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# IB Physics HL Notes

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Physics Study Notes Chapter 1 Physics and Physical Measurement 11 SI system of fundamentzaa1nd derived units 0 Physics seeks to explain the Universe 0 Order of magnitude is known as power of tens 0 Every measurement and quantity is made of two important parts 1 The actual number 2 The appropriate units 0 The International System SI of units is used in science 0 Following units below are the fundamental units Quantity SI unit SI symbol Mass Kilogram Kg Length Meter M Time Second 5 Electric current Ampere A Amount of substance Mole Mol Temperature Kelvin K Luminous intensity Candela Cd 0 Derived units are all the other units that can be alternatively expressed as combinations of the SI fundamental units Distance or Displacement 0 Example speedvelocity Speed or Velocity Time Units of Distance or Displacement Units of Time 0 Units of Speed or Velocity me tres m 1 ms seconds s 0 For most questions the best way to represent derived and fundamental units to represent all exponents as negative values instead of denominators 0 Some derived units are so common that they are given a different name for memorization purposes 2 1 Newton 0 1 kgms 0 All derived units can be converted into the fundamental units for the purpose of calculating safely but takes way too much time 0 Not all the SI fundamental units can be used effectively for enormous or very minute measurements 0 Astronomy and astrophysics uses different units such as the astronomical unit and the light years for measurements relevant to their field of work 0 Those different units can be easily converted into the SI fundamental units by using simple arithmetics 12 Uncertainties and error in experimental measurements An experimental error means there is a difference between the experimental value that was taken from the actual experimentlab and the literature results 0 Experimental errors can be categorized as random or systematic WARNING REPEATING READING DOES NOT REDUCE SYSTEMATIC ERRORS BUT DOES REDUCE RANDOM ERRORS DUE TO INCREASED AMOUNT OF PRECISION Random errors are errors that deviate from the literature result in both directions Systematic errors are the types of errors that deviate from the literature result in one direction with similar magnitudes Sources of random errors include o The readability of the instrument 0 The observer being less than perfect o The effects of changes in the surroundings Sources of systematic errors include 0 An instrument with zero error 0 An instrument that wasn39t calibrated right 0 The observer was being less than perfect for every measurement in the same away An accurate experiment is one that has a small systematic error 0 In other words the experimental value is very close to the literature value but doesn39t have to be very consistent A precise experiment is one that has a small random error 0 In other words the experimental value is very consistent but doesn39t have to be very close to the literature value An accurate and precise experiment contain an experimental value that is both very consistent and very close to the literature value Error bars are a way to represent the uncertainties in your experimental valuesdata The bestfit lines of the graph should pass through all of the rectangles created by the error bars An uncertainty range is the likely range for the measurement Device Example Uncertainty Analogue scale Rules meter sticks i half the smallest scale division Digital scale i the smallest scale division i uncertainty value stated by a manual Electronic balances digital meters When taking the uncertainty values of an average value Subtract the value from the highest value and the lowest value Take the largest difference between the average value and the two values listed above Use that value as the uncertainty value OOOO Example I If the time taken for a trolley to go down a slope is measured five times the readings in seconds might be 201 182 197 216 and 194 The average of these five readings is 198s The deviation of the largest and smallest readings can be calculated The largest value is taken as the uncertainty range In this example the time is 198s i018s 0 Significant digits are used as a guide to the amount of certainty 0 A simple rule for calculations is to quote the answer to the same number of significant values to the least precise significant values that was used 13 Estimations and assumptions 0 Since almost everyday situations are so complex simple assumptions are made in order to understand certain concepts and problems 0 The following assumptions are not always absolutely true but they allow us to gain an understanding in the situation 0 These assumptions are possible in ideal worlds but we are in reality therefore in real life the experimental value is always different compared to the theoreticalideal value 0 DO NOT ASSUME TOO MUCH Assumptions Examples to be used on Friction is negligible Many situations involving mechanics Please approach this assumption with caution No heat or heat energy is lost Almost all thermodynamic situations Mass of connecting string is negligible Situations involving picture frames and other areas in mechanics Resistance of an ammeter is zero Problems involving electrical circuits Resistance of a voltmeter is infinite Problems involving electrical circuits Internal resistance of an electrical cellbattery is zero Problems involving electrical circuits Material obey Ohm s law Problems involving electrical circuits Machine is 100 efficient does not lose energy its surroundings Many situations such as energy production plants etc Gas is ideal follows the ideal gas law Some thermodynamic situations Collision is elastic Used in mechanics only gas molecules have perfectly elastic collisions 0 Ohm s law is when the current across a conductor between two points is directly proportional to the voltage o V IR when an electrical component of a circuit obeys Ohm s law the voltage is directly proportional explained later to the current assuming that temperature of the electrical component is constant and the system does not lose heat energy to its surroundings 0 The ideal gas law is a law where the product of the pressure that the gas is under and the volume it takes is equal to the product of the temperature a scientific constant and its substance AKA the number of mole o Gas law PV nRT where P pressure kPA or atm V v0lumedm3 or L or ml n the number of males that substance has mol R Scientific constant depends on the units used T Temperature K Physicists uses 00821 and Chemists use 8314 0 In order to understand motion by using mathematics a branch of mathematics known as calculus is used 0 It is not necessary for the IB course but it does help Symbol Pronounced Meaning Example Ax Delta x The change in x At means the change in time 6x Delta x The small change in x 6t means the small change in time Delta x divided by The average rate of 5 means average At delta t or Delta x the change of x the t speed or velocity over delta x average IS usually taken over a large period of time 536 Delta x divided by The average rate of 5 means the 51 delta t or Delta x the change of x the gtera ge speed or over delta x average IS usually I taken over a small Ve Oclty period of time 6136 Derivative of x The instantaneous E means the j t dt dVded by the rate of change of x instantaneous Speed derivative of t or the change of x IS at t Derivative of x over taken at one instant of the derivative of t time 14 Graphs analvsis uncertainties in calculated results and graphs 0 Plotting graphs is useful to find trends and relationship between two or more variables 0 Graphs in IB physics should have the following o Title and sometimes a legend depends on how clear accurate and neat your graph is o Scales of the axes should be suitable sudden or unexpected jumps in the number should not be present The origin of the axes should be present Both the quantity and units should be labeled on the axes The data points are clear and are plotted correctly Error bars are included if appropriate or necessary OOOO O A bestfit line is added don t join the dots should show the overall trend If a bestfit line is a curve draw it in as one smooth line instead of multiple choppy line segments If the bestfit line is straight draw it with a ruler Rule of thumb the number of data points above and below the bestfit line should be equal Identify and explain any points that does not make sense with the bestfit line Three items should be heavily analyzed on a physics graph Yintercept Since a straight linegraph can only the axes once the intercepts especially the y intercept is very important If a graph intercept the axes at zero or goes through the origin the relationship between the variable is directly proportional Gradient A straight line graph has a constant gradient The triangle used to calculate the gradient should be large as possible The gradient has units derived from dividing the units of the yaxis by the units of the x axis Special situation if the xaxis is a measurement of time the gradient represent the rate of quantity on the yaxis changes The gradient of a curve at a point is the gradient of the tangent to the curve at the point Area under the graph If the gradient is a straight line the area under the graph can be easily determined by finding the area using geometric formulas and etc If the graph is a curve the area can be calculated by counting the squares however the unit of one square must be determined and represented via keylegend The unit for the area under the graph is the product of the units of the yaxis and the x axis If the line of the gradient is known the area under the graph can be determined by using a calculus technique known as integration All straight line graphs can be described by using one general equation ymxb O O 0 Both m and b are constants while y and x are the variables b the yintercept of the graph Mthe gradient of the graph All physics equations could potentially be graphed as a straight line with a little mathematical rearrangement o Must identify which symbols are variables and constant o The symbol that correspond to x and y are variables and those that correspond to m and c are constant o If a variable reading is squared or cubed or square rooted or etc that result is still a variable and it is possible to plot it on one of the axes o Any mathematical combination of the readings on one axis can be plotted because it is still considered as a variable o Be careful of certain symbol as m and c can be mistaken for mass and the speed of light instead of the gradient and the y intercept and vice versa Rules of logs o logcd logc 1ogd o 1ogcd logc 1ogd o 1ogcquot n1ogc o log 1ogc 1 11ogc Vectors are quantities where they have a magnitude and a direction they can be represented as arrows Scalars are quantities where they only have a magnitude o Eg 50kmh