the power often very useful. The power necessary to a force to make a body move in a constant velocity is equal to the product of force to velocity: 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 ∗ 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 With the word machine, we identify all devices able to perform a work. The unit of measurements is W (Watt), or which other units can we find from formula? 01.04.2020 Ed2 Pag. 47  Module 02 – Physics Kinetic Energy The capacity to perform a work of a moving object is called, kinetic energy: 1 𝐸𝐸𝑘𝑘 = 𝑚𝑚𝑉𝑉 2 2 From kinetic energy relation follows that higher the velocity of an object is, bigger its kinetic energy will be, and also its capacity to do a work. That shows also that the kinetic energy increases at the mass object increasing. In the International System kinetic energy is expressed in Joule, like the work. In fact, the unit of the energy is the product of the unit of the mass to the square of the unit of the velocity. 01.04.2020 Ed2 Pag. 48  Module 02 – Physics Kinetic Energy As already seen, an object falling from a certain height performs a work, because weight force and displacement have the same direction. To do a work every object must have energy. In this case, it’s not kinetic but potential energy. Generally, an object put at a certain height, has a potential energy caused by its position. The potential gravitational energy can be written as follows: 𝐸𝐸𝑝𝑝 = 𝑚𝑚𝑚𝑚𝑚 The unit of measurement of potential energy is the Joule, the same as for work and energy. 01.04.2020 Ed2 Pag. 49  Module 02 – Physics Kinetic Energy An object standstill at a certain height from the ground, has high potential energy and zero kinetic energy. During the fall, the potential energy decreases and the kinetic one increases. We can prove that during the movement of an object, the sum of kinetic and potential energy remains constant. The sum of kinetic energy and potential energy of a body is called MECHANICAL ENERGY. Like all the energies, the mechanical energy is measured in joule [J]. 01.04.2020 Ed2 Pag. 50  Module 02 – Physics Law of dynamics: first law If a body is in rest and all forces acting on it have a resultant equal to zero, the body will be standstill and if it has a uniform motion, will keep its motion. The first law of dynamics is called also law of inertia. Inertia is the property of the body which determines its resistance to accelerate when subjected to a force. 01.04.2020 Ed2 Pag. 51  Module 02 – Physics Law of dynamics: second law Experimentally it is possible to verify that the force applied and the acceleration generated are directly proportional. Instead, keeping the force constant and varying the mass of the body, the acceleration generated will result inversely proportional to the mass of the object. We can than say that the force is proportional to the acceleration, with constant of proportionality m (mass): 𝐹𝐹 = 𝑚𝑚𝑚𝑚 01.04.2020 Ed2 Pag. 52  Module 02 – Physics Law of dynamics: third law The third law of dynamics says that to every action corresponds always an equal and opposite reaction. So mutual actions between bodies are always equal and directed to the contrary. 01.04.2020 Ed2 Pag. 53  Module 02 – Physics Impulse The second principle of dynamics, replacing acceleration with average acceleration definition, can be written: Δ𝑉𝑉 𝐹𝐹 = 𝑚𝑚𝑚𝑚 = 𝑚𝑚 Δ𝑡𝑡 From this formula it can deduce: 𝐹𝐹Δ𝑡𝑡 = 𝑚𝑚Δ𝑉𝑉 Taking into account both force and time interval, another magnitude can be considered: the IMPULSE OF THE FORCE. 𝐼𝐼 = 𝐹𝐹Δ𝑡𝑡 01.04.2020 Ed2 Pag. 54  Module 02 – Physics Momentum The momentum of a body is the product of the mass to the velocity. It is indicated with the letter P: 𝑚𝑚 𝑝𝑝 = 𝑚𝑚𝑚𝑚 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑜𝑜𝑜𝑜 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑘𝑘𝑘𝑘 ∗ 𝑠𝑠 Considering the following relation: 𝐼𝐼 = 𝐹𝐹Δ𝑡𝑡 = 𝑚𝑚Δ𝑉𝑉 = 𝑚𝑚 𝑉𝑉𝑓𝑓 − 𝑉𝑉𝑖𝑖 Follows the law of impulse: 𝐼𝐼 = Δ𝑝𝑝 = 𝑝𝑝𝑓𝑓 − 𝑝𝑝𝑖𝑖 The impulse of an applied force during a time interval is equal to the momentum variation of the body during the same time interval. 