WJEC AS-1 Physics Summary Revision Notes PDF

Table Of Contents ================= {#section.TOCHeading} [Table Of Contents 1](#table-of-contents) [Unit 1.1 Basic Physics 3](#unit-1.1-basic-physics) [1.1 -- Definitions 3](#definitions) [1.1.1 -- SI Units 3](#si-units) [1.1.2 -- Standard Form 4](#standard-form) [1.1.3 -- Scalars and Vectors 4](#scalars-and-vectors) [1.1.4 -- Density 4](#density) [1.1.5 -- Moments 4](#moments) [1.1.6 -- Bodies in Equilibrium 4](#bodies-in-equilibrium) [1.1.7 -- Centre of Gravity 5](#centre-of-gravity) [Unit 1.2 -- Kinematics 6](#unit-1.2-kinematics) [1.2 -- Definitions 6](#definitions-1) [1.2.1 -- Kinematics 6](#kinematics) [1.2.2 -- Motion Graphs (Displacement-Time Graphs) 6](#motion-graphs-displacement-time-graphs) [1.2.2 -- Motion Graphs (Velocity-Time Graphs) 6](#motion-graphs-velocity-time-graphs) [1.2.3 - Equations of Motion for Uniform Acceleration 7](#equations-of-motion-for-uniform-acceleration) [1.2.4 -- Falling Objects (Vertical Motion Under Gravity) 7](#falling-objects-vertical-motion-under-gravity) [1.2.5 -- Projectile Motion 7](#projectile-motion) [Unit 1.3 -- Dynamics 8](#unit-1.3-dynamics) [1.3 -- Definitions 8](#definitions-2) [1.3.1 -- Newton's Laws of Motion 8](#newtons-laws-of-motion) [1.3.2 -- Newton's 3^rd^ Law 8](#newtons-3rd-law) [1.3.3 -- Momentum 9](#momentum) [1.3.4 -- Elastic and Inelastic Collisions 9](#elastic-and-inelastic-collisions) [1.3.5 -- Newton's 2^nd^ Law 9](#newtons-2nd-law) [Unit 1.4 -- Energy Concepts 10](#unit-1.4-energy-concepts) [1.4 -- Definitions 10](#definitions-3) [1.4.1 -- Work 10](#work) [1.4.2 -- Energy 10](#energy) [1.4.3 -- The Work-Energy Relationship 11](#the-work-energy-relationship) [1.4.4 -- Power 11](#power) [1.4.5 -- Dissipative Forces and Energy 11](#dissipative-forces-and-energy) [Unit 1.5 -- Solids Under Stress 12](#unit-1.5-solids-under-stress) [1.5 -- Definitions 12](#definitions-4) [1.5.1 -- Forces on Solid Materials 12](#forces-on-solid-materials) [1.5.2 - Hooke's Law 13](#hookes-law) [1.5.3 -- Spring in Series and Parallel 13](#spring-in-series-and-parallel) [1.5.4 -- Work of Deformation and Energy 13](#work-of-deformation-and-energy) [1.5.5 -- Stress, Strain and Young's Modulus 13](#stress-strain-and-youngs-modulus) [1.5.6 - Types of Solid 15](#types-of-solid) [1.5.7 -- Stress-Strain Graphs for Metals 16](#stress-strain-graphs-for-metals) [1.5.8 -- Brittle Materials and Rubber 16](#brittle-materials-and-rubber) [1.5.9 -- Hysteresis 17](#hysteresis) [Unit 1.6 -- Using Radiation to Investigate Stars 18](#unit-1.6-using-radiation-to-investigate-stars) [1.6 -- Definitions 18](#definitions-5) [1.6.1 -- Stellar Spectra and Black Bodies 18](#stellar-spectra-and-black-bodies) [1.6.2 -- Wien's Law 19](#x1.6.2-wiens-law) [1.6.3 -- Stephan-Boltzmann Law 19](#stephan-boltzmann-law) [1.6.4 -- Luminosity, Intensity and Distance 19](#luminosity-intensity-and-distance) [1.6.5 -- Multiwavelength Astronomy 20](#multiwavelength-astronomy) [Unit 1.7 -- Particles and Nuclear Structure 21](#unit-1.7-particles-and-nuclear-structure) [1.7 -- Definitions 21](#definitions-6) [1.7.1 -- A Brief History of Our Understanding of the Atom 21](#a-brief-history-of-our-understanding-of-the-atom) [1.7.2 -- Quarks and Leptons 22](#quarks-and-leptons) [1.7.3 -- Hadrons 23](#hadrons) [1.7.4 -- Interactions (forces) Between Particles 23](#interactions-forces-between-particles) [1.7.5 -- Conservation Laws. 25](#conservation-laws.) [Unit 1 Definitions 26](#unit-1-definitions) [Data Sheet 30](#data-sheet) Unit 1.1 Basic Physics ====================== 1.1 -- Definitions ------------------ REFERENCE TERM ESSENTIAL POINTS ----------- ------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------- 1.1.1 Quantity In SI a quantity is represented by a number and a unit 1.1.3 Scalar A scalar is a quantity that has a magnitude (and unit) only 1.1.3 Vector A vector is a quantity that has a magnitude (unit) and direction 1.1.3 Resolving a vector to find its components This means finding component vectors in the horizontal and vertical directions 1.1.4 Density The mass per unit of volume 1.1.5 Moment The moment about a point is defined as the force multiplied by the perpendicular distance from the point to the line of action of the force 1.1.5 The principle of moments For a system to be in equilibrium, the sum of the anticlockwise moments about a point must be equal to the sum of the clockwise moments about the same point 1.1.6 Translational equilibrium The resultant force in any given line is zero 1.1.6 Rotational equilibrium The net moment about any pivot is zero 1.1.7 Centre of gravity The centre of gravity is the single point within a body at which the entire weight of the body may be considered to act. 1.1.1 -- SI Units ----------------- All physical quantities consist of a numerical magnitude and a unit. The '**systeme international**' or SI units are a set of internationally agreed units for all quantities in physics. There are 7 base units, but we only use 6 of them at A-Level: BASE QUANTITY SI BASE UNIT ------------------------ -------------- Mass, m Kilogram, kg Length, l Metre, m Time, t Second, s Temperature, T Kelvin, K Current, I Ampere, A Amount of substance, n Mole, mol Luminous Intensity, L Candela, cd All other units are known as derived units. Learn these three base unit expressions to save time in the exam: UNIT BASE UNIT -------- ------------- Newton Kgms^-2^ Joule Kgm^2^s^-2^ Watt Kgm^2^s^3^ We can use this knowledge of base quantities and units to check equations for homogeneity. **An equation is said to be homogeneous if both sides have identical base units.** **\ ** 1.1.2 -- Standard Form ---------------------- PREFIX MULTIPLYING FACTOR SYMBOL -------- -------------------- -------- Tera x10^12^ T Giga x10^9^ G Mega x10^6^ M Kilo x10^3^ k Centi x10^2^ c Milli x10^-3^ m Micro x10^-6^ µ Nano x10^-9^ n Pico x10^-12^ p Femto x10^-15^ f These prefixes don't have to be learned as they are on the datasheet. 1.1.3 -- Scalars and Vectors ---------------------------- QUANTITY DEFINITION EXAMPLE ---------- ------------------------------------------------------ -------------------------------------------- Scalar A quantity that has magnitude and a unit only. Mass, distance, time and speed. Vector A quantity that has magnitude, direction and a unit. Displacement, velocity, force and current. To calculate the resultant of two vectors, use Pythagoras' theorem. [\$F\_{\\text{res}} = \\sqrt{a\^{2} + b\^{2}}\$]{.math.inline}. And to find the direction of the resultant, use [\$\\tan\^{- 1}\\frac{o}{a}\$]{.math.inline} 1.1.4 -- Density ---------------- To calculate the density of an object, the formula [\$\\rho = \\frac{m}{V}\$]{.math.inline} were, - ρ = density, measured in kgm^-3^ - m = mass, measured in kg - V = volume, measured in m^-3^ In general, solids have high density values, gases have very low-density values and liquids have intermediate density values. 1.1.5 -- Moments ---------------- Moment is defined as the product of the force and the perpendicular distance between the line of action of the force and the pivot. The formula for calculating moment force is: \ [*Moment*= *Force* × *Distance*]{.math.display}\ \ [*M* = *F*.*D*]{.math.display}\ In some cases, you will need to use trigonometry to find the perpendicular distance before you can take moments, e.g. a trap door in an attic. We can approach this in either of two ways: 1. Look at the line of action of the tension force, draw on the perpendicular distance to the pivot and use trigonometry to find the distance d. 2. Resolve the tension to find the component which is perpendicular to the pivot. Use this with distance a. The principle of moments states: **for equilibrium, the sum of the anticlockwise moments must be equal to the sum of the clockwise moments about the same point.** 1.1.6 -- Bodies in Equilibrium ------------------------------ There are two condition that must be satisfied if an object can be said to be in equilibrium: **TYPE OF EQUALIBRIUM** **DEFINITION** --------------------------- ----------------------------------------------- Translational equilibrium The resultant force in any given line is zero Rotational equilibrium The net moment about any pivot is zero 1.1.7 -- Centre of Gravity -------------------------- **This is the point at which all the weight of an object is considered to act** and makes calculations like those seen in moments much easier. **For a uniform object, the centre of gravity is in the centre of the object.