to the west is a vector while 50kmh is a scalar Vectors Scalars Displacement Distance Velocity Speed Acceleration Mass Force All forms of energy Momentum Temperature Field strength Voltage Gravity Density and area Vectors can be split by resolving them these split vectors are considered as the components of the original vectors Usually vectors are split into mutually perpendicular horizontal left to right or vice versa and vertical up to down and vice versa component vectors Vectors are represented as a bold letter an arrow above a letter a line above a letter and a squiggly line below a letter Scalars are represented as a normal letter Vectors are best shown as arrows o The relative magnitudes of the vectors involved are shown by the relative length of the vector arrow usually a scale is used to show how the length of the vector is relative to the problem o The direction of the vectors is shown by the direction of the arrows Vectors can be added and subtracted The way to take directions of vectors into account when adding or subtracting them is to use the parallelogram law of vectors Trigonometric functions such as sine and cosine can be used to solve problems involving vectors Chapter 2 Mechanics 21 Kinematic Concepts 0 The technical terms used below should not be confused with their everyday use 0 For example speed and velocity are not the same thing same thing for displacement and distance 0 Vector quantities always have a direction regardless of where the direction is going 0 In other words velocity and speed are NOT the same thing this is important if the object is not travelling in a straight line 0 The units of acceleration come from its definition the change in velocity 0 Whenever the motion of an object changes there is acceleration 0 When an object is travelling at constant speed at one moment but changes its direction later there is a case of acceleration because the direction changed therefore there is a change in velocity which means the object had to accelerate to the other direction 0 A deceleration means slowing down it could mean negative acceleration if the velocity was positive Kinematic Commonly Definition Example SI Unit Vector or Terms used symbol Scalar Displacement S The distance The displacement M Vector moved in a from London to Rome particular is 143 1O6m to the direction southeast Velocity V or u The rate of The velocity during a Ms391 Vector change of flight from London to displacement Rome is 16Oms391 to the southeast Speed V or u The rage of The speed during a Ms391 Scalar change of flight from London to distance Rome is 16Oms391 Acceleration a The rate of The average Ms392 Vector change of acceleration of a plane velocity on the runway during takeoff is 35ms392 in a forward direction This means that on average the velocity of the plane increases by 35ms391 per every second 0 Average value the mean value over a period of time is different compared to the instantaneous value the value at one particular point of time 0 If two objects are moving in the same line but are travelling at different speeds then their relative velocities can be determined by using simple additions and subtractions 0 Three types of graphs are useful in mechanics 1 Displacement vs time graph distance vs time graph 2 Velocity vs time graph speed vs time graph 3 Acceleration vs time graph 0 2 common methods to find physical quantities and properties from the graph are 1 The gradient of the line o Can give either the average value by using the straight line part of the gradient o Or can give the instantaneous value by finding the tangent to the graph at one point 2 The area under the line o For a velocity vs time graph the area under the line can give the displacement travelled over time since the product of velocity and time is displacement o For an acceleration vs time graph the area under the line can give the total velocity of the object over time since the product of acceleration and time is velocity 1 Displacement vs time graph a The gradient of a displacement vs time graph gives the velocity b The area under a displacement vs time graph is not useful 2 Velocity vs time graph a The gradient of a velocity vs time graph gives the acceleration b The area under a velocity vs time graph gives the displacement 3 Acceleration vs time graph a The gradient of an acceleration vs time graph gives the jerk or the rate change of acceleration of an object but it is not useful at the moment b The area under an acceleration vs time graph gives the velocity 0 There are 5 useful equations of uniform motion however these equations are only useful when the acceleration is constant 0 There are also 5 useful symbols sdispacement u initial velocity v final velocity t time taken aacceeration vuat ltuvt 3 2 172 uz Zas t atz s u 2 t atz 317 2 0 The first equation is derived from the definition of acceleration which is the rate of change of velocity over time 1 t atv u vuat The second equation is derived from the definition of velocity which is the rate of change of displacement over time 3 average velocity E vu average velocity Combine the two equations and svu t 2 ltvugtt 3 2 The third fourth and fifth equations are derived from both the first and the second equations ltvugtt 3 2 vum uatu sltTgtt lt2uatgtt 3 2 Zut atz H T 2 2 tat2 s u 2 ltvugtt 3 2 v atu ltvv att 3 2 lt2v atgtt 3 2 2vt atz 3 2 2 t atz 312 2 Zas 122 u2 172 uz Zas When an object is falling down in a vertical motion in a uniform gravitational field while ignoring the effect of air resistance that object is experiencing freefall In the absence of air resistance all falling objects have the same acceleration of freefall regardless of their mass Terminal velocity is the maximum velocity that an object can travel due to the system that the object is under A force is the cause of a velocity change The SI unit for the measurement of forces is the newtonN or kgms392 A force causes a change in velocity Since a change in velocity means there is an acceleration a force causes an acceleration 0 IF there is no change in velocity or constant velocity a force is not necessary 0 Since only one force can act on one object the description of a force should include o The magnitude 0 The direction 0 The object that it acts 0 The object that exerts the force 0 The nature of the force 0 The following forces below are all the forces that pushes or pulls objects that exists in nature Gravitational force freefall Electrostatic force electrons electric shock Magnetic forces The ability of a positive nucleus to attract a negative electron Normal reaction Friction The forces that slows down an object in motion due to the surface drag Tension Hanging pictures and frames Compression Gas syringes OOOOOOO Up thrust The initial force to start a motion of an object 0 Lift Lifting a book directly up from a desk 0 Forces can be divided into two categories contact forces and force between the distance that separates the objects 0 Contact forces include but not limited to friction o Forces between the distance that separates the objects include but not limited to Electrostatic forces 0 The spring constant is the amount of force required to stretch a piece of string per m 0 It39s SI unit is Nm391 0 A freebody diagram shows the all the forces that an object is receiving 0 It can only show one object 22 Newton39s three laws of motion First law 0 Newton39s first law states that an object continues in uniform motion or uniform velocity NO ACCELERATON in a straight line or at rest unless a resultant external forces acts 0 When the net force on an object is zero that object is said to be in an equilibrium 0 ZON two things either an object is travelling at uniform velocity or at zero speed 0 The following table shows the formal descriptions of the 9 forces mentioned above Name of force Description Gravitational forces The force between objects due to its mass cause of weight Electrostatic forces The forces between objects due to their electric charges Magnetic forces The forces between magnets and electric currents Normal reactions The force between two surfaces that acts at right angles to the surface Friction The force that opposes the relative motion of surface Tension When a string is stretched it has equal yet opposite forces on its ends pulling outwards Compression When a rod is compressed it has equal yet opposite force on its pushing inward Up thrust The upward forces that act on an object when it is submerged in a fluid cause of buoyancy Lift The force exerted on an object when a fluid flows over it in an asymmetrical way enables airplanes to fly due to aerodynamics 23 Newton39s three laws of motion Second law 0 Newton39s second law enables us to measure force 0 In formal terms his second law is that the resultant force is proportional to the rate of change of momentum 0 In SI unit terms the resultant force is equal to the rate of change of momentum 0 Momentum is the product of mass of an object and it s velocity Amomentum 2 of force Atime 0 In terms of symbols A ZF A where p is momentum Amv At mAv ZF Tt ma where a is acceleration 24 Newton39s three laws of motion Third law 0 Newton39s third law enables us to know that forces come in pairs 0 In formal terms his third law is when two bodies A and B interact the force that A exerts on B is equal to the opposite of the force that B exerts on A 0 In simpler terms For every action on one object there is an equal but opposite reaction on another object 0 In terms of symbols FABFBA 0 There are two important key points 0 The two opposing forces in the pair act on DIFFERENT objects in other words two equal yet opposite forces that act on the same object are NOT Newton39s third law force pairs 0 The two opposing forces in the pair must be equal opposite and must be the same type of force 25 Mass and Weight 0 Due to everyday languages mass and weight are often confused to be the same thing 0 Mass is the amount of matter contained in an object measured in kg 0 Weight of an object is essentially the mass of the object multiplied by the gravitational pull 0 For example in Jupiter your mass would still be the same however your weight will be about 25 times heavier due to the larger gravitational pull caused by Jupiter39s strong gravitational pull 0 Gravitational force mg 26 Momentum 0 Linear momentum is defined as the product of mass and velocity 0 Impulse is the change of momentum 0 According to Newton39s second law force is the change of momentum or final momentum subtracted by the initial momentum divided by time 0 The law of conservation of linear momentum states that The total linear momentum of a system of interacting particles remains constant assuming that are no resultant external forces 0 When two objects collide with each other two possible situations can occur o The first scenario is an elastic collision where no mechanical energy is lost during the collision I Elastic collisions occur rarely in real life the only situations where