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Definitions Topic 2 1. Distance is a scalar ( magnitude only) quantity and is the total distance of the path taken and depends on the path taken. Displacement is vector quantity ( direction and magnitude) and is a measure of the net distance traveled and does not depend on the path taken. Scalar quantities only measure magnitude. For example: You are going 40 km/ h. Vector quantities have both magnitude (“how much” or “how big”) and direction . 2. Speed is a scalar quantity and equal to total distance over time : v = s t 3. Velocity is a vector quantity and equals total displacement over time : v = Δs Δt 4. Free Fall 1 5. Newton’s Laws of Motion NEWTON’S FIRST LAW OF MOTION An object at rest tends to stay at rest and an object in motion tends to remain in motion with constant velocity, unless acted on by an unbalanced force (a non-zero net force). OR If the net force acting on a body is equal to zero, the body will move with constant velocity and zero acceleration. NEWTON’S SECOND LAW The acceleration of an object is directly proportional to the net external force acting on it and is inversely proportional to its mass. The direction of acceleration is in the same direction as the net force acting on the object NEWTON’S THIRD LAW Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. OR If body A exerts a force on body B (an “action”) then body B exerts an equal and opposite force on body A (a “reaction”). These two forces have the same magnitude but opposite direction. 2 6. Translational equilibrium occurs when a body is not accelerating. That is, the net force acting on the body is zero. 7. Inertia : The tendency of a body to maintain its state of rest or in uniform motion in a straight line is called inertia. Hence Newton’s First Law is often called the law of inertia. 8. The contact force that acts perpendicular to a common surface of contact is usually referred to as the Normal Force (‘normal’ means perpendicular) and labeled F or FN in diagrams. 9. Change in momentum based on force and time is called impulse. Impulse changes momentum in much the same way that force changes velocity causing acceleration. Formulas - Units Linear momentum ( p) is defined as the product of an object’s mass and its velocity. p mv (Linear momentum defined) 10. ELASTIC COLLISIONS Net momentum before collision = Net momentum after collision Total Kinetic Energy is conserved. Law of Conservation of Momentum and Collisions The total momentum of an isolated system of bodies remains constant (i.e. when no external forces act on a system, the total momentum of the system stays the same). pbefore p after 3 11. Inelastic Collisions In an inelastic collision KE is conserved. The law of conservation of energy still holds true. Completely Inelastic Collision ( v v A vB ) A completely inelastic collision is a collision where the two bodies stick and move together as one after the collision. e.g. a bullet imbedding itself in wood. mAu A mBuB mA mB v (Completely inelastic collision) NOTE: FORMULA NOT IN DATA 12. Work in physics is given a very specific meaning to describe what is accomplished by the action of a force when it acts on an object as the object moves through a distance. Work is defined to be the product of displacement and the component of the force parallel to the displacement. When a constant force acts in the same direction as displacement the work done by the force is: Work = Force x Displacement W Fs 13. Work due to gravity is independent of path followed = mgh Work done BY gravity on an object that is moving horizontally ( by another force), is zero because the angle at which gravity acts is completely vertical with no horizontal component i e perpendicular to the displacement, ( 90 0 ) . 4 14. Energy is one of the most important concepts in science. By definition , energy is the ability to do work. Kinetic energy is the energy of motion. The work – energy theorem relates the work done on an object to the kinetic energy ( K) of that object: The net work done on an object by all forces acting on it is equal to the change in kinetic energy of the object. W = ΔEk CHANGE in Ek ( unit: Joules J = N m) 15. Kinetic Energy * Brainpop: Kinetic Energy Kinetic energy is the energy associated with a body in motion. Kinetic Energy is: 1 2 p2 E mv 2 2m ( E k Kinetic Energy defined) Note: 16. Potential Energy (Stored Energy) * Potential Energy is energy associated with the position of a system (not its motion). There are three types of potential energy: Gravitational potential energy (PE of a diver is converted into KE as she falls). Elastic potential energy (energy stored in the diving board as the diver jumps on it or energy stored in a compressed spring). Electrical potential energy (covered later). 