** This can be easily found by connecting diagonally opposite corners (the same works for 2D and 3D objects. **A tilted object will topple over when its weight (acting from the centre of gravity) acts just outside the base of the base of the object.** The toppling angle, θ, we can say [\$\\theta = \\ \\tan\^{- 1}\\frac{b}{h}\$]{.math.inline} Unit 1.2 -- Kinematics ====================== 1.2 -- Definitions ------------------ REFERENCE TERM ESSENTIAL POINTS ----------- ---------------------------- ----------------------------------------------------------------------------------------------------------------------------------------------------- 1.2.1 Displacement The (straight line) distance travelled in a specific direction. 1.2.1 Mean speed The total distance travelled in the time taken to carry out the whole journey. 1.2.1 Mean velocity The total displacement during the total time taken. 1.2.1 Instantaneous speed The rate of change of distance 1.2.1 Instantaneous velocity The rate of change of displacement 1.2.1 Mean acceleration The change in velocity during the time taken 1.2.1 Instantaneous acceleration The rate of change of velocity 1.2.5 Terminal velocity The terminal velocity is the constant, maximum velocity of an object when resistive forces on it are equal and opposite to the 'accelerating' force 1.2.1 -- Kinematics ------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------- QUANTITY DEFINITION SYMBOL UNIT EQUATION -------------- ----------------------------------------------------------------- -------- -------- ----------------------------------------------------- Displacement The (straight line) distance travelled in a specific direction. x (s) m Velocity Rate of change of displacement. v ms^-1^ \ [\$\$v = \\frac{x}{t}\$\$]{.math.display}\ Speed Rate of change of direction v ms^-1^ \ [\$\$v = \\frac{x}{t}\$\$]{.math.display}\ Acceleration Rate of change od velocity a ms^-2^ \ [\$\$a = \\frac{\\Delta v}{t}\$\$]{.math.display}\ -------------------------------------------------------------------------------------------------------------------------------------------------------- Mean' is the average measured over a significant amount of time. If calculated over a whole journey, we can use: [\$\\text{mean\\ velocity\\ }\\left( \\overline{v} \\right) = \\frac{\\text{total\\ displacement}}{\\text{total\\ time\\ }}\$]{.math.inline} or [\$\\overline{v} = \\frac{\\Delta v}{2}\$]{.math.inline} 'Instantiations' is the speed or velocity at any one instant and is calculated by taking a very small-time interval (or a tangent to the curve on a displacement-time graph). 1.2.2 -- Motion Graphs (Displacement-Time Graphs) ------------------------------------------------- There is one 'rule' for displacement time graphs: - The gradient of the graph at any point gives a value for the velocity at a point. In situations where the velocity is changing, in it very difficult to judge just by looking at the graph whether or not the acceleration/deceleration is constant. An exam question may ask you to calculate the gradient several times in order for you to make a judgement on whether or not the change in velocity is constant. If the acceleration is uniform, the curve on a displacement-time graph would be parabolic. 1.2.2 -- Motion Graphs (Velocity-Time Graphs) --------------------------------------------- There are two 'rules' for velocity-time graphs - The gradient of the graph gives us a value for the acceleration at that point - The area between the graph and the x-axis gives a value for the displacement 1.2.3 - Equations of Motion for Uniform Acceleration ---------------------------------------------------- The acceleration of a body is uniform if its velocity changes by equal amounts in equal times. There are four equations that we can use to describe the motion of a body moving in a straight line with uniform velocity. \ [*v* = *u* + *at*]{.math.display}\ \ [\$\$x = \\frac{1}{2}\\left( u + v \\right)t\$\$]{.math.display}\ \ [\$\$x = ut + \\frac{1}{2}at\^{2}\$\$]{.math.display}\ \ [*v*^2^ = *u*^2^ + 2*ax*]{.math.display}\ 1.2.4 -- Falling Objects (Vertical Motion Under Gravity) -------------------------------------------------------- When air resistance is considered, the acceleration is non-uniform and reduces to zero as the object gains speed (reaches terminal velocity) **An object is describes as 'freely' falling when in the absence of air resistance.** Objects in free fall accelerate the Earth with the same acceleration, called **acceleration of free fall** or **acceleration** **due to gravity**. The symbol for acceleration is g and has a value of 9.81ms^-2^. 1.2.5 -- Projectile Motion -------------------------- - **A projectile is an object which is thrown/kicked/otherwise made move upwards and carries its path under the influence of gravity.** - The path of a projectile is called a **parabola.** - Projectile motion is defined as **uniform velocity in one direction and uniform acceleration in a perpendicular direction**. (Assuming negligible air resistance). Unit 1.3 -- Dynamics ==================== 1.3 -- Definitions ------------------ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ REFERENCE TERM ESSENTIAL POINTS ----------- --------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1.3.1 Force A force on a body is a push or a pull acting on the body from some external body. 1.3.1 \ The product of the mass of a body and its acceleration is equal to the vector sum of the forces acting on the body. This vector sum is called the resultant force. [*ΣF* = *ma*]{.math.display}\ 1.3.2 Newton's 3^rd^ law If body A exerts a force on body B, then B exerts an equal and opposite force on A 1.3.3 Momentum The momentum of is the product of its mass and velocity 1.3.3 Principle of conservation of momentum The vector sum of the momenta of bodies in a system stays constant even if forces act between the bodies, provided there is no external resultant force. 1.3.4 Elastic collision A collision in which there is no change in tot E~k~ 1.3.4 Inelastic collision A collision in which E~k~ is lost. 1.3.5 Newton's 2^nd^ law The rate of change of momentum of an object is proportional to the resultant ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 1.3.1 -- Newton's Laws of Motion -------------------------------- +-----------------------+-----------------------+-----------------------+ | NEWTON'S LAW | DEFINITION | FORMULA | +=======================+=======================+=======================+ | Newton's 1^st^ law | An object will remain | | | | at rest or moving | | | | with uniform velocity | | | | unless acted upon by | | | | a resultant force. | | +-----------------------+-----------------------+-----------------------+ | Newton's 2^nd^ law | When acted upon by a | \ | | | resultant force, the | [*ΣF* = *ma*]{.math | | | object will |.display}\ | | | accelerate in the | | | | direction of the | Where: | | | force with the | | | | acceleration directly | - F = resultant | | | proportional to the | force (N) | | | size of the force and | | | | inversely | - M = mass (kg) | | | proportional to its | | | | mass. | - A = acceleration | | | | ms^-2^) | +-----------------------+-----------------------+-----------------------+ | | Or in terms of | | | | momentum: The rate of | | | | change of momentum is | | | | directly proportional | | | | to the resultant | | | | force. | | +-----------------------+-----------------------+-----------------------+ | Newton's 3^rd^ law | If body A exert a | | | | force on body B, then | | | | body B will exert an | | | | equal and opposite | | | | force on body A. (Or | | | | every action has an | | | | equal and opposite | | | | reaction) | | +-----------------------+-----------------------+-----------------------+ 1.3.2 -- Newton's 3^rd^ Law --------------------------- If body A exert a force on body B, then body B will exert an equal and opposite force on body A. (Or every action has an equal and opposite reaction). Forces come in pairs. If a hammer exerts a force on a nail, the nail exerts a force of equal magnitude but opposite direction on the hammer. One of these forces is called the action force (it doesn't matter which). The other is called the reaction force. **Although the two forces are always equal and opposite they never 'cancel out' since they act on different objects.