WJEC AS-1 Physics Revision Notes PDF

Contents {#contents.TOCHeading} ======== [Unit 1: Motion, Energy and Matter 3](#unit-1-motion-energy-and-matter) [Unit 1.1 Basic Physics 3](#unit-1.1-basic-physics) [1.1.1 - SI Units 3](#si-units) [1.1.2 - Prefixes and Standard Form 4](#prefixes-and-standard-form) [1.1.3 Scalars and Vectors 5](...

Contents {#contents.TOCHeading} ======== [Unit 1: Motion, Energy and Matter 3](#unit-1-motion-energy-and-matter) [Unit 1.1 Basic Physics 3](#unit-1.1-basic-physics) [1.1.1 - SI Units 3](#si-units) [1.1.2 - Prefixes and Standard Form 4](#prefixes-and-standard-form) [1.1.3 Scalars and Vectors 5](#scalars-and-vectors) [1.1.4 - Density 6](#density) [1.1.5 - Moments (turning effect/ torque) 7](#moments-turning-effect-torque) [1.1.6 - Bodies in Equilibrium 8](#bodies-in-equilibrium) [1.1.7 - Centre of Gravity 8](#centre-of-gravity) [Unit 1.2 -- Kinematics 9](#unit-1.2-kinematics) [1.2.1 - Motion 9](#motion) [1.2.2 - Motion Graphs (Displacement-Time graphs) 9](#motion-graphs-displacement-time-graphs) [1.2.2 - Motion Graphs (Velocity-Time graphs) 10](#motion-graphs-velocity-time-graphs) [1.2.3 - Equations of Motion for Uniform Acceleration 10](#equations-of-motion-for-uniform-acceleration) [1.2.4 - Falling Objects -- Vertical Motion Under Gravity 11](#falling-objects-vertical-motion-under-gravity) [1.2.5 - Projectile Motion 12](#projectile-motion) [Unit 1.3 -- Dynamics 13](#unit-1.3-dynamics) [1.3.1 - Newton's laws of motion 13](#newtons-laws-of-motion) [1.3.2 - Newton's 3^rd^ Law 13](#newtons-3rd-law) [1.3.3 - Momentum 14](#momentum) [1.3.4 - Elastic and Inelastic Collisions 16](#elastic-and-inelastic-collisions) [1.3.5 - Newton's 2^nd^ Law 16](#newtons-2nd-law) [Unit 1.4 -- Energy Concepts 17](#unit-1.4-energy-concepts) [1.4.1 - Work 17](#work) [1.4.2 -- Energy 17](#energy) [1.4.3 -- The Work-Energy Relationship 18](#the-work-energy-relationship) [1.4.4 -- Power 18](#power) [1.4.4 -- Dissipative Forces and Energy 18](#dissipative-forces-and-energy) [Unit 1.5 -- Solids Under Stress 20](#unit-1.5-solids-under-stress) [1.5.1 Forces on Solid Materials 20](#forces-on-solid-materials) [1.5.2 Hooke's Law 20](#hookes-law) [1.5.3 - Springs in series and parallel 21](#springs-in-series-and-parallel) [1.5.4 -- Work of deformation and Strain Energy 21](#work-of-deformation-and-strain-energy) [1.5.5 -- Stress, Strain and Youngs Modulus 22](#stress-strain-and-youngs-modulus) [1.5.6 -- Types of Solid 23](#types-of-solid) [1.5.7 -- Stress-Strain Graphs for Metals 24](#stress-strain-graphs-for-metals) [1.5.8 -- Brittle Materials and Rubber 26](#brittle-materials-and-rubber) [1.5.9 -- Hysteresis 27](#hysteresis) [Unit 1.6 -- Using Radiation to Investigate Stars 28](#unit-1.6-using-radiation-to-investigate-stars) [1.6.1 -- Stellar Spectra and Black Bodies 28](#stellar-spectra-and-black-bodies) [1.6.2 -- Wien's Law 29](#wiens-law) [1.6.3 -- Stephan-Boltzmann Law 29](#stephan-boltzmann-law) [1.6.4 -- Luminosity, Intensity and Distance 30](#luminosity-intensity-and-distance) [1.6.5 -- Multiwavelength Astronomy 31](#multiwavelength-astronomy) [Unit 1.7 -- Particles and Nuclear Structure 32](#unit-1.7-particles-and-nuclear-structure) [1.7.1 - A Brief History of Our Understanding of the Atom 32](#a-brief-history-of-our-understanding-of-the-atom) [1.7.2 -- Quarks and Leptons 32](#quarks-and-leptons) [1.7.3 -- Hadrons 33](#hadrons) [1.7.4 -- Interactions (Forces) Between Particles 34](#interactions-forces-between-particles) [1.7.5 -- Conservation Laws 37](#conservation-laws) Unit 1: Motion, Energy and Matter ================================= Unit 1.1 Basic Physics ---------------------- ### 1.1.1 - SI Units All physical quantities consist of a numerical magnitude and a unit. For example, the length of your desk may be two (numerical) metres (unit). The "**systeme internationale**" or SI units are a set of internationally agreed units for all quantities in physics. E.g.: - Charge -- Coulomb (C) - Force -- Newton (N) - Energy -- Joule (J) There are also a set of 7 fundamental quantities, or base quantities which can be used to define or derive any other quantity. The units of base quantities are known as base units (or SI base units). **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 quantities and units are known as derived quantities (e.g. energy and force) and derived units (e.g. joules and newtons). It is possible to express and derived quantity or unit in terms of the base quantities and units. To do this, we must use a defining equation. *Example 1: Define the newton, N, in terms of base units.* *F=ma* *\[N\] = kgms^-2^* *Example 2: Electrical current, I, is defined by the equation I=Q/t where Q = charge and t = time. The SI unit for the charge is the coulomb, C. Express this unit in terms of SI base units.* *Q=IT* *\[C\] = As* 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. (NB: This does not confirm the magnitude of any constants in an equation) ### 1.1.2 - Prefixes and Standard Form Many problems arise in which the quantities are either much larger or much smaller than the basic quantities. The data is thus given in standard form or using SI multipliers (prefixes) **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 (NB: the SI unit for mass (kilogram) is the only SI unit with a prefix already included. Only one prefix can be used at a time. Consider 3x10^-6^kg. We cannot write this as 2µkg, we must convert it to grams then add. ### 1.1.3 Scalars and Vectors - Scalar -- **A scalar is a quantity that has magnitude and a unit only.** For example, mass, distance, time, and speed. - Vector - **A vector is a quantity that has a magnitude, direction, and a unit.