5 17. Gravitational Potential Energy Gravitational potential energy is defined as the energy a body has because of its height relative to a given point. EP = mgh ( mgy ) (Gravitational potential energy defined) Gravitational Potential Energy Difference Experimentally we can only quantify changes in potential energy. Gravitational potential energy difference is defined as the work that must be done by an external force to move an object through a vertical displacement Δh. The work done by the external force is stored as potential energy. Δ EP = mg Δh (Gravitational potential energy difference) Conservation of Energy is one of the most important laws in Physics.: Energy can not be created or destroyed; it may be transformed from one form into another, but the total amount of energy of a system never changes. 18. The work- energy theorem applies to changes in kinetic and potential energy that can also be used to explain changes in thermal, mechanical , electrical and nuclear energy as well. It is important to understand how energy changes or transforms form one form to another or from one location to another. Drawing: Conservation of Mechanical Energy is: E Ek Ep = Constant (Mechanical energy is conserved when only gravity does work) For example, when a ball is thrown vertically Ek is converted to Ep; and on the way down Ep is converted back to Ek. But E is always constant (provided only gravity does work i.e. no air resistance 6 19. Power * Brainpop: Power Definition of work has no reference to time but it is often necessary to know how quickly work can be done. Power is defined as the rate at which work is performed. Power = work (or energy) time P=W t Note: Power is a scalar quantity. 20. Efficiency Efficiency is defined as the amount of useful work performed per amount of available energy. Efficiency Usefuloutput Efficiency = Power output Totalinput 21. The centripetal acceleration ( ac ) of an object in uniform circular motion is NOT in the same direction as the tangential velocity vector. If it were, the object would accelerate and motion would not be uniform. Therefore, centripetal acceleration is a good example of how you can cause acceleration just by changing direction without changing speed. As a matter of fact, the centripetal acceleration is directed towards the center. This centripetal force ( Fc causing the acceleration) causes the velocity vector to continuously change direction thereby maintaining uniform circular motion. The centripetal force is always perpendicular to the direction of motion and does no work. Therefore, there is no change in kinetic energy and no change in speed (energy-work theorem) but a change in velocity. If there were no centripetal force the object would move in a straight line. 7 22. Newton’s Universal Law of Gravitation Every point mass of matter in the universe attracts every other point mass with a force that is proportional to the product of the masses of the two particles and inversely proportional to the square of the distance between them. Translating this into an equation, we have: Fg GMm r2 (Newton’s Universal Law of Gravitation) Point mass assumption: If the separation between the two objects is large compared to their radii we can treat spherical objects as point masses particles with all their mass concentrated at the center (Figure 12-2 Young and Freedman 2000 p.359) and r = distance between the two centers of the spheres. Gravitational forces always act along a line joining the two particles (Figure 12-1 Young and freedman 2000; 359). Even when the masses of the two particles are different, the two interacting forces have equal magnitude (and form an action-reaction pair Newton’s 3rd Law). Don’t confuse g with G. ^ CP DVD - Jolly’s Method of measuring of G 8 23. Gravitational field strength ( g) and gravitational force (F) definition : Physicists wondered how a mass knows the presence of another mass nearby that will attract it. They developed the idea of a gravitational field. A mass M is said to create a gravitational field in the space around it. This means that when another mass ( m) is placed at some point near M it feels the gravitational field. The gravitational field strength ( g) at a certain point is the force per unit mass ( F/m) experienced by a small point mass m…. at that point : g= F m = g = GM R2 9 10 TOPIC 3 1. Temperature is a measure of the ‘hotness’ (or ‘coldness’) of a substance. More specifically, it is a measure of the average kinetic energy of individual atoms and/or molecules. To measure temperature we need a property that changes as the ‘hotness’ changes. The most commonly used property is linear expansion e.g. mercury (or alcohol) thermometer. 2. Internal Energy The internal energy is the total kinetic energy of the molecules, plus any potential energy between the molecules. The kinetic energy of the molecules arises from their random translational (linear) and rotational motion. The potential energy arises from the forces between the molecules. Discuss pushing a block along a rough horizontal surface at constant velocity (Hamper and Ord 2007; 52-53). Is any work being done on the block? Is the KE or PE increasing? Where is the energy going? 