** 1.3.3 -- Momentum ----------------- Momentum is defined as the product of mass and velocity. \ [*p* = *mv*]{.math.display}\ Where: - p = momentum (kg ms^-1^) - m = mass (kg) - v = velocity (ms^-1^) **The principle of conservation of momentum states: the total momentum before a collision is equal to the total momentum after the collision, provided no external forces act.** In the lab, we can often investigate momentum changes using riders on air tracks. A rider sits on s cushion of air so that: - There is zero resultant vertical force as the upward force on the rider due air pressure is equal and opposite to the downwards gravitational force. - There is zero frictional force on the rider and the force due to air resistance is very small. Therefore, we can consider riders (usually two) on the air track to constitute an almost isolated system. A single rider moving at low speed is seen to travel at very close to constant velocity, in line with Newton's 1^st^ law. 1.3.4 -- Elastic and Inelastic Collisions ----------------------------------------- COLLISION MOMENTUM E~K~ TOTAL ENERGY ----------- ----------- --------------- -------------- Inelastic Conserved Not Conserved Conserved Elastic Conserved Conserved Conserved 1.3.5 -- Newton's 2^nd^ Law --------------------------- Newton's 2^nd^ law states that the resultant force (F) is proportional to the rate of change of momentum (∆p/t)h Or, [\$F \\propto \\frac{\\Delta p}{t}\$]{.math.inline}, which can be expressed as [\$F = k\\frac{\\Delta p}{t}\$]{.math.inline} where k is some constant. Most problems involve a constant mass undergoing a change in velocity. We can then write: [\$F = \\frac{m \\cdot \\Delta v}{t}\$]{.math.inline} Some problems instead involve a change in mass at a constant velocity, e.g. a jet engine ejecting a certain mass of gas per second with a constant velocity. For these problems we can write: [\$F = \\frac{v \\cdot \\Delta m}{t}\$]{.math.inline}. Unit 1.4 -- Energy Concepts =========================== 1.4 -- Definitions ------------------ REFERENCE TERM ESSENTIAL POINTS ----------- ------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------ 1.4.1 Work Work done by a force is the product of the magnitude of the force and the distance moved in the direction of the force. [*W* = *Fx*cos *θ*]{.math.inline} 1.4.2 Principle of conservation of energy Energy cannot be created or destroyed, only transferred from one form to another. 1.4.2 E~p~ The energy possessed by an object by virtue of its position 1.4.2 E~k~ This is energy possessed by an object by virtue of its motion 1.4.2 E~elastic~ The energy possessed by an object when it has been deformed due to forces acting on it 1.4.2 Energy The energy of a body or system is the amount of work it can do 1.4.4 Power The work done per second/energy transferred per second 1.4.1 -- Work ------------- If a body moves as a result of a force being applied to it, the force is said to be doing work on the body. The work is given by: - [*W* = *Fx*]{.math.inline} where: - W = work, J - F = force, N - X = distance moved in the direction of the force, m 1.4.2 -- Energy --------------- Energy is often defined as the ability to do work. Doing work involves a transfer of energy from one form to another. The amount of work done tells us how much energy has been transferred from one form to another. Work done is always equal to the energy transferred. Gravitational potential energy is the energy stored in an object due to its position. It can be found using the formula: - [*E*~*p*~ = *mgh*]{.math.inline} where: - E~p~ = gravitational potential energy, J - M = mass, kg - G = acceleration due to gravity - H = height, m Kinetic energy is the energy possessed by an object due to its motion. It can be found using the formula: - [\$E\_{k} = \\frac{1}{2}mv\^{2}\$]{.math.inline} where - E~k~ = kinetic energy, J - M = mass, kg - V = velocity, ms^-1^ Elastic potential energy is the energy possessed by an object when it has been deformed due to the forces acting on it. It can be found using the formula: - [\$E\_{\\text{elastic}} = \\frac{1}{2}Fx = \\frac{1}{2}kx\^{2}\$]{.math.inline} where - E~elastic~ = elastic potential energy, J - F = force, N - X = extension, - K = spring constant, Nm^-1^ The principle of conservation of energy states: Energy cannot be created or destroyed, only changed from one form to another. 1.4.3 -- The Work-Energy Relationship ------------------------------------- We have seen that when a force is applied which causes a block to move a distance, work has been done on the block. This means that there is a transfer of energy. If no friction is acting on the block, it will accelerate, and the energy transfer causes an increase in the E~k~ of the block. The increase in E~k~ is equal to the work done. This can be expressed as: [\$Fx = \\frac{1}{2}mv\^{2} - \\frac{1}{2}mu\^{2}\$]{.math.inline} or [\$Fx = \\frac{1}{2}m{\\Delta v}\^{2}\$]{.math.inline} 1.4.4 -- Power -------------- Power is defined as the rate of doing work (or the rate of energy transferred). [\$P = \\frac{\\text{Fx}}{t} = \\frac{E}{t}\$]{.math.inline} where: - P = power, W - F = force, N - X = distance, m - T = time, s - E = energy transferred, J However, [\$\\frac{x}{t} = v\$]{.math.inline} so we can also say [*P* = *Fv*]{.math.inline}, where v = velocity, ms^-1^. 1.4.5 -- Dissipative Forces and Energy -------------------------------------- - The increase in gravitational potential energy is equal to the work done against the force of gravity. - The increase in elastic potential energy is equal to the work done against the tension within the object when it is stretched. These processes are reversible. If we release the system , they will naturally return to their previous states -- the energy can transfer in the opposite direction. However is a force does work by moving an object against a frictional force or aerodynamic drag, the energy that is transferred cannot be recovered in the same way. This is because the energy is then possessed in an increase in the disordered motion of the molecules of the system (the initial energy) and generally results in a rise in temperature. \ [\$\$\\eta = Efficiency = \\frac{\\text{Total\\ Useful\\ Output}}{\\text{Total\\ Input}}\\text{\\ \\ }\$\$]{.math.display}\ If we multiply this formula by 100 we would get the percentage efficiency of the system. Efficiency has no units. Unit 1.5 -- Solids Under Stress =============================== 1.5 -- Definitions ------------------ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ REFERENCE TERM ESSENTIAL POINTS ----------- -------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1.5.2 Hooke's Law The tension in a spring or wire is proportional to it extension from its natural length, provided the extension is not too great. 1.5.2 Spring constant (K) The spring constant is the force er unit extension (Nm^-1^). 1.5.5 Stress ([*σ*]{.math.inline}) Stress is the for per unit CSA when equal opposing forces act on a body (Nm^-2^) 1.5.5 Strain ([*ε*]{.math.inline}) Strain is defined as the extension per unit length due to an applied stress. 1.5.5 Young modulus ([*E*]{.math.inline}) \ [\$\$E = \\frac{\\sigma}{\\varepsilon} = \\frac{\\text{stress}}{\\text{strain}}\$\$]{.math.display}\ 1.5.6 Crystal Solid in which atoms are arranged in a regular array. There is a long-range order within crystal structures. 1.5.6 Crystalline Solid Solid consisting of a crystal (or many) usually arranged randomly. The latter is strictly a polycrystalline solid. Metals are polycrystalline. 1.5.6 Amorphous Solid A truly amorphous solid would have atoms arranged quite randomly. Examples are rare. In practice we include solids such as glass or brick in which there is no long-range order in the wat atoms are arranged, though there may be ordered clusters of atoms. 