elastic collisions occur is the collision between gas molecules I Inelastic collision is where energy is lost can be lost in forms of sound and heat however momentum is still conserved 27 Work 0 Work is done when a force moves an objects in the direction of the force Work done F 3 C036 Work done F orce distance 0 When an object travels in a constant speed or does not move there is no acceleration therefore there is no force therefore the work done by the object is zero 0 In a force vs distance graph the total work can be determined by finding the area under the graph 0 To find out the work done when lifting an object vertically is to find out the product of mass gravitational force and the height 0 To find out the work done in compressing or extending a spring is kxz 28 Energy and power 0 The amount of energy transferred is equal to the work done 0 Energy is a measure of the amount of work done 0 It means that the units of energy and the units of work are the same joules 0 When energy is lost by one object it must be gained by another in other words energy cannot be destroyed 0 Due to the part that energy cannot be destroyed there are several statements about energy that is known as the principle of conservation of energy 0 The principle of conservation of energy can be stated in several ways 0 The total energy of any closed system must be constant 0 Energy is neither created or destroyed it just switches form for example in mechanics energy turns from gravitational potential energy into kinetic energy 0 Finally there is no change in the total energy in the Universe 0 There are 12 different types of energies that exists in nature Kinetic energy Gravitational potential energy Elastic potential energy Electrostatic potential energy Thermal energy Electrical energy Chemical potential energy Nuclear energy ONLY NUCLEAR FUSlON Internal energy Radiant energy Solar energy nuclear fusion OOOOOOOOOO 0 Light energy 0 Kinetic energy can be defined as the product of mass and velocity squared divided by 2 mvz 2 0 Gravitational potential energy can be defined as the product of mass the Earth39s gravitational potential energy and the change in height 0 Gravitational potential energymgh 0 Kinetic energy 0 Elastic potential energy is the product of spring constant and the change in displacement squared divided by 2 kxz 0 Elastic potential energyT 0 Power is defined as the rate at which energy is transferred in other words the change of energy used over time 0 Power can also be stated as the rate at which work is done 0 The SI unit for power is joules per second Js391 or watts W 0 When something is moving at a constant velocity v against a constant frictional force f the power can be stated as the product of the frictional force and the velocity o Power F orceVelocity fv 0 Efficiency is the ratio of useful energy to the total energy transferred 0 Efficiency can be defined as useful work OUT useful energy OUT o Efficiency total energy transformed total energy transformed useful energy OUT 0 Efficiency TotalenergyIN usefulpower OUT 0 Efficiency total power IN 29 Uniform circular motion 0 Uniform circular motion is used to describe an object that is going around in a circular motion at a constant speed 0 The magnitude of the velocity or the speed is constant during the circular motion 0 However the direction of the velocity of the object is constantly changing 0 Since there are changes in direction the object is undergoing acceleration 0 The acceleration of an object in a circular motion is called centripetal acceleration 0 Since there is acceleration in order to drag a mass into a circular motion it requires a force 0 This force which causes centripetal acceleration is called the centripetal force 0 Centripetal acceleration is defined as the quotient of velocity squared and the radius of the circular path that the object makes during the actual circular motion 122 o C entripetal acceleration 7 where v instantaneous velocity of an object at a certain point in time and r is the radius 0 Centripetal force is defined as the product of the mass and the centripetal acceleration which can be redefined as the product of the mass and the velocity squared divided by the radius of the circular path that the object makes during the actual circular motion 2 o C entripetal force my 0 Centripetal force is the sum of all the forces that allows the object to move in a circular motion o In other words it is not a new force 0 Finally since there is no change in displacement made during a circular motion circular motion does not do any work o This statement is very IMPORTANT Chapter 3 Thermal Phvsics 31 Thermal concepts 0 The words hot and cold are just the we humans call labels that identify the direction in which thermal energy or heat will be naturally transferred when the two objects are placed in thermal contact 0 The direction of the natural flow of thermal energy is between two objects is determined by the how hotness of each object o In other words thermal energy travels naturally from hot to cold 0 The temperature of an object is a measure of how hot an object is 0 Temperature can also be stated as the average kinetic energy per molecule 0 Thermal energy is transferred naturally down the temperature difference 0 When two objects with different temperature initially reach the same temperature via thermal contact they are said to be in thermal equilibrium 0 Heat is not the substance that flows from one object but is the thermal energy that has been transferred 0 Thermal energy is known to be the non mechanica transfer of energy between a system and its surroundings 0 Two temperature units are mainly used in physics the Kelvin scale and the Celsius scale 0 To convert from Kelvin to Celsius and viceversa you only need to use simple arithmetic to find out 0 The relationship between the Kelvin and the Celsius scale is TK tC 273 o OK273 Celsius and 273KO Celsius 0 The size of the units are identical for both scales 0 Ideal gases are gases that follows the gas laws for all values of pressure volume and temperature 0 Mole mentioned before but is the basic SI unit for the amount of substance o One mole of any substance is equivalent to the amount of that substance that contains the same number of atoms of 12g of carbon12 0 The Avogadro s constant is the number of atoms in 12 g of carbon12 o This constant is 602 x 1023 0 Molar mass is the mass of one mole of a substance o For example if an element had an atomic number of 18 18g of that substance would equal to mass of total atoms of that element 32 Hezatand internal energy 0 The macroscopic point of view considers the system as a whole and how it interacts with surroundings o The macroscopic point of view of a boiler may show the fact that it releases heat energy to the surroundings 0 The microscopic point of view looks inside the system to see how tis component parts interact with each other o The microscopic point of view of a car may show how the engine uses internal combustion to make the car move 0 Molecules have kinetic energy because they move o They either have translational kinetic energy where they move left or right o Or they have rotational kinetic energy where the molecules move about one or more axes 0 Molecules have potential energy because of their intermolecular forces o Since removing two molecules require energy to break that work can be transferred from potential energy 0 The internal energy of a substance is the total amount of energy that the substance has o The temperature of a substance is a measure of the average kinetic energy of the molecules in a substances 0 Molecules can be arranged into the phase of the substance solids liquids and gases o Solids have a fixed volume and a fixed shape I Molecules are held in position by bonds I Bonds are not rigid therefore the molecules move around an average position I The higher the temperature the molecules move around more o Liquids also a has fixed volume but its shape can easily change compared to solids I The molecules of a liquid are also vibrating but they are not fixed in position unlike the molecules of a solid I The forces between the molecules are still strong 0 Not strong enough to keep the molecules steadily but it keeps the molecules close to each other s 0 The forces between the molecules are weak enough to allow the molecules to more freely around each other o Gases always expand to fill the container they are in I They are not fixed in position I Intermolecular forces are very weak I Gas molecules move very quickly I Occasionally collide with each other 0 Work is the amount of energy that is transferred over a distance by a force in a macroscopic view 0 Heat is the amount of thermal energy that is transferred from one component of a system to another part of a system in a microscopic view 0 In both cases energy is transferred 33 Specific heat capacity and thermal capacity 0 When we assume that a material can be heated up with no loss of energy then the increase in temperature depends on three items o The energy need to enter the material o The mass of the material o The actual substance that the material is made for example pure aluminum 0 The thermal capacity of an object is the energy required to raise the object39s temperature by 1 kelvin or Celsius C where C thermal capacity Q heat energy and AT change in temperature the unit for thermal capacity is JK391 0 Since different objects will have different values of thermal capacity the specific heat capacity of an object is defined as the energy required to raise the temperature of a unit mass of a substance by 1K o Specific here does not mean specific material but it means per mass o The equation for specific heat capacity of a material is c where c is the specific thermal capacity Q is the heat energy m is the mass of the specific heat capacity and AT is the change in temperature 0 Three important notes must be known before progressing o One type of gas may have different values of specific heat capacity I The environment and the conditions decides which specific heat capacity is appropriate o Temperature difference is from the addition of a certain amount of energy I In other words the same amount of energy is required to raise a material from 0 degree to 10 degrees and 999990 degrees to 1000000 degrees o When an object is raised to a temperature higher than the room temperature because the object is hotter it will lose thermal energy to the cooler environment due to the effects of thermal equilibrium I This statement can be nullified if the assumption that the heat energy of the material is not lost to the system 0 There are two basic methods to measure the heat capacity of an object o The object would be connected to an electrical circuit and will be supplied with energy to raise its temperature o In this case the specific heat capacity can be converted by using electrical symbols and variables by replacing c i into c l where I is the electrical current