01.04.2020 Ed2 Pag. 55  Module 02 – Physics Conservation of Momentum When two or more bodies act upon one another, their total momentum remains constant, provided no external forces are acting upon them. This can be explained by watching to bodies collide. Each ball has its own momentum before the collision. After the collision, the sum of the two balls’ momentum will be the same as the sum prior to the collision even though their velocities may have changed. Example: The gyroscopic wheel. Considering the axis x as the gyroscopic rotation axis, if an applied torque causes a rotation about the axis y, the wheel will react with a rotation about the axis z. 01.04.2020 Ed2 Pag. 56  Module 02 – Physics Friction The friction is a dissipative force existing between two surfaces in contact and contrasting their relative motion. These are mainly interaction forces between atoms of the materials in contact. Up to the classical interpretation, three different kinds of friction exist: THE SLIDING FRICTION: it is caused by the sliding between two plane surfaces THE ROLLING FRICTION: it is caused by the rolling on curve surfaces THE FLUID FRICTION: that is relative to a body immersed into a fluid or to different layers of the same fluid moving with a different velocity. 01.04.2020 Ed2 Pag. 57  Module 02 – Physics Friction The friction can be static or dynamic. It takes a greater force to start two surfaces sliding (static friction) than it takes to keep them sliding once they are moving (dynamic friction). Kinetic friction is always smaller or equal to the static friction. If we exert a force on a block placed on a horizontal surface, the block initially will resist sliding as the horizontal force increased. This means there is an equal and opposite force opposing the horizontal pull force. This is the force of friction, it is a static friction. If we increase the force, a point is reached where the block will just break free. The value of the pull force at which this happens is called Limiting Friction. 01.04.2020 Ed2 Pag. 58  Module 02 – Physics Rolling Friction The rolling friction occurs when a cylindrical body or a wheel rolls without creeping on a certain surface. The rolling is possible thanks to the sliding friction between the wheel and the ground. The rolling friction is caused especially by the friction of the rotation axis of the wheel, and the contact area between the wheel and the ground: 𝐹𝐹𝑣𝑣 = 𝜇𝜇𝑣𝑣 𝐹𝐹𝑛𝑛 01.04.2020 Ed2 Pag. 59  Module 02 – Physics Density The absolute density of a body, often indicated with ρ, is equal to its mass on the volume. If m is the mass and V is the volume, we have: 𝑚𝑚 𝜌𝜌 = 𝑉𝑉 In the international system the density unit is kilogram per cubic meter [Kg /m3]. The water has a reference density of 1000 kg/m³. 01.04.2020 Ed2 Pag. 60  Module 02 – Physics Relative Density The relative density is defined as the ratio of the density of the body in object to the distilled water at 4 °Celsius. 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑜𝑜𝑜𝑜 𝑡𝑡𝑡𝑡𝑡 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑚𝑚𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝛿𝛿 = = 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑜𝑜𝑜𝑜 𝐻𝐻2 𝑂𝑂 𝑚𝑚𝑠𝑠 To find out the relative density of the fluids, some appropriate instruments, called densimeters, are used. 01.04.2020 Ed2 Pag. 61  Module 02 – Physics Density of air The density of the air at sea level is 1.225 kg/m3 when the air temperature is 15°C and the pressure is 101.3 kPa. The air density reduce as the altitude increases. The air density is affected by temperature and pressure. It is proportional to air pressure and inversely proportional to air temperature: 𝑃𝑃𝑃𝑃 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑎𝑎𝑎𝑎𝑎𝑎 𝑇𝑇 01.04.2020 Ed2 Pag. 62  Module 02 – Physics Specific Weight The absolute specific weight is defined as the ratio of the weight of a sample material to its volume: 𝑊𝑊 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 = 𝑉𝑉 In the International System the unit of measurement is the Newton per cubic meter [N/m3]. The relative specific weight is indicated as γ, and is defined as the ratio of the body weight, to the weight of distilled water, at 4°C, of same volume: 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑊𝑊 𝑚𝑚 