1.5.6 Polymeric Solid A solid which is made up of chain like molecules 1.5.7 Ductile Material A material that can be drawn out into a wire. This implies that plastic strain occurs under enough stress. 1.5.7 Elastic strain This is strain that disappears when the stress is removed, that is the specimen returns to its original shape and size 1.5.7 Plastic (or inelastic) strain This is strain that decreases only slightly when the stress is removed. In a metal it arises from the movement of dislocations within the crystal structure. 1.5.7 Elastic limit This is the point at which deformation ceases to be elastic. For a specimen it is usually measured by the maximum force, and for a material, by the maximum stress, before the strain ceases to be elastic. 1.5.7 Dislocations in crystals Certain faults in crystals which (if there are not too many) reduce the stress needed for planes of atoms to slide. The easiest dislocation to picture is an edge dislocation: the edge of an intrusive, incomplete plane of atoms 1.5.7 Grain boundaries The boundaries between crystals (grains) in a polycrystalline material 1.5.7 Ductile fracture The characteristic fracture process in a ductile material. The fracture of a rod or wire is preceded by local thinning which increases the stress. 1.5.8 Brittle material Material with no region of plastic flow, which, under tension, fails by brittle fracture. 1.5.8 Brittle fracture The fracture under tension of brittle materials by means of crack propagation. 1.5.9 Elastic hysteresis When a material such as rubber is but under stress and the stress is then relaxed, the stress-strain graphs for increasing and decreasing stress don't coincide but form a loop. This is hysteresis. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 1.5.1 -- Forces on Solid Materials ---------------------------------- ![](media/image2.png)If equal and opposite forces are applied to the opposite ends of an object, its particles (molecules/atoms/ions) will be forced into a new equilibrium position with respect to one another. The forces can be: a. Compressive b. Tensile c. Shear 1.5.2 - Hooke's Law ------------------- Hooke's law states that **the extension of a spring is proportional to the applied load, provided the limit of proportionality is not exceeded.** The mathematical formula for Hooke's Law is: [*F* = *kx*]{.math.inline} were. - F = applied load (N) - K = spring constant (Nm^-1^) - X = extension of the material (m) 1.5.3 -- Spring in Series and Parallel -------------------------------------- ***\[see inkodo 1.5 class notes pdf for worked examples\]*** 1.5.4 -- Work of Deformation and Energy --------------------------------------- When a material is stretched by a force, the work done is stored as strain energy (elastic potential energy). This energy is equal to the work done, as long as the material has not exceeded its elastic limit. For materials that follow Hooke\'s law, the force and extension are proportional up to the **limit of proportionality**, meaning the force-extension graph is a straight line. The strain energy can be calculated by finding the area under this graph, which is a triangle. The strain energy [*E*]{.math.inline} stored in the material is given by the formula: \ [\$\$E = work\\ done = \\frac{1}{2}\\text{Fx}\$\$]{.math.display}\ where F is the force and x is the extension. Since Hooke\'s law states \ [*F* = *kx*]{.math.display}\ k is the spring constant; the strain energy can also be written as: \ [\$\$E = \\frac{1}{2}kx\^{2}\$\$]{.math.display}\ This shows that strain energy is proportional to the square of the extension and depends on the spring constant K. 1.5.5 -- Stress, Strain and Young's Modulus ------------------------------------------- Stress is the force applied per unit area of the material\'s cross-section, given by the formula: [\$\\sigma = \\frac{F}{A}\$]{.math.inline} where: - σ is stress (in pascals, Pa or Nm^-1^), - F is the applied force (in newtons, N), - A is the cross-sectional area (in square meters, m²). Strain is the ratio of the change in length of a material to its original length, given by: [\$\\epsilon = \\frac{\\Delta L}{L\_{o}}\$]{.math.inline} where: - ϵ is strain (a dimensionless quantity), - ΔL is the change in length (in meters, m), - L~o~ is the original length (in meters, m). When a tensile stress is applied to a material, it produces a corresponding strain. As long as the stress is not too large, the strain is directly proportional to the stress. Within the **limit of proportionality**, the ratio of stress to strain is called **Young's modulus**. This is expressed as: [\$E\_{Y} = \\frac{\\sigma}{\\epsilon} = \\frac{F \\bullet L\_{o}}{A \\bullet \\Delta L}\\ \$]{.math.inline}where: - E~Y~ (in pascals, Pa or Nm−2\\text{Nm}\^{-2}Nm−2). If stress and strain are measured to the breaking point of a material, a graph can be plotted showing the relationship. The graph would include: - **Point A**: the **limit of proportionality**, - **Point B**: the **elastic limit**, - **Point C**: the point of **ultimate tensile stress** (UTS), which is the maximum stress a material can withstand before it breaks. The **ultimate tensile stress (UTS)** is the maximum stress a material can endure without failure. The **gradient of the straight line** in the initial portion of the stress-strain graph is the **Young's modulus**. Young's modulus is a material property that measures its stiffness, with a higher value indicating a stiffer material. It is independent of the material\'s dimensions and depends only on the material\'s nature. A diagram of a stress reaction Description automatically generated 1.5.6 - Types of Solid ---------------------- - Crystalline Solids: - Have short- and long-range atomic order, with a regular pattern of atoms or molecules extending over at least 100 atomic diameters. - Examples include most metals and many minerals (e.g., salt). - These materials are often **polycrystalline**, meaning they consist of many small crystals or **grains**, each with a different orientation. - The boundaries between grains are called **grain boundaries**. - The structure is strong because the grains are aligned in a regular pattern. - **Amorphous Solids**: - Lack long-range order in the arrangement of atoms or molecules. - The structure is like a \"frozen\" or \"instantaneous\" snapshot of a liquid, with no repeating pattern. - Examples include glass and brick, which may have ordered **clusters of atoms** but no large-scale order. - Completely random atomic structures are rare, but amorphous materials have no regular arrangement like crystalline solids. - **Polymeric Solids**: - Composed of long chains of carbon atoms, often bonded to hydrogen and other elements, typically with over 1,000 atoms in each chain. - Can be **natural** (e.g., cellulose, nylon) or synthetic. - The bonds in polymer chains are strong but flexible, allowing for rotation, making polymers both **strong and flexible**. - **Cross-links** (connections between chains) can be introduced to increase stiffness and rigidity in the polymer material. 