t is the TrlT2 T1 time V is the voltage m is the mass T2 is the final temperature and T1 is the initial temperature o There are three sources of experimental errors from this method I The first source of error is the loss of the thermal energy from the object I The second source of error is container used for the substance will also be heated up which can be written as the unnecessary transfers of energy I Finally the third source of error it will take some time for the energy to be shared uniformly throughout the object o The other method is to mix two substances in their liquid state where we already know the specific heat capacity of one of the two substances The equation assuming that no thermal energy is lost to the environment is maca Ta Tmax mbcb Tmax Tb o There are two sources of experiment errors from this method I The first source of error is the loss of thermal energy from the apparatus especially when the liquids are being transferred I The change of temperature of the container also needs to be taken into consideration as that can also lead to unnecessary transfers of energy 34 Phases or states of matter and latent heat of objects 0 When a substance changes phase from solid to liquid or vice versa and liquid to gas or vice versa the temperature of the substance still remains constant even though thermal energy is being transferred towards the substance 0 The amount of energy associated with the phase change of substances is known as latent heat o There are two types of latent heat I There is the latent heat of fusion which is the amount of heat energy required for the substance to change from solid to liquid I The same can be applied for the latent heat of vaporization except for vaporization the substance is changing from liquid to gas o MOLECULES DO NOT EXPERIENCE A CHANGE IN SPEED DURING A PHASE CHANGE I For eg the molecules in water vapor at 100 degrees Celsius have the same average speed as the molecules in liquid water at 100 degrees Celsius o The specific latent heat of a substance is the amount of energy per unit mass absorbed or released during a change of phase I The specific latent heat of fusion of a material is defined as the amount of energy per unit mass absorbed or released when a material is changing from a solid to a liquid I The specific latent heat of vaporization of a material is the essentially the same for the specific latent heat of fusion but it only applies to when a material is changing from a liquid to a solid I The specific late heat of a material can be shown asL where the units are Jkg391 0 Evaporation takes place at the surface of liquids o If the liquid is below its boiling point on average the liquid molecules do not have enough energy to leave the surface and turn into gaseous forms o Since the faster moving molecules are escaping the liquid most of the kinetic energy is leaving the liquid which means that the temperature or the average kinetic energy of a substance is decreasing o In other words evaporation causes cooling of the liquid 0 The rate of evaporation takes place depends on 3 factors o The surface area of the liquid larger area means faster evaporation o The temperature of the liquid increased temperature means faster evaporation o The pressure of the air above the liquid increased pressure means slower evaporation 0 There are two methods to measure the specific late heat of a material o The first method is to add electrical energy via electrical circuit to a material in its liquid state o The amount of thermal energy added to the material can be calculated by using electrical energy therefore in this situation the specific latent heat of vaporization of a material can be written as L where I is the electrical current t is the time V is m2 the voltage m1 is the original mass of the substance before adding the electrical energy and m2 is the final mass of the substance after adding the electrical energy o There are 2 sources of experimental error from this method I The first source is the loss of thermal energy from the apparatus I The second source is the loss of water vapor before and after the timing o The second method is by using the specific heat capacity of a material to calculate the specific latent heat of fusion of a material by adding both the liquid and solid state of the material o If we assume that no energy is lost from the system then the energy lost by the liquid cooling down and the energy gained by the solid should be equivalent ln other Words mliquid Cliquid Tliquid Tmix msolidLfusion msolid CliquidTmix There are 3 sources of experimental errors from this method I The first source is the loss or gain of energy from the apparatus I The second source is the initial temperature of the solid 0 If the initial temperature of the solid was not at its melting point energy would have to be added or taken away to make sure that the temperature of the solid would be at its melting point I The third source is the clinging of the liquid to the beaker during the transfer 35 Molecular model of an ideal gas 0 There are many assumptions that must be made when dealing with ideal gases 0 The assumptions are Newton39s laws apply to the behavior of molecules There are no intermolecular forces between the molecules The molecules are treated as points instead of complicated combination of atoms The collisions between the molecules are elastic where no energy is lost There is no time spent during the collisions OOOO 0 When a molecule bounces off a wall of the container the momentum of the molecule changes due to the change in direction o REMINDER MOMENTUM IS A VECTOR THEREFORE IT HAS MAGNITUDE AND DIRECTION 0 There must be a force on the molecule from the wall and there is a force must be equal yet opposite from the molecule to the wall 0 Each time there39s a collision there is a force that is exerted on the wall and the molecule 0 The force per unit area of the wall is known as pressure where it can be written as F o P 2 where F IS force and A IS surface area Chapter 4 Oscillations and waves 41 Simple harmonic motion SHM 0 Many systems involve vibrations or oscillations 0 During an oscillation an object continually move back and forth from a fixed position 0 They retrace the same path through space while taking the same amount of time between repeats 0 Oscillations involve the interchange of kinetic and potential energy 0 The following table shows the kinetic energy and the potential energy in each type of oscillations Oscillation Kinetic Energy Stored potential energy Mass moving between two Movement energy of the mass Elastic potential energy stored in horizontal springs the strings Mass moving on a vertical spring Movement energy of the mass Elastic potential energy stored in the strings and gravitational potential energy Simple pendulum Movement energy of the Gravitational potential energy of pendulum rod the pendulum rod A buoy bouncing up and down in Movement energy of the buoy Gravitational potential energy of water the buoy and the water A oscillating ruler as a result of Movement energy from the Elastic potential energy stored in one end being displaced while moving sections of the ruler the bent part of the ruler the other is fixed 0 The following table shows the properties and characteristics of a waveoscillation and its definition Characteristics Properties Symbol Definition Displacement X The instantaneous distance SI units m of the moving object from the fixed position in a specified direction Amplitude A The maximum displacement SI units m from the fixed position Frequency f The number of oscillations completed per unit time the SI unit is the hertz Hz or s391 Period T The time taken SI units s for one complete oscillations 1 T f Phase difference 6 Phase difference is measured in either degrees or radians 0 Simple harmonic motion is defined as the motion when the acceleration of an object is always direct towards and is proportional to the displacement fixed point 0 The acceleration is caused by a restoring force that is always towards the fixed position and also proportional to the displacement from the fixed position F is directly proprotional to x or F kx where the k is a constant Since F ma a is directly proportional to x or a kx where the k is a constant 0 The negative signifies that the acceleration vector is always the opposite of the displacement vector 0 Also the acceleration vector is always facing the fixed position 0 The acceleration of an object in a simple harmonic motion is the product of negative displacement and a constant 0 That constant is often identified as the square of a constant to or 002 I The symbol to is known as angular frequency 0 There are two points that are important about simple harmonic motion 0 The time period or T does not depend on the amplitude 0 Not all oscillations are simple harmonic motions but there are many natural simple harmonic motions seen everyday 42 Kinematics of simple harmonic motion 0 To see if an oscillation is a simple harmonic motion the following procedure must be followed 0 Identify all the forces acting on an object when it is away from the fixed position via a free body diagram I A free body diagram is a diagram that shows all the types of forces that is acting up one and ONLY one object 0 Calculate the force by using Newton39s second law I Since the force is proportional the displacement and the its vector is always opposite of the displacement vector if the oscillation follows the two qualities above that oscillation is a simple harmonic motion 0 Once the simple harmonic motion has been identified the equation of motion must be in the following form where the acceleration is the product of the force divided by the mass and the negative displacement k k 0 a a2x or E x a is the angular frequency and o2 E k 0 a m 0 The following table shows the acceleration velocity and displacement of an object during a simple harmonic motion 0 Since acceleration is the second derivative of displacement and velocity is the first derivative of displacement using calculus to determine some of the equations is one of the easy way to remember important formulas Function Asint Acost Asinwt Acoswt Originial Asint Acost Asinwt Acoswt Displacement First derivative of Acost Asint Awcoswt Asinwt function Velocity Second derivative Asint Acost Aw2sinwt Aw2coswt of function Acceleration Function Asint Acost Asinwt Acoswt Originial Asint Acost Asinwt Acoswt Displacement First derivative of Acost Asint Awcoswt Awsinwt function Velocity Second derivative Asint Acost Aw2sinwt Aw2coswt of function Acceleration All the equations above are made with the assumptions that the object was at the fixed position and started to move at the maximum positive or negative velocity Also A equals the maximum displacement which can be written as X0 The velocity of the object during simple harmonic motion can be written as v iaW The angular frequency is also related to the period T by the following equation Zn