3. Thermal Energy (Heat) * Brainpop: Heat Thermal energy (or heat) is energy that is transferred from one body to another because of a difference in temperature. Heat always flows from hot to cold, never in the reverse. Heat continues to flow from the warmer object to the cooler object until they reach thermal equilibrium. Heat is transferred by three methods: conduction, convection, and radiation. Thermal equilibrium is reached when two bodies are at the same temperature 11 4. Specific Heat Capacity Thermal Capacity If heat is added to an object its temperature rises, but the actual increase in temperature depends on the materials that make up the object. Thermal capacity (C) is defined as the amount of thermal energy (heat) required to raise the temperature of an object by 1K (1Cº). Units: [J K-1 = J Cº -1]. C Q T (Thermal capacity ) Calorimetry I: Specific Heat Capacity The amount of heat Q required to change the temperature of a given material is proportional to the mass m of the material and to the temperature change T. Q mcT Specific heat capacity ( c) is defined as the amount of thermal energy (heat) required to raise the temperature of 1kg of a substance by 1K (1Cº). Specific heat capacity c is an intrinsic/characteristic property of the substance. SI unit: [J kg-1 K-1] c Q mT ( Specific Heat Capacity ) Note: 12 5. Phase change During a phase change additional heat energy is used to overcome forces between the molecules. When matter changes state energy is needed to enable the molecules to move more freely and thus molecules gain potential energy. The kinetic energy, and hence the temperature, remains the same. After all the substance has been melted/vaporized the temperature will rise again with additional heat input. Calorimetry II: Specific Latent Heat Specific Latent Heat of Fusion (Lf) is the heat required to change 1kg of a substance from solid to liquid. Specific Latent Heat of Vaporization (Lv) is the heat required to change 1kg of a substance from liquid to vapor. Specific latent heat is an intrinsic property of the substance 6. Evaporation Molecules of a liquid move about with various random speeds (and kinetic energies). The faster, and hence more energetic molecules, can escape the surface of the liquid and become a gas. This phenomenon is known as evaporation. While boiling occurs throughout the liquid, evaporation only occurs at the surface. The average kinetic energy of the molecules left behind, and hence the temperature of the liquid, is reduced. Evaporation occurs at temperatures lower than the boiling point and the values of latent heat increases slightly with a decrease in temperature. For example at 20°C, Levap for water is 2.45 x 106 J/kg compared to 2.26 x 106 J/kg for Lv at 100°C. The rate of evaporation (i.e. the number of molecules escaping per unit time) can be increased by: increasing the surface area (more molecules near the surface increases the chance to escape); increasing the temperature of the liquid (more KE enables more molecules to escape); increasing airflow above the liquid (removing escaped molecules allows more to escape). Does not depend on depth of liquid because evaporation basically occurs at the surface 13 7. The Kinetic Model for an Ideal Gas This model makes assumptions about the molecules of a gas, which reflect a simple view of a gas, but nonetheless correspond well (i.e. allows for accurate, verifiable predictions) to the essential features of a real gas at low pressure and far from liquefaction (condensation) point. The assumptions are summarized by the following four points: There are large numbers of molecules N, each with mass m, moving in random directions at a variety of speeds; The molecules are spread out, such that their average separation is much greater than the average diameter of each molecule, hence the volume of the molecules is negligible compared with the volume of the gas itself; The molecules only interact with and exert forces on each other when they collide, therefore molecules move with constant velocity between collisions; ADD: the forces are only important when the molecules are colliding Collisions with each other and the walls of the container are assumed to be perfectly elastic (i.e. momentum and kinetic energy are both conserved). 8. Gas Pressure is defined as the force per unit area exerted on the walls of the container ( note : not between gas particles) as a result of particle collisions with the walls. The force exerted by molecules is equal to the rate of change in momentum F = p/Δt (true form of Newton’s 2nd Law) [Figure 13-6(b) (Giancoli 2005; 368)]. P F p t mv A A At (Gas P is proportional to v and inversely proportional t) Hence, the pressure exerted by a gas is proportional to the speed of gas molecules and the frequency of collisions. Hence, Gas pressure is inversely proportional to the time between collisions. Note: Collisions between gas particles do not affect the pressure. 