1.5.7 -- Stress-Strain Graphs for Metals ---------------------------------------- ![A graph with lines and dots Description automatically generated](media/image4.png) Region OP Straight line -- extension is proportional to the load applied (obeys Hooke's law) ------------ -------------------------------------------------------------------------------------------------------------------------- Point P Limit of proportionality Point E Elastic limit -- up to this point the material will return to its original shape and size after the force is removed. Point Y~1~ Yield point -- large extension occurs with little or no extra stress as planes of atoms start to slip past each other. Point Y~2~ Material stretches so much in some materials (e.g. copper) that the stress is actually reduced for a while. Region EX Plastic region -- material will not return to original size once it's entered this region. Point X~1~ Material breaks -- signifies the ultimate tensile strength for most materials. Point X~2~ Some very ductile metals (like copper) become narrower and extend rapidly just before breaking. This is known as necking Metals and minerals like salt have a regular atomic pattern, so when force is applied to a crystalline material, it is transmitted equally due to the long-range atomic order. For small extensions, the force (FFF) is proportional to the extension (xxx), meaning the material follows Hooke\'s law and the graph is a straight line from O to P. Plastic deformation occurs when a material is stretched beyond its elastic limit. At this point, atoms in one plane can slip over atoms in another if the force is large enough. This is made easier by dislocations, which explain why ductile materials deform more easily in the plastic region. Dislocations happen when molten metal cools and forms crystal defects. A common mistake is missing half a plane of atoms, called **edge dislocation**. These dislocations are important for plastic deformation because the bonds around the dislocation are strained and weaker, making them more likely to break. When the material is under tension, and the force is small, the bonds stretch reversibly, and the material behaves elastically. As the force increases and passes the yield point, the strained bonds stretch further and break, allowing the dislocation to move. This movement continues as the bonds snap and reform, moving the dislocation from left to right through the crystal. This makes it appear as though the planes of atoms have slipped, but in reality, only a line of bonds is broken at a time, which is easier than breaking an entire plane. To strengthen metals and reduce plastic deformation, the grain size can be reduced, which limits the movement of dislocations. Foreign atoms can also be added to the metal, creating dislocation points that hinder the movement of dislocations and make plastic deformation harder. 1.5.8 -- Brittle Materials and Rubber ------------------------------------- [Brittle Materials] Glass is categorised as an amorphous material and is very brittle. Cast iron is also a brittle material. The graph shown is the stress-strain curve for cast iron and glass (smaller line). Neither curve has a 'plastic' region since both are brittle materials. Although the glass has a similar value for its young modulus to that of cast iron, i.e. similar stiffness, it has a significantly lower value for its ultimate breaking stress of about 700 MPa, meaning that it has less strength that iron. [Rubber] The behaviour of a polymer is primarily dictated by its cross-links---strong covalent bonds between adjacent polymer chains or different parts of the same molecule. When there are few cross-links, the polymer chains can slide past one another, making the material stretchy, like rubber. Adding more cross-links, such as by introducing sulfur to latex, makes the polymer more rigid, creating a material called vulcanite. The more cross-links there are, the harder it is for the chains to move, making the polymer stiffer and less flexible. Looking at the stress-strain curve for rubber, there are three distinct regions that can be explained by the molecular structure and behaviour of the material: - ![](media/image6.png)Region OA (Initial Stiffness):\ When force is applied to rubber, it initially resists stretching due to the presence of van der Waals forces, which are weak, short-range bonds between the polymer molecules. These forces hold the molecules together loosely, causing the material to resist deformation but still stretch a small amount. This explains the initial stiffness in the material as shown in the flat portion of the curve (OA). - Region AB (Easy Extension):\ As force increases, the van der Waals forces weaken rapidly with distance, and the molecules begin to untangle and uncoil. In this phase, the rubber stretches much more easily with less force, and the material behaves more elastically. The graph in this region is relatively flat, indicating a significant extension without much increase in force. The rubber is stretching without much resistance as the chains uncoil and move more freely. - Region BC (Stiffening):\ After the molecules have fully uncoiled (at point B), further stretching requires breaking or elongating the strong covalent bonds between polymer chains and the cross-links that hold the material together. These bonds are much stronger and harder to break than the van der Waals forces, making further stretching more difficult. This causes the graph to steepen in region BC, where the material becomes stiffer and stronger, behaving more like other covalently bonded solids. Rubber molecules themselves are long and thin, with swivel joints along the chain that allow them to bend and twist, contributing to the material\'s elasticity. In natural rubber (latex), there are few cross-links, allowing the polymer chains to be more flexible and easily stretch. The weak van der Waals forces between molecules keep them loosely bonded, explaining the initial stiffness (region OA) and the easy extension in region AB as the molecules untangle. Once the rubber has been stretched and the molecules are aligned, the material starts to resist further deformation, as the strong covalent bonds and cross-links between chains need to be stretched or broken in region BC, leading to a much stiffer material that behaves like a solid with strong covalent bonds. In summary, the stress-strain behaviour of rubber can be explained through the molecular interactions between van der Waals forces (in region OA and AB) and covalent bonds and cross-links (in region BC). The initial stretching is easy due to untangling of the chains, but as the material reaches its limit, further deformation requires breaking stronger bonds, making the material stiffer and stronger. 1.5.9 -- Hysteresis ------------------- Hysteresis is when the stress-strain is different depending on whether you are loading or unloading the material. The area between the two curves is equal to the energy per unit volume stored as thermal energy in the rubber after it has been loaded and then unloaded Unit 1.6 -- Using Radiation to Investigate Stars ================================================ 1.6 -- Definitions ------------------ REFERENCE TERM ESSENTIAL POINTS ----------- ------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1.6.1 Black Body A black body is a body (or a surface) which absorbs all the EM radiation that falls upon it. No body is a better emitter of radiation at any wavelength that a black body at the same temperature. 1.6.2 Wien's Displacement law The wavelength of peak emission from a black body is inversely proportional to the absolute temperature. [\$\\lambda\_{\\max} = \\frac{W}{T}\$]{.math.inline}. (W = Wien's Constant = 2.9x10^-3^ m K) 1.6.2 Absolute temperature The temperature in kelvin (K) is related to the temperature in Celsius. (0°C +273). At 0K the E~k~ of the particles in a body is the lowest it possibly it can be. 1.6.3 Stefan-Boltzmann Law [*Σ*]{.math.inline} EM radiation energy per unit time by a black body is given by [*P* = *AσT*^4^]{.math.inline} in which A is the SA and [*σ*]{.math.inline} is Stefan's constant ([*σ*]{.math.inline} = 6.67x10^-8^Wm^-2^K^-4^) 1.6.4 Luminosity of a star The luminosity of a star is the [*Σ*]{.math.inline}E it emits per unit time in the form of EM radiation. Unit: W. \[[∴]{.math.inline}we can write luminosity instead of power in Stefan's Law\] 1.6.5 Intensity The intensity of radiation at a distance R from a source is given by [*I*= *P*/4*πR*^2^]{.math.inline} Unit: Wm^-2^ 1.6.1 -- Stellar Spectra and Black Bodies ----------------------------------------- Most of our knowledge about the universe comes from electromagnetic radiation. Photographs of constellations are captured using visible light (wavelengths between 400-700nm). Until recently, this was the only accessible wavelength range due to the Earth\'s atmosphere blocking most of the electromagnetic spectrum. However, space telescopes now allow us to observe the universe across the entire electromagnetic spectrum, from radio waves to gamma rays. This multi-wavelength approach provides a more comprehensive understanding of cosmic processes. Starlight is analysed by separating its wavelengths, typically using a prism or diffraction grating. The results are then used to create an image or plot the energy density across different wavelengths. Stars do not have a defined surface; the light we observe comes from the photosphere, a gas layer several hundred kilometres thick. When a hot object like a star emits light, it produces a broad spectrum of wavelengths, similar to a black body spectrum. **[A black body is defined as a body (or surface) which absorbs all the electromagnetic radiation that falls upon it.]