k m T sincea T27l39 a m k 43 Energy changes during simple harmonic motion During simple harmonic motion energy is interchanging between kinetic and potential energy Due to the principle of conservation of energy as long there is no resistive forces that dissipates the energy used during the simple harmonic motion the total energy must remain constant When there total energy used during the simple harmonic motion is constant the oscillation is said to be undamped The kinetic energy can be calculated from using 12 iax02 x2 2 2 2 mvz miU X0 X ma2x02 x2 Equot2 2 T 2 The potential energy can be calculated from E mwzxz P T 2 The total energy can be calculated by combining the two equations above ma2x02 x2 mwzxz mwz mwz mwz EtEk E1 2 2 2 x02 x2 2 x2 2 x02 x2 x2 mwzxoz T 2 0 In summary the energy in a simple harmonic motion is proportional to the following three items o The mass o The amplitude squared o The frequency squared 44 Forced oscillations and resonance 0 Damping is when a frictional force similar to restoring force where the force vector is always in the opposite direction of the displacement vector of the oscillating object 0 Because the oscillating the object particle is dissipating energy to overcome the force the overall energy of the system is gradually decreasing 0 Since the energy of the simple harmonic motion is proportional to the amplitude squared the amplitude gradually decreases exponentially over time 0 There are three types of damping light damping heavy damping and critical damping 0 Light damping the situation when the system is under damped is when the resistive force only takes a small fraction of the energy each period o The time period of the oscillation is not affected and the oscillations will not stop until a significant number of cycles has passed Heavy damping occurs when the system is over damped During heavy damping large resistive forces can completely prevent the oscillations from taking place in a shorter period of time compared to light damping o Critical damping involves a force so resistive that the time required for the oscillation to stop is minimum o In most critical damping situations the oscillation doesn t even finish its first cycle before it is completely stopped 0 When an oscillation is at the natural frequency of vibration if the system the system will allow the oscillation to increase its amplitude compared to other frequencies 0 Most oscillations starts with a driving force that is delivered from outside the system o This driving force is known as applying the driving frequency 0 When the driving frequency is applied a combination of natural and forced oscillations take place 0 Soon a steady condition is achieved within the system where the system oscillates at the driving frequency and the amplitude of the force oscillations is fixed 0 This steady condition is known as resonance a state when a system is subject to an oscillating force at exactly the same frequency as the natural frequency of the system 45 Travelling waves 0 Light and sound are examples of wave motion o Waves motions are when energy is transferred from one place to another o Waves transfer energy without a net motion of the medium used for travel o The waves are composed of oscillations and the oscillations are all simple harmonic motions 0 Waves can be separated into two types o A continuous wave involves a succession of individual oscillations o A wave pulse involves just one oscillation 0 There are two categories of waves o There are transverse and longitudinal waves 0 Transverse waves are the type of waves where the oscillations are at the right angles to the direction of the energy transfer 0 Wave fronts highlights the parts of the transverse wave that are travelling together 0 The rays highlight the direction of the energy transfer 0 The top of the transverse wave is known as the crest while the bottom of the transverse wave is known as the trough 0 Longitudinal waves are the type of waves where the oscillations are parallel to the directions of the energy transfer 0 Points of the wave where there is a high pressure of medium particles are known as compressions 0 Points of the wave where there is a low pressure of medium particles are known as rarefactions 46 Waves chz acteristics 0 The displacement time graph represents the oscillations for one point on the wave 0 The displacementposition graph represents all the points along the wave at one instant of time 0 The graphs can be used to represent both longitudinal and transverse waves 0 They do not specify the direction of the displacement 0 Wavelength is the shortest distance measured in meters along the wave between that are in phase with one another 0 Wave speed is the speed measured in meters per second or ms391 at which the wave fronts pass a stationary observer 0 The intensity of a wave is the power per unit area that is received by the observer the unit is Wm392 the intensity of a wave is proportional to the amplitude of the wave squared distance A velocit T y time T 1 712 12191 47 Electromagnetic spectrum and wave properties 0 Electromagnetic waves move as a transverse wave through space 0 They can travel through a vacuum and therefore are able to travel at the speed of light 0 All EM waves travel at the same velocity but all of them have different properties because of the wide range of wavelengths that the EM spectrum covers 0 When a wave meets the boundary between two different media the wave is partially reflected and partially transmitted 0 When waves pass through apertures gaps in a wall or something that partially blocks the displacement of the waves the waves tend to spread out even around the obstacles 0 This property of waves is known as diffraction 0 When a two dimensional wave were to entre and pass the boundary between two media the wave will change directions or refract 0 Due to the fact that there was a change in velocity there is a change in direction 0 Snell39s law states that the ratio of the sine of the incident angle and the reflective angle should be equivalent to the ratio of the speeds in the different media 0 Interference occur when two waves of the same type meet 0 The type of the resulting wave be determined by using the principle of superposition 0 The overall displacement is essentially the same as adding the vector sum of the displacement 0 If the waves have the same amplitude and the same frequency while starting from the identical point or in phase with each other it creates a constructive interference and creates a super wave 0 If the waves have the same amplitude and the same frequency while starting from different points or out of phase with each other it creates a destructive interferences and the two waves cancel each other path difference nl constructive interference path difference n O5A destructive interference n natural numbers O1234 48 Nature of reflections 0 A reflection is when an incident ray is reflected off a surface with a one or more reflected rays where both of the angle of the incident ray and reflected ray is equal to each other the angle is measured off the normal line of the surface 0 There are two laws of reflections o The incident angle is equal to the reflected angle 0 The incident ray and the reflected ray and the normal all lie in the same plane 0 The second line is only used for precision purposes only and is frequently omitted Chapter 5 Electric Currents 51 Electric potential energy and electric potential energy 0 When an electrical charge is placed within an electrical field that charge feels a force 0 Since there is a force and that charge will move a certain distance work will be done 0 Electric potential energy is the energy that a charge has because of its position in an electric field 0 The formula to find the change in electric potential energy is essentially the same as the formula to find work Change in eletric potential energy F distance Energy charge distance 0 Voltage or electrical potential difference is the quantity of the energy difference of charges in an electrical field 0 In other words voltage is essentially the amount of energy per unit charge 0 By using the definition above voltage can be written as the equation below Energy 0 Potential difference between two points Unit charge moved 0 The common unit used for voltage is volts or V but the SI fundamental form of voltage is JC391 0 In most atomic cases a joule of energy is way too much energy for an atom to create individually o For this purpose a smaller unit of energy known as electronvolt was created for this purpose 0 Energy Potential diff erenceCharge o 1eV 1V16 X 10 19C 1C 116 gtlt 1O 19C 16 X 1O 19 52 Electric current 0 Current is essentially the moving of electric charges 0 In other words its defined as the rate of flow of electrical charge charge time The unit for current I A CS1 0 There are two types of currents 0 When a current flows one direction it is known as a direct current 0 When a current constantly changes direction it is known as an alternating current 0 In a mathematical form Current I 1 ampere 1 coloumbsecond 0 A circuit is a path that the current follow 0 A circuit must be complete in order for the current to exist 0 Currents flows throughout an object when there is a potential difference across that object 0 Electrical cell batteries and power supply are devices that creates the potential differences 0 One note about electric current is that it always travels from the negative part of an electric power cell to the positive part in an electrical circuit 0 Conduction electrons the electrons that carries electrical energy in an electrical circuit always travel from the positive part of an electrical cell to the negative part 0 Resistance is the mathematical between the voltage and the current o In other words when an electrical device has a high resistance a large amount of electrical energy is required in order for a current to flow R V Current 39 I o The unit for resistance is the ohm which can be written as 0 VA391 or EsC392 Voltage or Potential Difference o Resistance 0 Ohm noticed that the electrical current across a piece of metal is directly proportional to the voltage potential difference providing that the temperature of the metal stays the same o If the current and potential difference are proportional the device is known as ohmic or it follows Ohm s law o If the current and the potential difference are not proportional the device is non ohmic 0 Electrical power dissipation is essentially the amount of electrical energy that the electrical device used per unit time In other words it is the product of the voltagepotential difference and the current o Power Voltage or Potential Difference Current o Power Energy per unit charge Charge per unit time o Power Energy per unit time E Q E o Power VI 5 E E where E electrical energy Q electrical charge and S time 0 Power can also be represented through the following equations 0 PVIIgtltRII2R o PVIV 53 Electric circuits 