14 TOPIC 4 and 11 ( SL Option A) Oscillations and Waves 1. Oscillations are essentially any motion that moves back and forth repetitively. Oscillations can also be referred to as waves, cycles or vibrations. 2. SIMPLE HARMONIC MOTION takes place when an object ( particle) that is disturbed away from its fixed equilibrium position experiences an acceleration and force that is proportional and OPPOSITE to its displacement. In general to check whether SHM will take place we must check that : 1. There is a fixed equilibrium position 2. Acceleration and force must be opposite and directly proportional to displacement : a ~ -x 3. Period (T) is the amount of time it takes to complete one cycle or one oscillation , wave or vibration . [SI Unit: s]. Frequency (f) = number of cycles , oscillations, vibrations or waves per second [SI unit: Hz = s-1]. 4. Displacement (x) and Amplitude (A or x0) Displacement (x) is the net distance from the equilibrium point. It can be positive or negative depending on the chosen coordinate system. Amplitude (A or x0) is the maximum displacement from equilibrium 5. Angular frequency (ω) is a scalar measure of the angular rate of rotation. Angular frequency is found by multiplying the frequency by 2π [SI unit: s-1]. 2 T 2 f Angular frequency (ω) add s-1 = Hz 15 6. Damping SHM is an important motion to study when considering oscillations but it does not consider friction and other resistance forces. The effect of these forces on an oscillating system is that the oscillations will eventually stop and the energy of the system will be dissipated mainly as thermal energy to the environment and the system itself. Oscillations taking place in the presence of resistance forces are called damped oscillations. The behavior of the system depends on the degree of damping. There are three different types of damping: 2. Under-damping 3. Critical damping 4. Over –damping 7. Resonance - frequency of external force is equal to natural frequency of the system. This results in oscillations with large amplitudes. Fig 1.20 p.208 Bridge video 16 8. Definition of a wave : a wave is a disturbance that travels in a medium transferring energy and momentum from one place to another. The direction of energy transfer is the direction of propagation of the wave. Examples: Sound is a type of wave called a longitudinal wave that travels through the medium air. The energy vibrates parallel to the direction of propagation of the wave. Light is a type of electromagnetic wave called a transverse wave, that travels through a vacuum . The energy vibrates perpendicular to the 9. Refraction When waves strike a transparent surface part of it is reflected and part of it is transmitted where it is refracted. Refraction is the bending of waves when they pass from one medium to another. It occurs because the wave speed changes as it passes through different mediums (analogous to driving a car along the edge of the road: if one tire moves off the edge of the road into sand or thick mud it slows down, pulling the car off to the side of the road) In the diagrams below the wave is passing from a less dense medium to a more dense medium and so the wave slows down and bends or refracts. ADD: As wave travel to more dens medium wavelength, velocity and amplitude DECREASE BUT FREQUENCY DOESN’T CHANGE Normal Line of reference In diagram (b) the RAY is said to bend toward the normal when going from a less dense to a more dense material. add: The WAVE bends UP. 17 In diagram( b )below light is passing from water to air or more dense to less dense and the RAY bends away from the normal. The WAVE bends 10. Snell’s Law n1 sin θ1 = n2 sinθ2 Snell’s law explains the relationship between the angle of refraction ( θ ) of a light ray as it passes from one media to another . It allows you to determine the angle if the density of the substance is known as related to the index of refraction ( n). 11. Diffraction 12. Interference Open the following link http://www.physicsclassroom.com/Class/waves/ Define wave interference. Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium Distinguish between constructive and destructive interference. Constructive interference : the displacement of the two waves is in the same direction and is additive resulting in one over all larger displacement. 18 Destructive interference : the displacement of the two waves is in the opposite direction and is subtractive resulting in one over all smaller displacement or sometime zero displacement. 13. Polarization – property of transverse waves: a wave is polarized if the displacement of the wave always lies in the same plane. 