** Nothing is a better emitter of radiation at any wavelength than a black body at the same temperature. ![](media/image8.png)Although stars aren\'t black, they are nearly perfect emitters, so their light should produce a continuous spectrum with all wavelengths. However, specific wavelengths can be absorbed by atoms in a star\'s atmosphere and upper photosphere, resulting in an absorption spectrum that reaches our telescopes. The spectra of stars provide valuable information about their temperature, chemical composition, and more. By analysing the shape of the continuous spectrum and the positions of dark lines (Fraunhofer lines), astronomers can compare stars, study their motion, and even gather evidence about the universe\'s age. The intensity of radiation from a black body varies with wavelength, and curves depicting this variation show how the intensity changes for black bodies at different temperatures. The shape of the curve (the black body spectrum) is similar for each temperature. However: - The higher the temperature, the higher the peak intensity. - The higher the temperature, the lower the peak intensity [*λ*]{.math.inline} (peak shifted to the left at higher temperatures). - The lower the temperature, the longer the 'flat' section of the curve is before the curve 'lifts off'. x1.6.2 -- Wien's Law -------------------- Weien's displacement law states that the wavelength, [*λ*~max~ ]{.math.inline}, of peak emission from a black body is inversely proportional to the absolute temperature, T, of the body: \ [\$\$\\lambda\_{\\max} = \\frac{W}{T}\$\$]{.math.display}\ Where: - λ~max~ = wavelength (m) - W = Wien constant (2.90 x10^-3^m k) - T = temperature (k) 1.6.3 -- Stephan-Boltzmann Law ------------------------------ The total electromagnetic radiation energy emitted per unit time by a black body is given by: \ [*P* = *AσT*^4^]{.math.display}\ Where: - P = power (w) - A = surface area (m^2^) - [*σ*]{.math.inline} = Stefan constant (5.67 x10^-8^ Wm^-2^K^-4^) - T = absolute temperature (K) The importance of these for astronomers is that many astronomical objects emit thermal radiation, which approximates to black body radiation. Examples are stars with surface temperature up to tens of thousands of kelvins; accretion discs around black holes (up to 10^6^k); CMBR (2.713K). 1.6.4 -- Luminosity, Intensity and Distance ------------------------------------------- The luminosity of a star is the total energy it emits per unit time as electromagnetic radiation, measured in watts (W). This makes luminosity equivalent to a star\'s power, meaning Stefan\'s law could use luminosity instead of power. The diagram shows how radiation from a small source like a star spreads out. As the distance from the star increases, the radiation covers a larger area, reducing the intensity of the radiation. **Intensity may be defined as the amount of light energy striking each metre square per second.** The inverse square law states that the intensity of the radiation from a star is inversly proportional the the distance from the star squared. This can be represented as: \ [\$\$I = \\frac{P}{4\\pi R\^{2}}\$\$]{.math.display}\ Where: - I = intensity of the radiation, measured in Wm^-1^ - P = total power (luminosity) produced by the star, measured in W - R = distance from the star, measured in m Note that [4*πR*^2^]{.math.inline} is the surface are of an 'imaginary' sphere of radius R. The assumption that we can treat stars as black bodies allows us to determine the temperature and diameter of a star from measurements of its spectrum as long as we know the distance. ***\[see inkodo 1.6 class notes pdf for examples\]*** ***\ *** 1.6.5 -- Multiwavelength Astronomy ---------------------------------- The electromagnetic spectrum provides insights into various processes in the universe. The Sun primarily emits energy as near infrared, visible, and near ultraviolet radiation due to the temperature of its photosphere, which is around 5800K. Generally, objects with higher temperatures emit radiation at shorter wavelengths. A galaxy can be studied using different telescopes which are sensitive to different wavelengths of the electromagnetic spectrum. This is called multiwavelength astronomy. With the exception of visible light astronomy, the colours are 'false colours'; the colour is an intensity code rather than an actual colour. The images below show the same galaxy. Each images was taken using a different telescope sensitive to different wavelengths. ![](media/image10.png) [ ] Some non-thermal processes result in the emission of radiation:21 cm HI and synchrotron radiation. These can give us an additional information about the hydrogen clouds and about magnetic fields. So, a study of how radiation across the EM spectrum provides us with much more information than observations in one spectral region alone. Unit 1.7 -- Particles and Nuclear Structure =========================================== 1.7 -- Definitions ------------------ REFERENCE TERM ESSENTIAL POINTS ----------- -------- ---------------------------------------------------------------------------------------------------------------------------------------------------------- 1.7.2 Lepton Leptons are electrons and electron-neutrinos (and analogous pairs of particles of the co called second and third generations) 1.7.3 Hadron Hadrons are particles consisting of quarks or antiquarks bound together. Only hadrons (and quarks or antiquarks themselves) can 'feel' the strong force. 1.7.3 Baryon A baryon is a hadron consisting of 3 quarks or 3 antiquarks. The best known are the nucleons. 1.7.3 Meson A meson is a hadron consisting of a quark-antiquark pair. 1.7.1 -- A Brief History of Our Understanding of the Atom --------------------------------------------------------- - The atom was regarded as an elementary particle in the 19^th^ century. - At the end of the century, electrons had been identified as a universal component of atoms. - Between 1908 and 1931 the concept of a positively charged atomic nucleus, containing virtually all the mass of the atom was discovered. - By the early 1930's the main constituents of the nucleus, protons and neutrons had been discovered and were initially thought to be elementary. This brings us up the understanding of the structure of an atom from GCSE. But there's more: - Collision experiments, known as deep inelastic scattering, in the 1960's and 1970's showed that the nucleons (protons and neutrons) aren't elementary particles. They are composed of 3 particles called quarks, bound together by strong interaction. These quarks are thought to be elementary particles. - The middle decades of the 20^th^ century produced discoveries of many particles, variously called hadrons, fermions, bosons, mesons, nucleons, baryons, neutrinos... 1.7.2 -- Quarks and Leptons --------------------------- The image below shows the standard practice model whereby the different quarks and leptons can be seen. Note they are grouped into generations. You are only expected to recognise that there are 3 generations of quarks and leptons, but questions will only involve the first class. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- **LEPTONS** **QUARKS** ------------- ---------------------------- ----------------------------- -------- ------------------------------------------ -------------------------------------------- Name Electron Electron Neutrino Name Up Down Symbol \ \ Symbol \ \ [*e*^−^]{.math.display}\ [*ν*~*e*~]{.math.display}\ [*u*]{.math.display}\ [*d*]{.math.display}\ Charge \ 0 Charge \ \ [ − *e* ]{.math.display}\ [\$\$\\frac{2}{3}e\$\$]{.math.display}\ [\$\$- \\frac{1}{3}e\$\$]{.math.display}\ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Each one of these particles has a corresponding antiparticle with an identical mass and equal but opposite charge. ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- **ANTI-LEPTONS** **ANTI-QUARKS** ------------------ --------------------------- -------------------------------------------------- -------- -------------------------------------------- -------------------------------------------- Name Anti-electron (positron) electron anti-neutrino Name Anti-up Anti-down Symbol \ \ Symbol \ \ [*e*^+^]{.math.display}\ [\$\$\\overline{\\nu\_{e}}\$\$]{.math.display}\ [\$\$\\overline{u}\$\$]{.math.display}\ [\$\$\\overline{d}\$\$]{.math.display}\ Charge \ 0 Charge \ \ [ + *e*]{.math.display}\ [\$\$- \\frac{2}{3}e\$\$]{.math.display}\ [\$\$+ \\frac{1}{3}e\$\$]{.math.display}\ ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- When a particle and its antiparticle meet, they annihilate each other, converting their mass into energy. In the case of electron-positron annihilation, this process produces two gamma photons moving in opposite directions. Leptons, the lightest subatomic particles, always exist independently and do not form composite particles. The important properties to remember are: - Lepton number: electrons and electron neutrinos have a lepton number of 1. Their antiparticles, positrons and electron anti-neutrinos, have a lepton number of -1. - Charge. Electrons have a charge of -e, and neutrinos have a charge of 0. - Antiparticles have equal but opposite charges. 1.7.3 -- Hadrons ---------------- Quarks and antiquarks do not exist separately but combine to form composite subatomic particles known as hadrons. There are three types of hadrons: - Baryons: consist of 3 quarks - Antibaryons: consist of 3 anti-quarks - Mesons: consist of one quark-antiquark pair. All quarks have a baryon number of [\$+ \\frac{1}{3}\$]{.math.inline} and all anti-quarks have a baryon number of [\$- \\frac{1}{3}\$]{.math.inline}. This means that all baryons must have a baryon number of 1 and all anti-baryons must have a charge of -1. The most common baryons are the proton and neutron. S ---------------------------------------------------------------------- **PROTON** **NEUTRON** ------------------- --------------------------- ---------------------- Charge \ \ [ + *e*]{.math.display}\ {.math.display}\ Baryon number 1 1 Quark composition UUD UDD ---------------------------------------------------------------------- Mesons consist of one quark and one anti-quark, as a result they have a baryon number of 0. The first-generation quarks and antiquarks combine to form the pions: --------------------------------------------------------------------------------------------------- **SYMBOL** **QUARK COMPOSITION** **CHARGE** --------------------------- ------------------------------------------- --------------------------- \ \ \ [*π*^+^]{.math.display}\ [\$\$u\\overline{d}\$\$]{.math.display}\ [ + *e*]{.math.display}\ \ \ \ [*π*^−^]{.math.display}\ [\$\$\\overline{u}d\$\$]{.math.display}\ [ − *e*]{.math.display}\ \ \ \ [*π*^0^]{.math.display}\ [\$\$u\\overline{u}\$\$]{.math.display}\ {.math.display}\ \ \ \ [*π*^0^]{.math.display}\ [\$\$d\\overline{d}\$\$]{.math.display}\ {.math.display}\ --------------------------------------------------------------------------------------------------- 1.7.4 -- Interactions (forces) Between Particles ------------------------------------------------ **INTERACTION** **AFFECTS** **RANGE** **COMMENTS** ----------------- --------------------------------------------------------- ----------------------- ----------------------------------------------------------------------- Gravitational All matter Infinite Very weak- negligible except between large objects such as planets Weak All leptons, all quarks ([∴]{.math.inline}all hadrons) Very short (10^-18^m) Only sufficient when the EM and strong interactions do not operate. Electromagnetic All charged particles Infinite Also experienced by neutral hadrons, as these are composed of quarks. Strong All quarks ([∴]{.math.inline}all hadrons) Short (10^-15^m) E.g. Nuclear binding. The following properties can be used to identify the force involved in a reaction. +-----------------------+-----------------------+-----------------------+ | **INTERACTION** | **LIFETIME** | **CRITERIA** | +=======================+=======================+=======================+ | Strong Interaction | 10^-24^s | - Only hadrons | | | | involved | | | | | | | | - There is no | | | | change in quark | | | | flavour. | | | | | | | | - Typically | | | | involved in | | | | collision between | | | | particles | +-----------------------+-----------------------+-----------------------+ | Electromagnetic | 10^-12^-10^-18^s | - The particles | | interactions | | bust have charge | | | | or charged | | | | components. | | | | Although a | | | | neutron is | | | | uncharged, it | | | | consists of | | | | charged quarks. | | | | | | | | - There is no | | | | change in quark | | | | flavour | | | | | | | | - One or more | | | | photons may be | | | | emitted. | +-----------------------+-----------------------+-----------------------+ | Weak interactions | 10^-8^s | - Neutral leptons | | | | (neutrinos) | | | | involved | | | | | | | | - There may be a | | | | change in quark | | | | flavour. | +-----------------------+-----------------------+-----------------------+ The three non-gravitational forces have important roles in the stability: - Electrons are bound to the nucleus by the electromagnetic force. - Protons and neutrons are held together in the nucleus by the strong force which opposes the electromagnetic repulsion of the protons. - The weak force is responsible for the decay of neutrons in neutrons neutron-rich nuclei, giving rise to [*β*^−^]{.math.inline}. z ![A diagram of a flowchart Description automatically generated](media/image12.png) 1.7.5 -- Conservation Laws. --------------------------- Reactions involving subatomic particles must obey the conservation of energy, momentum, charge, lepton number, and baryon number. This means that the total charge, lepton count, and baryon count must remain the same before and after the reaction. In all reactions charge must be conserved. The lepton number is defined for the first generation as shown in the table below. Other first-generation particles, photons, quarks (and hence baryons and mesons) are assigned a lepton number of 0. Lepton number is always conserved. ----------------------------------------------------------------------------------------------- **NAME** **SYMBOL** **LEPTON NUMBER** ------------------------ -------------------------------------------------- ------------------- Electron \ 1 [*e*^−^]{.math.display}\ Anti-electron \ -1 [*e*^+^]{.math.display}\ Electron anti-neutrino \ 1 [\$\$\\overline{\\nu\_{e}}\$\$]{.math.display}\ Electron anti-neutrino \ -1 [\$\$\\overline{\\nu\_{e}}\$\$]{.math.display}\ ----------------------------------------------------------------------------------------------- The baryon number (B) is defined such that baryons (e.g., protons) have a baryon number of +1, anti-baryons have -1, and leptons and mesons have a baryon number of 0. Baryon number is always conserved in reactions. It is important to consider the quarks involved in the reaction. Consider the example on pg10 of inkodo notes. In this reaction, one if the down quarks have changed to an up quark. This is known as a quark flavour change and, along with neutrino involvement, is exclusive to weak interaction. Unit 1 Definitions ================== ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- REFERENCE TERM ESSENTIAL POINTS ----------- ------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1.1.1 Quantity In SI a quantity is represented by a number and a unit 1.1.3 Scalar A scalar is a quantity that has a magnitude (and unit) only 1.1.3 Vector A vector is a quantity that has a magnitude (unit) and direction 1.1.3 Resolving a vector to find its components This means finding component vectors in the horizontal and vertical directions 1.1.4 Density The mass per unit of volume 1.1.5 Moment The moment about a point is defined as the force multiplied by the perpendicular distance from the point to the line of action of the force 1.1.5 The principle of moments For a system to be in equilibrium, the sum of the anticlockwise moments about a point must be equal to the sum of the clockwise moments about the same point 1.1.6 Translational equilibrium The resultant force in any given line is zero 1.1.6 Rotational equilibrium The net moment about any pivot is zero 1.1.7 Centre of gravity The centre of gravity is the single point within a body at which the entire weight of the body may be considered to act. 1.2.1 Displacement The (straight line) distance travelled in a specific direction. 