𝑌𝑌 = = ⟹ 𝑌𝑌 = = 𝛿𝛿 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑜𝑜𝑜𝑜 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑊𝑊𝐴𝐴 𝑚𝑚𝐴𝐴 01.04.2020 Ed2 Pag. 63  Module 02 – Physics Fluids: Viscosity and Fluid resistance The viscosity is a propriety of fluids that indicates the resistance to the sliding. It depends on the type of the fluid and on the temperature. Liquid decrease when T increase, gas instead has an opposite behavior. The viscosity is usually indicated by μ. In fluid dynamics, drag (or fluid resistance) indicates the forces that oppose the relative motion of an object through a fluid. The drag acts in an opposite direction in relation to the flow velocity. Unlike other resistive forces such as dry friction, which is nearly independent of velocity, drag forces depend on velocity. Profile drag is the sum of the form drag (due to the shape of the object) and the skin drag. 01.04.2020 Ed2 Pag. 64  Module 02 – Physics Bernoulli’s theorem According to this principle, the sum of static pressure 𝑝𝑝𝑠𝑠 and dynamic pressure 𝑝𝑝𝑑𝑑 is constant in any point of the motion field. 1 2 𝑝𝑝𝑑𝑑 + 𝑝𝑝𝑠𝑠 = 𝜌𝜌𝑉𝑉 + 𝑝𝑝𝑠𝑠 = 𝑝𝑝𝑡𝑡 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 2 Known static pressure and total one, is possible to calculate the dynamic pressure (the density is known from the altitude) and, consequently, is possible to determine the value of flight speed through a mathematical formula: 2 𝑝𝑝𝑡𝑡 − 𝑝𝑝𝑠𝑠 𝑉𝑉 = 𝜌𝜌 01.04.2020 Ed2 Pag. 65  Module 02 – Physics Venturi’s tube The Venturi effect, is the pressure increase of a fluid flow, at the velocity reduction. The experiment shows that the liquid reaches different levels in tubes: a lower one where the section becomes thinner while the velocity is high, and a higher level where the section enlarges and the velocity slowdowns. 01.04.2020 Ed2 Pag. 66  Module 02 – Physics Chapter 02.03 THERMODYNAMICS 01.04.2020 Ed2 Pag. 67  Module 02 – Physics Temperature In physics, the temperature is the property that characterizes the thermal state of two systems in relation to the direction of heat flow that is established between them. When two systems are in thermal equilibrium and there isn't any transfer of heat is said to have the same temperature. When there is a difference in temperature the heat will tend to move from system we called of higher temperature to the one of lower temperature, up to reach the thermal equilibrium. 01.04.2020 Ed2 Pag. 68  Module 02 – Physics Temperature KELVIN SCALE The basic unit of temperature in the International System is Kelvin [K]. A Kelvin is formally defined as 1 to 273.15 CELSIUS SCALE On daily applications, is often convenient to use the Celsius scale, or centigrade scale, in which 0° C is the melting point of ice and 100° C is at the boiling point of water at sea level. FARHENHEIT SCALE On this scale the freezing point of water corresponds to 32°F and the boiling point of water is 212° F. 01.04.2020 Ed2 Pag. 69  Module 02 – Physics Temperature: conversion factors 9 From Centigrade to Fahrenheit °𝐹𝐹 = °𝐶𝐶 ∗ + 32 5 5 From Fahrenheit to Centigrade °𝐶𝐶 = °𝐹𝐹 − 32 ∗ 9 From Centigrade to Kelvin K = °𝐶𝐶 + 273,15 01.04.2020 Ed2 Pag. 70  Module 02 – Physics Heat transfer The heat transfer is the phenomenon that occurs when the thermal energy passes through the matter for effect of a gradient of temperature. The gradient of temperature is the pushing force that permits the transition of thermal energy from a hotter object to a cooler one. RADIATION: The radiation doesn’t allow the direct contact and it doesn’t require a medium to propagate. The radiation happens as electromagnetic waves. CONVECTION: The convection happens when there is a convective movement connected to a thermal transfer. The convective movement is a type of transport caused by a gradient of pressure and by the force of gravity. This movement is absent in solids. CONDUCTION: The conduction is the thermal transfer that happens for contact. 