0 A component is a device that is connected to an electrical circuit o The component must also complete the circuit as well o The ohm s law where there s a mathematical relationship between the voltage and current applies to all the components in the circuit o The power supply of the circuit provides the energy o The whole circuit determines what kind of current flows through the circuit 0 A series circuit has component connected with each other in a continuous chain o The current is theoretically the same for all components in a series circuit o The total voltage is shared among the components o The resistance value of each component determines how much of the total voltage a component takes Voltagemml I X R1 I X R2 I X R3 I X Rn IRTotal R1 R2 R3 quot39Rnr RTotal R1 R2 R3 Rn 0 A parallel circuit is a type of circuit where there are branches and allows the electrons andor charges more than one possible route around the circuit o In a parallel circuit the voltage is the same for each component o However the total current of the circuit is the addition of the currents in each branch o Currentmtal I1 I2 I3 In V V V V V RTotal R1 R2 R3 Rn 1 1 1 1 1 RTotal R1 R2 R3 Rn 0 There are two electrical meters that are used to measure the current and the voltage in a circuit o The ammeter is used to measure the current in a circuit I It is in series with the circuit I A perfect ammeter would have zero resistance o The voltmeter is used to measure the voltage or the potential difference in a circuit I It is placed in parallel with a component I A perfect voltmeter would have infinite resistance 0 When a battery is connected to a circuit some energy will be used by the battery to expel the total voltage inside the battery o All batteries have internal resistance this component of the battery forces the battery to use a fraction of its energy to expel the voltage inside the battery o The energy used by the battery to expel the rest of the voltage is called the electromotive force I ELECTROMOTIVE FORCE IS NOT A FORCE I Electromotive force is a voltage I EMF is the total amount of voltage in a circuit I EMF I X RTOW I Ir R I Iri IR I IR EMF Ir 54 Potential divider circuits and sensors amp resistivity 0 There are two types of sensors o A light dependent resistor is a device whose resistance depends on the amount of light shining on its surface I There is an inverse relationship between the amount of light that is shined on the sensor and the resistance of the sensor I The higher the amount of light that is shined on the sensor the resistance of the sensor decreases and vice versa o A thermistor is a device who resistance depends on the temperature I There is an inverse relationship between the temperature and the resistance of the sensor I The higher the temperature the lower the resistance and vice versa 0 The resistivity of a material is defined in terms of the resistance the length of the material and its cross sectional area o The cross sectional area of a material in electricity is the area of the ONE circular part of acone o The unit of resistivity is Ohms meter Qm L R p 0a where R is the resistance of the material L is the length of the material and A is the cross sectional area of the material Chapter 6 Fields and Forces 61 Gravitational force and field 0 Newton39s theory of universal gravitation explains that every mass in the universe attracts all the other masses in the Universe 0 The value of the attraction force between two given point masses is given by the equation 0 F oc F Gmlzmz T 1O 11Nm 2kg 2 This law only deals with point masses 77117712 12 G is the proportionality constant G 667 X There is an equal yet opposite attractive force acting on each of the masses even if the masses are not equal 0 The interaction between two spherical masses turns out to be the same if the masses were concentrated at the centers of the spheres 0 The gravitational field strength at a specified point is the amount of force exerted per unit mass that a point mass experiences at the specified point o The mathematical formula for gravitational field strength is o F GMm 5 GM g the units for gravitational field strength is Nkg 1 r2 m r7 o The gravitational field strength is also the acceleration that an object experiences when it is placed in a gravitational field due to the gravity on the surface Force Force Acceleration I GFS Mass Mass 0 Gravitational field lines must be drawn as tangential lines to the surface of the object and the actual gravitational field itself GFS Acceleration o If the lines are closer the gravitational field is stronger and the direction of the arrow will be always going towards the center of the object 0 Between two objects there will be a point where the total gravitational field will be zero because the attraction force towards one object will equal to the attraction force towards the other o To calculate this point follow the formula below y is the total distance between two objects x is the point where the total gravitational field is zero I Substitute or modify the variable depending on the situation and the question GM1 GM2 x2 y2x2 62 Review of electric charge Electric Force and Field 0 Matters will haves 3 types of electrical charges positive negative and neutral o If there are equal amounts of positive and negative charge they will naturally cancel each other o Neutrally charged matter are matters that contains no charge or contains equal amounts of positive and negative charges 0 Electrostatic force is the interaction force that exist between the charges o The rule is that matters with a common charge will repel each other while the matters with an uncommon charge will attract each other o THERE IS NO NAUTRAL ATTRACTIVE OR REPULSIVE ELECTROSTATIC FORCES BETWEEN NEUTRALLY CHARGED OBJECTS 0 Electric charge is always conserved this statement is known as the law of conservation of electric charges 0 There are two materials in nature that may or may not allow the flow of charge o Conductors are materials that allow the flow of charge to flow through I They allow free electrons to maneuver within the object creating an electric current o Insulators on the other hand do not allow the flow of charge to flow through I They limit the maneuverability of free electrons prevent electric currents 0 An electric force between two point or test charges will either be o Repulsive if the charges are identical to each other o Attractive if the charges are opposite to each other o The force acted on one charge will have the same magnitude but an opposite direction compared to the force acted on the other charge 0 Coulomb has discovered that the force is proportional to the size of both charges and inversely proportional to the square of the distance between the charges 0 In mathematical terms F oc 122 and F kqr12q2k is the constant of proportionality k 898N C TZM 2 0 The electrostatic constant can also be written in terms of permittivity 8 k 1 41150 0 If there are two are more charges near a specific electric charge the total collective force acted on that specific charge due to the other charges can be determined by using vector addition 0 An electric charge or a combination of electric charges will create an electric field around it o Any test charges that are placed within the electric field will experience a force o However the value of the force will depend on the value of the test charge and the value of the electric charges that created the electric field in the first place o For experimental purpose the value of the test charge is small so that it will not disturb the other charges in its vicinity 0 The electric field strength is the amount of force per unit charge that a small positive test charge experiences when it is placed in an electric field o The mathematical formula for the electric field strength is o EFS S F is the force and q is the charge o The units for the electric field strength is NC391 o THIS FORMULA IS NOT USED WHEN THE CHARGE IS BETWEEN PARALLEL PLATES o USED WHEN THE FIELD SIZE IS AN IDEAL SPHERE 0 Electric field lines are drawn similarly to gravitational field lines except for field lines for parallel plates o Like gravitational field lines the direction of the arrow of the line shows the direction of the force and the closeness of the lines indicates the strength of the field at a specified point o For a positive charge the direction of the electric field lines are going away from the charge o For a negative charge the direction of the electric field lines are approaching the center of the charge o When there are two opposite charges within a vicinity draw the field lines where majority of the field lines from the positive charge merge with the field lines from the negative charge o For the straight line that connects the two charges make sure that the line segment between the charges has an arrow where it is facing the direction of the negative charge for the other two line segments make sure that the arrow is facing the opposite direction For parallel plates the electric field lines are quite simple I ALL LINES EXCEPT THE VERY OUTWARD LINES ARE PARALLEL AND STRAIGHT I THE GAPS BETWEEN THE STRAIGHT LINES ALL MUST BE EQUAL I THIS IS TO SHOW THAT THE ELECTRIC FIELD BETWEEN A PARALLEL FIELD IS UNIFORM I The outward lines are curvy compared to the inward lines the lines should be 0 able to make an oval like structure I To calculate the electric field strength between two parallel plates is to divide the potential difference between the two plates by the distance that separates the two plates Volta eor Potential Di erence V o EFS 9 ff Distance d 63 Magnetic force and fields and examples of magnetic fields induced by electric currents 0 The magnetic force and the electrostatic force have many similarities o It is caused by magnets and it effects other magnets o There are two poles similar to electric charge north and south 0 Like electrostatic force common poles will repel each other while uncommon poles will attract each other 0 Magnetic field lines are VERY similar to electric field lines o Magnetic field lines are also called flux lines o When a test magnetic north pole is placed within this magnetic field it will experience a force 0 Like the electric field lines the direction of the field lines will show the direction of the force and the strength of the force is determined by the closeness of the lines Chapter 7 Atomic and nuclear physics 71 Atomic structure 0 All matters is made out of atoms 0 There are only about a hundred different types of atoms that exists in nature that has been formally discovered by humans 0 Each atomelement has a name and a chemical symbol 0 All atoms that has been discovered can be located on the periodic table of elements 0 Atoms consist of a combination of the following three items o Protons o Neutrons o Electrons 0 An atom is essentially a small central nucleus surrounded by electrons arranged in different levels 0 Protons and neutrons have a