1.2.1 Mean speed The total distance travelled in the time taken to carry out the whole journey. 1.2.1 Mean velocity The total displacement during the total time taken. 1.2.1 Instantaneous speed The rate of change of distance 1.2.1 Instantaneous velocity The rate of change of displacement 1.2.1 Mean acceleration The change in velocity during the time taken 1.2.1 Instantaneous acceleration The rate of change of velocity 1.2.5 Terminal velocity The terminal velocity is the constant, maximum velocity of an object when resistive forces on it are equal and opposite to the 'accelerating' force 1.3.1 Force A force on a body is a push or a pull acting on the body from some external body. 1.3.1 \ The product of the mass of a body and its acceleration is equal to the vector sum of the forces acting on the body. This vector sum is called the resultant force. [Σl*F* = *ma*]{.math.display}\ 1.3.2 Newton's 3^rd^ law If body A exerts a force on body B, then B exerts an equal and opposite force on A 1.3.3 Momentum The momentum of is the product of its mass and velocity ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- REFERENCE TERM ESSENTIAL POINTS ----------- --------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1.3.3 Principle of conservation of momentum The vector sum of the momenta of bodies in a system stays constant even if forces act between the bodies, provided there is no external resultant force. 1.3.4 Elastic collision A collision in which there is no change in tot E~k~ 1.3.4 Inelastic collision A collision in which E~k~ is lost. 1.3.5 Newton's 2^nd^ law The rate of change of momentum of an object is proportional to the resultant 1.4.1 Work Work done by a force is the product of the magnitude of the force and the distance moved in the direction of the force. [*W* = *Fx*cos *θ*]{.math.inline} 1.4.2 Principle of conservation of energy Energy cannot be created or destroyed, only transferred from one form to another. 1.4.2 E~p~ The energy possessed by an object by virtue of its position 1.4.2 E~k~ This is energy possessed by an object by virtue of its motion 1.4.2 E~elastic~ The energy possessed by an object when it has been deformed due to forces acting on it 1.4.2 Energy The energy of a body or system is the amount of work it can do 1.4.4 Power The work done per second/energy transferred per second 1.5.2 Hooke's Law The tension in a spring or wire is proportional to it extension from its natural length, provided the extension is not too great. 1.5.2 Spring constant (K) The spring constant is the force er unit extension (Nm^-1^). 1.5.5 Stress ([*σ*]{.math.inline}) Stress is the for per unit CSA when equal opposing forces act on a body (Nm^-2^) 1.5.5 Strain ([*ε*]{.math.inline}) Strain is defined as the extension per unit length due to an applied stress. 1.5.5 Young modulus ([*E*]{.math.inline}) \ [\$\$E = \\frac{\\sigma}{\\varepsilon} = \\frac{\\text{stress}}{\\text{strain}}\$\$]{.math.display}\ 1.5.6 Crystal Solid in which atoms are arranged in a regular array. There is a long-range order within crystal structures. 1.5.6 Crystalline Solid Solid consisting of a crystal (or many) usually arranged randomly. The latter is strictly a polycrystalline solid. Metals are polycrystalline. 1.5.6 Amorphous Solid A truly amorphous solid would have atoms arranged quite randomly. Examples are rare. In practice we include solids such as glass or brick in which there is no long-range order in the wat atoms are arranged, though there may be ordered clusters of atoms. 1.5.6 Polymeric Solid A solid which is made up of chain like molecules ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- REFERENCE TERM ESSENTIAL POINTS ----------- ------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 1.5.7 Ductile Material A material that can be drawn out into a wire. This implies that plastic strain occurs under enough stress. 1.5.7 Elastic strain This is strain that disappears when the stress is removed, that is the specimen returns to its original shape and size 1.5.7 Plastic (or inelastic) strain This is strain that decreases only slightly when the stress is removed. In a metal it arises from the movement of dislocations within the crystal structure. 1.5.7 Elastic limit This is the point at which deformation ceases to be elastic. For a specimen it is usually measured by the maximum force, and for a material, by the maximum stress, before the strain ceases to be elastic. 1.5.7 Dislocations in crystals Certain faults in crystals which (if there are not too many) reduce the stress needed for planes of atoms to slide. The easiest dislocation to picture is an edge dislocation: the edge of an intrusive, incomplete plane of atoms 1.5.7 Grain boundaries The boundaries between crystals (grains) in a polycrystalline material 1.5.7 Ductile fracture The characteristic fracture process in a ductile material. The fracture of a rod or wire is preceded by local thinning which increases the stress. 1.5.8 Brittle material Material with no region of plastic flow, which, under tension, fails by brittle fracture. 1.5.8 Brittle fracture The fracture under tension of brittle materials by means of crack propagation. 1.5.9 Elastic hysteresis When a material such as rubber is but under stress and the stress is then relaxed, the stress-strain graphs for increasing and decreasing stress don't coincide but form a loop. This is hysteresis. 1.6.1 Black Body A black body is a body (or a surface) which absorbs all the EM radiation that falls upon it. No body is a better emitter of radiation at aby wavelength that an black body at the same temperature. 1.6.2 Wien's Displacement law The wavelength of peak emission from a black body is inversely proportional to the absolute temperature. [\$\\lambda\_{\\max} = \\frac{W}{T}\$]{.math.inline}. (W = Wien's Constant = 2.9x10^-3^ m K) 1.6.2 Absolute temperature The temperature in kelvin (K) is related to the temperature in Celsius. (0°C +273). At 0K the E~k~ of the particles in a body is the lowest it possibly it can be. REFERENCE TERM ESSENTIAL POINTS ----------- ---------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1.6.3 Stefan-Boltzmann Law [*Σ*]{.math.inline} EM radiation energy per unit time by a black body is given by [*P* = *AσT*^4^]{.math.inline} in which A is the SA and [*σ*]{.math.inline} is Stefan's constant ([*σ*]{.math.inline} = 6.67x10^-8^Wm^-2^K^-4^) 1.6.4 Luminosity of a star The luminosity of a star is the [*Σ*]{.math.inline}E it emits per unit time in the form of EM radiation. Unit: W. \[[∴]{.math.inline}we can write luminosity instead of power in Stefan's Law\] 1.6.5 Intensity The intensity of radiation at a distance R from a source is given by [*I*= *P*/4*πR*^2^]{.math.inline} Unit: Wm^-2^ 1.7.2 Lepton Leptons are electrons and electron-neutrinos (and analogous pairs of particles of the co called second and third generations) 1.7.3 Hadron Hadrons are particles consisting of quarks or antiquarks bound together. Only hadrons (and quarks or antiquarks themselves) can 'feel' the strong force. 1.7.3 Baryon A baryon is a hadron consisting of 3 quarks or 3 antiquarks. The best known are the nucleons. 1.7.3 Meson A meson is a hadron consisting of a quark-antiquark pair. Data Sheet ========== ![A table with symbols and numbers Description automatically generated with medium confidence](media/image14.png) A math equations and formulas Description automatically generated with medium confidence ![A white sheet of maths Description automatically generated](media/image16.png) A maths table with mathematical equations Description automatically generated with medium confidence

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