01.04.2020 Ed2 Pag. 71  Module 02 – Physics Heat The heat is the macroscopic form of the energy, when passing from a physical system to another, due to temperature difference. The heat is measured in Joule [J], in the International System. In practice, the calorie is still often used as the unit of measure. Sometimes very technical units are used, like kWh o BTU. It’s important to remember that the temperature is not the measure of the heat. 01.04.2020 Ed2 Pag. 72  Module 02 – Physics Heat The specific heat is the quantity of heat necessary to increase of 1 K (or 1°C) the temperature of a unit quantity (1 Kg or 1 g) of a substance. In the International System, the unit of measurement of the specific heat is: 𝐽𝐽 𝑘𝑘𝑘𝑘 ∗ 𝐾𝐾 The heat capacity is the measure of the heat energy required to increase of 1°C (or 1 K) the temperature of an object: ∆𝐸𝐸 𝐶𝐶 = 𝑚𝑚𝑚𝑚 = ∆𝑇𝑇 𝐽𝐽 In the International System, the unit of measurement of the heat capacity is 𝐾𝐾 01.04.2020 Ed2 Pag. 73  Module 02 – Physics Themodynamics’ law FIRST LAW OF THERMODYNAMICS The first law of thermodynamics is the following: if the system does a transformation from state A to state B and it exchanges heat (Q) and work (W) with the environment, these parameters depend on the transformation joining the two thermodynamic states. Instead, the difference (Q – W) is independent from the transformation. 𝑄𝑄 − 𝑊𝑊 = ∆𝑈𝑈 Where U is the internal energy of the system. 01.04.2020 Ed2 Pag. 74  Module 02 – Physics Themodynamics’ law SECOND LAW OF THERMODYNAMICS The second law of thermodynamics can be resumed in two theorems: It’s impossible to realize a process that has, as unique result, the transformation in work of a heat of a source at uniform temperature. It’s impossible to realize a process that has, as unique result, the transfer of heat quantity from a body to another with higher temperature. 01.04.2020 Ed2 Pag. 75  Module 02 – Physics Gas There are three fundamental relationship that exist between the volume, pressure and temperature of a gas: Boyle’s Law: establishes the relationship between volume and pressure at a constant temperature (Isothermal transformation). Charles’ Law: establishes the relationship between volume and temperature at a constant pressure (Isobaric transformation). Pressure Law: establishes the relationship between pressure and temperature at a constant volume (Isochoric transformation). Adiabatic process is a process where no heat is absorbed or given out from the system. 01.04.2020 Ed2 Pag. 76  Module 02 – Physics Perfect Gas An ideal gas is a model of gas for which the laws of perfect gas are admitted: 𝑝𝑝𝑝𝑝 = 𝑛𝑛𝑛𝑛𝑛𝑛 where P is the pressure, V is the volume, n is the number of mole, R is the constant of perfect gas and T is the temperature. The fundamental proprieties of a perfect gas are: The molecules are as points. The interactions, between the gas and the container side, are total elastics. There aren’t distance interaction forces between molecules. The molecules are all identical. The gas cannot be liquefied only by compression. The specific heat is constant, while in the case of real gasses, it changes according to the temperature. 01.04.2020 Ed2 Pag. 77  Module 02 – Physics Gases In mechanics the work done by a constant force F, which produces a displacement ΔS of the body, is defined as: 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 = 𝐹𝐹 ∗ 𝑠𝑠 If we want to calculate the work done by a gas during an expansion, we must use: 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 = 𝑃𝑃 ∗ ∆𝑉𝑉 Derived using this logic process: 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 = 𝐹𝐹 ∗ 𝑠𝑠 = 𝑃𝑃 ∗ 𝐴𝐴𝐴𝐴 = 𝑃𝑃∆𝑉𝑉 01.04.2020 Ed2 Pag. 78  Module 02 – Physics Cycle of Operation A closed system may pass through a series of process and return to its initial state when it is said to have passed through a cycle. The processes through which the system has passed may be shown on a state diagram. When a closed system goes through a cycle, the sum of the heat energy taken in is equal to the work put out and any heat wasted. 01.04.2020 Ed2 Pag. 79  Module 02 – Physics Chapter 02.04 OPTICS (LIGHT) 01.04.2020 Ed2 Pag. 80  Module 02 – Physics Light The definition of lights nature was always a fundamental problem for physics. The mathematician Newton suggested a corpuscle model: he considered the light as composed by beams of particles that are produced by luminous bodies. The astronomer Huygens attributed to the light an undulating nature and he explained the propagation with laws of undulating motion. Nowadays these theories are complementary: the quantum mechanics shows that the light follows alternatively undulating and corpuscle behaviors. 