relative mass of 1 while electrons have a negligible mass 0 Protons and electrons have a positive and negative charge while neutrons have a neutral charge 0 There is a very famous experiment where a scientist named Rutherford fired alpha particles at a gold foil 0 This experiment showed evidence that there was atoms existed and their basic structure was discovered from the experiment 0 The experiment known as the GeigerMarsden experiment is when alpha particles were fired at a thin gold parchment 0 Most of the alpha particles passed through the gold parchment due to their relative size and velocity 0 However some of the alpha particles were repelled with huge angles o Approximately 1 in 8000 particles rebounded from the foil while some of the alpha particles were deflected from the nucleus 0 This experiment showed that there were positively charged sub particles called proton 0 Later experiment of electron energy levels comes from the emission and the absorption spectrums 0 The existence of isotopes showed evidence of neutrons 72 Emission spectra and Absorption spectra 0 When an element is supplied with enough energy it emits light waves 0 This light can be analyzed by refracting the light to see what colors make the light 0 A continuous spectrum is a spectrum where all the possible frequencies of light are present 0 An emission spectrum contains only a few frequencies on the spectrum 0 An absorption spectrum is the opposite of the emission spectrum where only a few frequencies on the spectrum are missing 0 An atom s electrons are bound to the nucleus due to the electrostatic attraction force of the protons inside the nucleus 0 The only way that electrons can be delocalized is to add energy to the electron 0 Electron are fixed within the energy levels within an element 0 The energy levels of an element are fixed 0 When an electron move from different energy levels energy is either absorbed or emitted 0 When an electron move towards a higher energy level energy is absorbed 0 When an electron move towards a lower energy level energy is emitted 0 The energy that is either absorbed or emitted as packets of light called photons o Photons with more energy corresponds with light with higher energy higher frequency or shorter wavelength 0 The energy of a photon is given by the equation below 0 The energy of a photon is the product of Planck39s constant and the frequency of the light 0 E hf where h is Planck39s constant which is 663 X 1O 34s 0 Frequency can also be written as the speed of light since we are dealing with electromagnetic waves over the wavelength 0 Since f 1 the equation E hf can be written as E h 73 Nuclear structure 0 A nuclide is the name given to an atom which a specific number of protons and a specific number of neutrons 0 Isotopes are elements with the same number of protons but different numbers of neutrons 0 All protons in a given nucleus are positive 0 Since all the protons have a positive charge theoretically all the protons should be repelling each other inside the nucleus 0 This is prevented by a short ranged but powerful force that keeps all the protons and neutrons in the nucleus intact o This force is known as the strong nuclear force 0 Small nuclei tend to have equal numbers of neutrons and protons 0 Larger nuclei tend to have more neutrons then protons 0 Nuclei that has too many neutrons are unstable and would likely to go under nuclear decay by emitting alpha and beta particles 0 Nuclei that has too less neutrons are also unstable and would likely to go under nuclear decay by emitting positrons o Positron is the antimatter version of an electron o More details will be explained in chapter 13 notes 73 Radioactivity 0 There are three main types of nuclear decay o Alpha decay where alpha particles or positive helium nuclei are emitted o Beta decay where beta particles are emitted o Gamma decay where gamma radiation is emitted 0 When radioactive decay occurs in living beings or living beings are exposed to it DNA and RNA structures are changed resulting in mutations 0 The following table shows the properties of alpha beta and gamma radiations Property of decay Alpha Beta Gamma Produces Alpha partices Beta particles Gamma Positive helium nuclei Antineutrinos for beta electromagnetic waves negative decay OR Positron for beta positive decay Typical material to stop Paper Aluminum Lead it Penetration ability Low Medium High Length Typically a couple of Almost one meter Theoretically infinite centimeters Speed About 1O7ms391 Variable speed average Speed of light due to 1O8ms391 EM properties 3 X 1O8ms 1 Electric charge Positive Negative None pure energy 0 During a nuclear equation the sums of both the atomic number and mass number of both sides must be equal 73 Halflife and nuclear reactions dN o oc N dt 0 Halflife is the amount of time for a sample of the parent nuclei to lose 50 of the number of nuclide 0 Artificial transmutations are reactions where small nuclei or alpha particles are bombarded to the parent nuclei artificially where the parent nuclei absorbs the nuclei or the alpha particles and goes under nuclear decay 0 The mass of protons neutrons and electrons are very small so scientists created a mass unit called u which is 112 the mass of a carbon12 atom which is 166 X 1O3927kg o The rest mass of 1 proton is 1007276 u 1673 X 10 27kg o The rest mass of 1 neutron is 1008665 u 1675 X 10 27kg o The rest mass of 1 electron is 0000 549 u 9110 X 10 31kg 0 Mass defect is the difference of mass of a single nucleus and the total mass of the component of the nucleus o The nucleus release energy when it is trying to keep the protons together and producing the bonds between the protons and the neutrons o This energy known as binding energy is the amount of energy that is released when a nucleus is built from the component sub particles o This energy is also the product of the mass defect and the speed of light squared which Einstein discovered as the massenergy equivalence relationship o E mcz 0 The most common unit used to find the energy via Einstein39s equation is electronvolts o 1 u of mass converts into 9315 MeV o When the energy is divided by the speed of light squared the unit should look like MeVc392 o This new unit is a unit of mass 74 Fission Fusion and antimatter 0 Nuclear fission is the type of nuclear reaction where a large nucleus are broken into two or more smaller nuclei o Nuclear reactors and nuclear bombs use nuclear fission to get the energy they need o A typical reaction is to allow an uranium235 atom to absorb a neutron and split into two smaller nuclei and 3 neutrons o Those 3 neutrons can initiate further reactions and eventually lead into multiple chain reactions o Chain reactions are quite difficult because the neutrons need to lose enough energy to initiate further reactions but it is possible 0 Nuclear fusion is the type of nuclear reaction where small nuclei can form into lager nuclei o The sun uses nuclear reaction as fuel o A typical fusion reaction is when a deuterium and tritium forms into an alpha particle and a neutron 0 Whenever a nuclear reaction release energy the products of the reactions are in a lower energy state than the reactants 0 Scientists calculate the binding energy per nucleon for all different nuclei to compare their energy states o Iron56 has the largest biding energy per nucleon 0 Antimatter is the anti partice of matter o If matter and antimatter were to come together they would cancel each other Antimatter is rare but does exists When a beta plus decay occurs a proton is turned into a neutron and a beta plus particle and a neutrino is produced o When a beta negative decay occurs a neutron is turned into a proton a beta negative particle and an antineutrino is produced o A positron is an object that has a positive charge of 1 but the mass is equal to an electron I Commonly is known as a positron Chapter 8 Energy and power 81 Energy degradation and power generation 0 Any energy production in the real world transfers some of its energy to its surroundings o This transferred energy is now unavailable for human consumption o Most of this transferred energy is mostly in heat o This unavailable energy is known as degraded energy 0 Energy conversions are represented using Sankey diagrams o Sankey diagrams uses arrows from left to right that represents the energy changes that takes place during the energy production o The width of the arrows represent the powerenergy involved o Degraded unavailable or lost energy is shown with an arrow up or down 0 Most electrical power stations use a type of fuel to release thermal energy to boil water 0 The boiled water creates steam o That steam turns turbine and the kinetic energy from the motion of the turbine is then converted into electrical energy for human consumption 82 world energy sources 0 Energy changes form meaning it cannot be created or destroyed Due to this certain energy sources are renewable O o However certain energy sources are non renewabe o Nonrenewable energy sources can be used up and run out o The following table shows examples of renewable and non renewabe energy sources Renewable Energy sources Nonrenewable Energy sources Hydroelectric Coal Photovoltaic cells Oil Active solar heaters Natural gas Wind Nuclear Biofuel 0 Notes about certain energy sources o Both nuclear fusion and nuclear fission are technically non renewabe because they use a material as their source o However the amount of power they produce is so large that they are considered as renewable in terms of energy produced o If the fuel of an energy sources is properly managed that can determine if that energy source system is renewable or non renewabe 0 Possible sources that human hasn39t fully used are o Full radiation energy of the sun o Gravitational potential energy of the sun and the moon o The nuclear energy stored within atoms in other words our own fusion reactor o Heat energy of the Earth 0 Energy density is the amount of energy within a unit mass of the fuel o The units for measuring energy density is Jkg391 Energy released from fuel o Energy density Mass of fuel consumed 0 The following table below shows the fuel whether it is renewable or not and it s average energy dens y Fuel Renewability Average Energy Density MJkg391 Coal No 27 Oil No 42 Gas No 54 Nuclear fission No 90000000 Waste No 10 Solar Yes Potentially infinite or not available Wind Yes Potentially infinite or not available Tidal Yes Potentially infinite or not available 83 Fossil fuel power production 0 Coal oil and natural gas are fossil fuels 0 Fossil fuels are produced from accumulation of dead matter for over tens or hundreds of millions of years Coal is formed from the dead plant matter Compressed into solid form due to external pressure from other buried materials Oil is formed from microscopic marine life Compressed into solid form due to external pressure such as ocean pressure Natural gas can be found in underground pockets or as