14. Malus’s Law Malus’s Law describes the intensity of the polarized light after it passes through the polarizer . Basically the intensity of light decreases as the orientation – transmission axis of the polarizer changes. Light intensity is maximum when θ = 0º ( parallel) and zero when θ = 90º ( perpendicular). Figure 11.5-1 shows a graph of the relative light intensity of polarized light after it is transmitted through an analyzer that is oriented at different angles. According to Malus’s Law, light intensity follows a cos2θ shape as the axis of the analyzer is rotated. Light intensity is maximum when θ = 0º and zero when θ = 90º. See below : 19 15. Brewster's Law In 1812, Sir David Brewster found experimentally that, the reflected ray is 100% polarized when the angle between the refracted ray and the reflected ray is 90º. The angle of incidence, called the Brewster's or Polarizing angle θp, required for 100% polarization is determined by the refractive index of the two materials (using Snell's Law). θp + θr = 900 θr = 900 - θp If the ray is incident from air (n1 = 1.00), then: n tan p (Brewster's Law, Ray incident 20 TOPIC 5 – 6 – 12(HL only) Electromagnetism 16. Electromagnetism is one of the 4 fundamental forces of the universe along with gravity, the strong and weak nuclear forces. Electric force is much stronger than gravity. 17. Electricity is the phenomena associated with interaction between electrical charges. Electrostatics is the study of charged objects at rest. Electric charge is the fundamental property of matter based on the atom: e- , p + , and n 0 . Electric force is the force that keeps e- , p + , and n 0 together. The fundamental law of electricity is that opposite charges attract and like charges repel. 18. The electric field is a force field or vector field that allows one to determine the force (F) acting on a charge ( q): E=F q units : NC-1 19. Electric Potential Difference or Electric Potential – Voltage ( V) : Voltage also called emf ( electromotive force) ε – is the amount of work done per unit charge. Also defined as the change in electric potential energy per unit charge. 20. E = V / d Parallel Plates n the case of parallel plates the electric field is determined by E = V/ d where d is the distance between the plates. The electric field is uniform and has the same value at all points between the plates. Its direction is from high potential to low potential. Work done to move a charge is not uniform and depends on distance the charge moves : W = Eqd 21 21. The Electron Volt: A Unit of Energy The electron volt ( eV) is a unit of energy that can also be converted to joules ( J) 1 eV = 1.6 x 10-19 J NOT IN DATA BOOKLET TOPIC 7 – 13 Nuclear Physics/ Quantum Mechanics 22. The Electromagnetic Spectrum Visible light is part of the electromagnetic spectrum which are waves of energy that are produced by one of the major forces in the universe called electromagnetism 23. The Dual Nature of Light The wave-particle nature of light states that light can travel as waves or as tiny packets of energy called photons or quanta. So , energy can be quantitized. The energy of a photon is given by E = hf where h is Planck’s constant = 6.626x10-34 Js and v is the frequency . Einstein relates the energy of a photon to mass : E = mc2 . 24. ELECTRON ABSORPTION – EMISSION As atoms absorb energy the electrons can get further from the nucleus with this gained energy. n= 1is called the ground state and represents the atom and its electrons in the lowest possible energy state. The excited state or states n= 2, n= 3 etc. are different energy states that the atom can exist when absorbing energy. 25. Isotopes: Two isotopes of one element have same number of protons but different number of neutrons 22 26. Nuclear Forces : Strong Nuclear Force vs. Coulomb Force The strong nuclear force is defined as a short range force that holds neutrons and protons together in the nucleus. The other nuclear force is called the Coulomb force . It only involves protons that repel each other (remember the fundamental law of electricity: like charges repel , opposite charges attract). The Coulomb force causes an electromagnetic repulsion force. 27. The half-life ( t1/2) of a radioactive sample is defined as the time it takes for the amount of the substance to decay to ½ its original value. 28. The unified atomic mass unit is defined as being 1/12th the mass of a carbon-12 atom. 29. The mass defect ( denoted as ᵟ )states that the mass of the nucleus of an atom is less than the protons and neutrons that make up the nucleus ( you can ignore the electrons since they are not part of the nucleus). 