01.04.2020 Ed2 Pag. 81  Module 02 – Physics Light Lights consists of minute packets of energy called Photons. Lights is a part of the Electromagnetic Spectrum occupying a narrow frequency band between infra red at 1014 Hz and ultra violet at 1015 Hz. 01.04.2020 Ed2 Pag. 82  Module 02 – Physics Light The light has an ended velocity and so it doesn’t outright spread. The velocity of light propagation (c) is 300000 Km/s in the empty space. When the light passes through a transparent substance, as the water and the glass, its velocity (c) reduces according to the refraction coefficient: in the empty space it is 1, while in the matter its value is bigger. The refraction coefficient of the air is very close to 1, so we can assume light speed in air very close to the speed in empty space. 01.04.2020 Ed2 Pag. 83  Module 02 – Physics Law of refraction, reflection A ray of light, striking a reflecting surface, is called an Incident Ray. The light ray reflecting off the surface is called the Reflected Ray. The angle between the incident ray and line drawn perpendicular to the reflecting surface is known as the Angle of Incidence. The angle between the reflected ray and a line drawn perpendicular to the reflecting surface is called the Angle of Reflection. 01.04.2020 Ed2 Pag. 84  Module 02 – Physics Law of refraction, reflection The reflection is an optical phenomenon that happens when the light hits a body. The two main laws of reflection are, for smooth and rough reflection surfaces: The incident ray and the reflected ray are on the same plane. The angle of incidence is equal to the angle of reflection. 01.04.2020 Ed2 Pag. 85  Module 02 – Physics Refraction 𝑚𝑚 The speed of light in a vacuum is 3 ∗ 108 but this reduces slightly as light 𝑠𝑠 passes into medium. This change in velocity causes the light to alter direction as it enters or leaves mediums, the change of direction is called Refraction. The angle between an incident light ray and a line drawn at right angles to the surface which we call, the normal, is the Angle of Incidence. The angle between the refracted light ray and the normal is known as the Angle of Refraction. Lower refractive index will be increasing the speed. 01.04.2020 Ed2 Pag. 86  Module 02 – Physics Refraction The reflective angle is higher than the refractive angle when the refractive index of the second middle is higher than the first one. 01.04.2020 Ed2 Pag. 87  Module 02 – Physics Refraction During the passage between two different mediums, the light beam breaks itself into two different rays: one is reflected and the other is refracted. The angle of refraction (φ2) is less than that of incidence (φ1). The ratio between the coefficient of refraction of the second substance (n2) to the coefficient of the first one (n1) is equal to the ratio of the sine of incidence angle to the sine of refracted angle (Snell’s Law): 𝑛𝑛2 sin 𝜙𝜙1 = 𝑛𝑛1 sin 𝜙𝜙2 01.04.2020 Ed2 Pag. 88  Module 02 – Physics Fiber Optics Optical fiber are strands of very pure silica glass that are thinner than a human hair. Using total internal reflection they receive and transmit light by reflecting it millions of times through the fiber with minimum attenuation or loss of intensity. The high frequency range of light makes it possible to simultaneously transmit huge amounts of digital information along a fiber. Ideally, light would enter the end of a glass fibre at 90° to the end surface and travel straight through it. If the glass were of very high purity, little intensity would be lost. Parameters to be considered regarding optical fibers are: diameter, coefficients of refraction, material. The great advantage is that they are not affected by the electromagnetic interference. 