byproducts from the production of coal and oil OOOO 0 The solar energy from the sun is turned into plant chemical energy via photosynthesis 0 This plant chemical energy is eventually turned into coal and oil via compression 0 This fossil fuel is combusted in order to release thermal energy 0 The thermal energy is used to heat water and create steam 0 The kinetic energy from the steam is transferred into the kinetic energy of turbines and electrical energy ready for human consumption is produced 0 The following tables shows the efficiency of fossil fuel power stations and both the advantages and disadvantages of fossil fuel Fuel Coal Oil Natural Gas Advantages Disadvantages High energy density Produces pollutions acid rain Easy to transport Greenhouse gases are produced Relative cheap Damage to the environment due to extraction Power plants can be built anywhere Non renewabe Can be used directly for heating homes Lot of fuel is required for production 84 Nuclear power 0 Most nuclear power stations use uranium235 as the fuel Fuel is not burned or does not go through combustion Nuclear fission is used to extract the energy Nuclear fission creates large amount of thermal energy Thermal energy is used to boil water Water turns into steam OOOOO Kinetic energy of steam turns turbine o Turbine generates consumable electrical energy 0 In nuclear fission chain reactions can occur 0 If an exponential chain reaction occurs then the reaction would run out of control 0 Two important factors determine the chance that a neutron will initiate a nuclear fissions o The number of parent nuclei available o The speed energy within the neutron 0 Critical mass is the minimum mass of the parent nuclei to ensure that there will be a linear chain reaction in a nuclear fission 0 In order to reduce the chances of having an exponential chain reactions the speed of the produced neutrons must slow down 0 Three components are important in a nuclear fission reactor o The moderator which slows the neutrons by allowing to collide with the nuclei within the moderator o The control rods which absorbs neutrons I They are introduced to control the chain reaction o The heat exchanger allows the nuclear fission reaction to occur in an area isolated from the rest of the system o Water can be used as a moderator and a coolant in most nuclear power plants 0 Natural uranium has only about 1 of uranium235 the uranium isotope used in nuclear fission 0 That natural uranium is enriched so that the percentage of uranium235 is increased 0 Nuclear power plants are also potentially dangerous o Uncontrolled nuclear reactions can cause an explosion and a thermal meltdown of the power plant o Radioactive by products are created I By products are radioactive for millions of years I Must be stored deep underground o Extraction of nuclear fuel is dangerous o Transportation of nuclear fuel and nuclear by products are dangerous 0 Nuclear power can be used to create nuclear weapons 0 Nuclear weapons uses nuclear fission the same way nuclear power plants uses nuclear fission o Only difference is that nuclear weapons intentionally allows nuclear fission chain reactions to occur o Nuclear weapons are very dangerous and destructive o Under heavy political military and moral debates and controversies 0 Fusion reactors offer potential large power production without many by products o No environment on earth is possible at the moment to allow nuclear fusion to occur 0 The following table below shows the advantages and disadvantages of nuclear power Advantages Disadvantages Extremely high energy density Nuclear wastebyproducts Large uranium reserves Potential disasters are devastating Non renewabe 84 Solzipower and rza iization StefanBoltzmann km 0 There are two ways to directly harness the sun39s radiant energy o A photovoltaic solar cell converts the radiated energy directly into potential difference I However very little voltage and current is produced I Solar cells are used to power devices that do not require a lot of energy I sing multiple cells in a series circuit would increase the voltage I using multiple cells in a parallel circuit would increase the current o An active solar heater is used to absorb as much as thermal energy from the sun I The thermal energy is used to heat water into steam I The kinetic energy of the steam would be used to turn a turbine I The kinetic energy from the motion of the turbine can be converted into consumable electrical energy 0 The solar constant is the amount of solar energy that falls on a unit area of the Earth39s atmosphere per second The unit for the solar constant is Wm392 The average solar constant is approximately 14OOWm392 The earth surface receives a lower amount compared to the atmosphere due to the atmosphere scattering and absorbing the energy o Different parts of the Earth39s surface will receive different amount of radiant energy due to the latitude the axis of the Earth o Seasons also have an impact on how much radiant energy a unit area of the Earth39s surface will receive o In order to find the surface area of a sphere the following formula is used o A 47tr2 where 7t is the constant 3141 and r is the radius of the sphere 0 Intensity is the amount of power received per unit area Power o I T since surface area is 47tr2 the equation can be written as Surface Area P o I 2 4TIT o The equation above has an inverse relationship between the intensity of the surface area and the actual surface area I This is known as the inverse square law 0 Albedo is the total reflected radiation received by a plant over the total radiation received by that same plant o It is a ratio 0 The following table shows the advantages and the disadvantages of solar energy Advantages Disadvantages No harmful by products Can only be utilized during the day Renewable source of energy Source of energy is unreliable Source of energy is theoretically free Low amount of energy is produced low energy dens y 0 The Stefan Botzmann law states that the total power that a star can produce is the product of the Stefan Botzmann constant the surface area of the star and the surface area temperature of the star raised to the power of four o The law can be written as an equation o The most important relationship that can be taken out of this law is that the power is proportional to the surface temperature raised to the power of four P JAT4 where 0 is the Stefan Boltzmann constant 0 567 x 1O 8Wm 2K 4 A 47tr2 which is the surface area of a sphere 85 Hydroelectric power 0 The source of energy in a hydroelectric dampower station is the gravitational potential energy of water o If water is allowed to flow down consumable electrical energy can be generated o The potential energy of the water is converted into kinetic energy of the water via water motion The kinetic energy of the water is then used to turn a turbine The kinetic energy of the turbine motion can be transferred into consumable electrical energy In other words the energy and power of a hydroelectric dam can be determined from the equation below HOWEVER The mass of water is generally not available therefore the product of the density and the volume of water must be used to determine the mass of the water E mgh pvgAh here p is the density of water 12 is the volume of water g is the gravitational force and Ah is the change in height Water can be stored in large reservoirs Tidal water stations trap water at high tide and use the kinetic energy of the tides and convert that into electrical energy Water can be pumped from a low reservoir to a high reservoir o This does require energy but it is one of the way to store energy The following table shows the advantages and disadvantages of hydroelectric power Advantages Disadvantages No harmful by products Can only be utilized in certain areas Renewable source of energy Area before the dam will be flooded Source of energy is technically free Damage to the local marine ecosystem 86 Wind Power Wind power starts from the Sun o The Sun heats the atmosphere o Certain part of the atmosphere will be hot while some parts will be cold o Due to thermodynamics there will be pressure changes due to rise of hot air and the sinking of cold air The change of pressure causes the flow of air in other words wind The kinetic energy of the wind can turn the wind blade OOO The kinetic energy from the motion of the wind blade turns a turbine The kinetic energy of the turbine motion generates consumable electrical energy The mathematical formula of the amount of electrical energy and power produced by a wind turbine can be represented by the formula below 172 o Kinetic energy of wind turbine m The cross sectional area that the wind blade covers is 7l39T392 where 7t is 314 and r is the blade length o The volume of the air is determined as the product of the velocity of the wind and the cross sectional area of the wind blades Volume 12 X A X t where v is the velocity t is time and A is the cross sectional area of the wind blades 0 The mass of the air can be determined as the product of the volume of the wind and the density of the wind Mass of wind Volume of wind gtlt Density of Wind 17 X A X t p where p is the density of air 0 So the kinetic energy of the wind can be determined as mvzvgtltAgtltpgtlttv2Agtltpgtlttgtltv3Aptv3 K 39 inetic energy 2 2 2 2 0 Power of the wind turbine can be determined as P Ekmv2Aptv3Apv3 0Wert 2t 2t 2 0 There are three important notes to know about the energy of the wind 0 Not all the kinetic energy can be harnessed when wind passes through wind blades it only loses a portion of its speed I The formula for both kinetic energy of the wind and power is only useful if all the kinetic energy of the wind is harnessed which is impossible o If the wind speed is doubled the total power will be increased by a factor of 8 o If the wind blade was to be doubled the total power will be increased by a factor of 4 0 The following table shows the advantages and disadvantages of wind power Advantages Disadvantages No harmful by products Source of energy is unreliable Renewable source of energy Low energy density Source of energy is theoretically free Produces noise pollution Best positions are usually far away from urban areas Cannot be stored easily Chapter 9 Motions in fields HL 91 Projectile motion 0 Projectile motion is the parabolic motion of an object that is in the gravitational field 0 Projectile motion is a vector so it has a vertical component and a horizontal component 0 The two components are independent when we assume that the gravitational force is constant 0 There are no forces in horizontal direction therefore no horizontal acceleration I Due to Newton39s second law the horizontal velocity is constant 0 There is a constant vertical force that is acting down this is gravitational force I There is always a vertical acceleration acting down on the object I The value of the vertical acceleration is 98ms392

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