30. So, the missing mass , or mass defect, was converted to energy and this energy is stored inside the nucleus to help keep it together. This energy is called the binding energy of the nucleus and is denoted by EB. This binding energy is the energy released in nuclear reactions when the atom is split. Unfortunately this led to the nuclear bomb. 31. MeV - electron volts : unit needed when calculating binding energy 1 MeV = 1 million electron volts 1 u = 1 atomic mass unit and is equivalent to 931.5 MeV To calculate the binding energy get the mass defect (ᵟ ) and multiply by 931.5 Binding energy = mass defect x 931.5 MeV 32. The wave theorists studied polarization and the interference/diffraction patterns produced when light is passed through small slits to support their theory. The followers of Einstein's particle (photon) theory, believed electromagnetic radiation is emitted and absorbed by matter as if it existed in individual ‘packets’ of energy called photons. The behavior of light acting as a stream of photons is illustrated by the photoelectric effect. 23 33. The Photoelectric Effect The photoelectric effect describes the emission of electrons when light strikes a metal surface. 34. Work function (Φ ) A certain amount of energy had to be imparted to an electron on the metal surface in order to liberate it. This was known as the metal’s work function, or Φ . If an electron absorbed energy E it would leave the metal as a photoelectron with a maximum kinetic energy of Emax = E – Φ ( i.e you have to subtract the energy it took to liberate the electron from the metal ). 35. Threshold frequency - The puzzling feature of this graph is that there exists a frequency, called the critical or threshold frequency fc , such that no electrons at all are emitted if the frequency of the light source is less than f c. REGARDLESS of the intensity of the light 24 36. de Broglie wavelength – hypothesis : Since an electromagnetic wave can behave like a particle, can a particle of matter behave like a wave? In 1923, the French physicist Louis de Broglie said yes. His hypothesis, which has been supported by experiment, is that a particle of mass m and speed v and thus linear momentum p = mv, has an associated wavelength. This wavelength is called the de Broglie wavelength.: λ=h p p = momentum = mv h = Planck’s constant = 6.63 x 10-34 J.s 1eV 1.6010 19 J = 4.14 x 10-15 eV.s Particles in motion can display wave characteristics and behave as if they had a wavelength. 37. Electron n a box Even though ‘electron in a box’ model is not a realistic model for an electron, it allows us to deduce that the electron’s energy is ‘quantized’ or discrete (i.e. there are no energy levels in between, like the rungs of a ladder). The fact that an electron, when treated as a wave, has a discrete set of energy levels supports the Bohr Model of the atom. 38. The Heisenberg uncertainty principle states that the simultaneous measurement of position and momentum will always have some uncertainty. In fact the more certain we are about position the less certain we are about momentum, and vice versa. 25 TOPIC 8 Energy , Power and Climate Change 39. The Kilowatt hour: Defined as the energy used in kilowatts in one hour. 40. Sankey diagram – diagram that represents energy flows 41. Energy degradation – excess energy lost and is “ less useful” and can not be used to perform mechanical work 42. Non- renewable energy source – finite sources that will run out e.g : fossil fuels, nuclear 43. Renewable energy source - energy that can renew itself eg. : solar, wind, wave - tidal, geothermal, hydroelectricity 44. Energy density– energy that can be obtained from one unit mass. Jkg-1 . High energy density = high power output 45. Efficiency = output energy input energy 46. The black body is a theoretical body that is a “ perfect” emitter of radiation Any body in the universe will radiate energy in the form of electromagnetic radiation. The Stefan – Boltzmann law states that the amount of energy per second or power (P) radiated by a body depends on the surface area (A), absolute temperature (T), and the properties of the surface called emissivity ( e) : 47. The Albedo - α The albedo of a body is defined as the ratio of power of radiation reflected or scattered from the body to the total power incident on the body: α = total scattered or reflected power total incident power total reflected radiation = total incident – total absorbed 26 48. Greenhouse effect – Basics The greenhouse effect is the warming of the earth caused by infrared radiation, emitted by the earth’s surface, which is absorbed by various gases in the earth’s atmosphere. The radiation is then partly radiated back towards the surface of the earth. In other words the energy from the sun can get in to the earth’s atmosphere but can not get out. The gases primarily responsible for this effect are : water vapor, carbon dioxide , methane and nitrous oxide. TOPIC 14 Digital Technology 49. Digital storage devices – CD, DVD, Floppy disk, 50. Capacitance 27 51. The Charged Coupled Device – CCD 28 52. Quantum Efficiency and CCD Imaging - 53. Magnification- 29 54. Resolution- 30