01.04.2020 Ed2 Pag. 89  Module 02 – Physics Fiber Optics A fiber optic consists of three main parts: 1. the core 2. the cladding 3. the jacket 01.04.2020 Ed2 Pag. 90  Module 02 – Physics Fiber Optics The core is the optical fibre and it is made from high purity silica glass or sometimes, plastic. The cladding is a dielectric material. This has a lower refractive index than the core. The cladding is used to: reduce loss of light from the core. reduce light scatter at the surface of the core. protect the fibre core from contamination. strengthen the cable. The jacket is the elastic covering that prevents abrasion of the core and cladding. It also stiffens the cable sufficiently to avoid the formation of mircobends when the cable runs over uneven surface. 01.04.2020 Ed2 Pag. 91  Module 02 – Physics Fiber Optics Fiber optics are classified in 2 types: Fibers which support many propagation of light propagation. (multi-mode fibers). Fibers which support only support a single mode of light propagation. (single-mode fibers). Technical differences between the first and the second type are essentially the fiber diameter and achievable performances. In single-mode fibers lights rays must be spread along the longitudinal axis of the fiber without important phenomena of reflection. The dispersion, due to refraction phenomena, is extremely reduced. In the single-mode fibers the core diameter is 9 μm and the cladding diameter is 125 μm. 01.04.2020 Ed2 Pag. 92  Module 02 – Physics Chapter 02.04 WAVE MOTION AND SOUND 01.04.2020 Ed2 Pag. 93  Module 02 – Physics Wave A wave is a perturbation, that spreading in the space, transports energy. Waves are originated by a source that produces a perturbation in the surrounding space. There are several types of waves: In the TRANSVERSAL WAVES the particles of the medium fluctuates perpendicularly to the propagation direction of the wave. In the LONGITUDINAL WAVES the particles of the medium fluctuates in the same direction of the wave propagation. 01.04.2020 Ed2 Pag. 94  Module 02 – Physics Fiber Optics A periodic wave is born by a point that pulse with periodic motion and it uses a period (T) to do a completely oscillation. The distance between two next peaks is called the length of the wave (λ). Amplitude is defined as the maximum displacement. 𝜆𝜆 The velocity (c), at which the wave is moving, is: 𝑐𝑐 = 𝑇𝑇 01.04.2020 Ed2 Pag. 95  Module 02 – Physics Interference Consider a wall with more than one opening, the waves will emerge through each gap with circular shape. Each radiating circular pattern will run across the neighbouring patterns. This is an example of interference phenomena. 01.04.2020 Ed2 Pag. 96  Module 02 – Physics Interference The interference is due to the superimposition of two or more waves There are two extreme cases: The waves have concordant phases: the generated wave has amplitude equal to the sum of single amplitudes. It’s a constructive interference case and the phase displacement is null. The waves have opposite phases and so they are completely void. It’s the destructive interference and the phase displacement is π. 01.04.2020 Ed2 Pag. 97  Module 02 – Physics Sound The sound is the sensation caused by the vibration of an oscillating body. Since the sound is an oscillating perturbation, the number of ripple in a second is called frequency (f) and it is measured by Hertz [Hz]. 1 𝑓𝑓 = 𝑇𝑇 The length of a wave indicates the space done by a wave in a complete period of oscillation (T) 𝑐𝑐 𝐿𝐿 = 𝜆𝜆 = 𝑐𝑐 ∗ 𝑇𝑇 = 𝑓𝑓 01.04.2020 Ed2 Pag. 98  Module 02 – Physics Sound In the formula: 𝑐𝑐 𝐿𝐿 = 𝜆𝜆 = 𝑐𝑐 ∗ 𝑇𝑇 = 𝑓𝑓 c is the speed of sound in the air (about 343 m/s on ground). The speed of sound is the speed at which the sound spreads in a specific substance. It varies according to the medium, substance proprieties and temperature. For example the speed sound is higher in the water than in the air. The sound spreads in different way according if the medium is a solid, a liquid or a gas. 01.04.2020 Ed2 Pag. 99  Module 02 – Physics Doppler Effect The Doppler effects is an apparent variation of the frequency or of the wave length. For example we can study the siren of an ambulance: It is heard higher than the effective sound while the vehicle goes towards the observed The sound seems lower when the ambulance moves away from the observed. 01.04.2020 Ed2 Pag. 100 Thank you for your attention. Pag.