** For example, displacement, velocity, force and current. [Adding and Subtracting Vectors] When adding vectors, we must first consider their direction as well as magnitude. The final vector is called the resultant. If the vectors are parallel to each other, it is a simple calculation (like seen at GCSE). A paper with writing on it Description automatically generated To calculate the resultant of two perpendicular vectors we use trigonometry. We find both the magnitude and the direction of the resultant vector. For example, consider the two vectors A and B below:  The resultant of these two vectors is the vector C where C = [\$\\sqrt{A\^{2}} + B\^{2}\$]{.math.inline} Direction [\$\\theta = {\\tan\^{- 1}(}\\frac{O}{A})\$]{.math.inline} A close-up of a paper with writing Description automatically generated ### 1.1.4 - Density Density is defined as mass per unit volume. 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. - Example gas densities include: - Hydrogen: 0.089 kgm^-3^ - Oxygen: 1.43 kgm^-3^ - Carbon Dioxide: 1.96 kgm^-3^ - Example liquid densities include: - Alcohol: 789 kgm^-3^ - Water: 1000 kgm^-3^ - Mercury 13534 kgm^-3^ - Example solid densities include: - Aluminium: 2700 kgm^-3^ - Steel: 7500 kgm^-3^ - Uranium: 18800 kgm^-3^ *[Example: A room in a house measured 5.0m x 4.0m x 2.5m. if the density of air is 1.3 kgm^-3^, what is the mass of the air in the room? ]* [\$\\rho = \\frac{m}{v}\$]{.math.inline} [*v* = 5 × 4 × 2.5 = 50.0*m*^3^]{.math.inline} [∴ *m* = *ρ* × *v*]{.math.inline} [*m* = 1.3 *x* 50.0 = 65.0*kg*]{.math.inline} ### 1.1.5 - Moments (turning effect/ torque) 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 many cases the force will naturally act in a direction that is perpendicular to the pivot direction, e.g. a seesaw or a baby's mobile. 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.** *[Example: find the weight of the teddy if it is 10 cm from the pivot when the star has a mass of 50g and is 15 cm from the pivot. **(see page 15 of unit 1.1 booklet)** ]* ***[\ ]*** ### 1.1.6 - Bodies in Equilibrium There are two condition that must be satisfied if an object can be said to be in equilibrium: 1. The resultant force (in any given line) is zero *\[This is called translational equilibrium\]* 2. The net moment (about any pivot) is zero *\[This is called rotational equilibrium\]* The second condition is, in effect, the principle of moments. ### 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. One example when the usefulness of the idea of a centre of gravity is when trying to calculate the stability of an object, i.e. its toppling angle. **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.** This is explained in terms of moments. ***\[see diagram on page 18 of unit 1.1 booklet for diagrams\]*** Consider the object with weight W and centre of gravity C. R is the reaction force of the object l contact with the ground. In the left image, the object is sitting flat on the ground and its weight clearly acts through its base. The reaction R and the weight W each act at the same perpendicular distance from the pivot at point A but in opposite directions. The object is in equilibrium. In the right image, a force F has been applied to tilt the object on to its corner. While the force is in place it will remain in this position. If the force is removed, it will fall back to its upright position (as in the left image). When titled, the reaction force acts from the pivot at point A Thus creates no moment. The weight creates an anticlockwise moment about A; hence the object rotates anticlockwise to return to its upright position. The toppling angle of the angle at which the weight acts just outside the corner of the base and the object topples. The toppling angle, θ, is shown. At a slightly higher value of the angle, the wright would act outside of the corner and start creating a clockwise moment which would cause the object to topple. If we zoom in on a small triangle inside of the pyramid, we get this diagram. Using trigonometry, we can say [\$\\theta = \\ \\tan\^{- 1}\\frac{b}{h}\$]{.math.inline} Unit 1.2 -- Kinematics ---------------------- ### 1.2.1 - Motion Definitions: -------------------------------------------------------------------------------------------------------------------------------------------------------------- **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}\ -------------------------------------------------------------------------------------------------------------------------------------------------------------- In addition, the words 'mean' and 'instantaneous' are applied to speed and velocity. '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) The graph below shows how the displacement of a particle travelling in a straight-line change with time. This curve is a complete description of the motion of the particle.  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 the acceleration/deceleration is constant. An exam question may ask you to calculate the gradient several times for you to make a judgement on whether or not the change in velocity is constant. If the acceleration in 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. The velocity-time graph above shows us an object accelerating from rest. In section OA, it accelerates from rest to a velocity of 25 ms^-1^. The Gradient is constant so the acceleration must be uniform. In section AB the gradient is zero, therefore the acceleration is zero, i.e. the velocity is uniform. Finally, in section BC, there is a constant negative gradient hence the object has a constant deceleration (uniform negative acceleration) ### 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 So far, we have worked under the assumption that the acceleration is constant. Strictly, this is only true when there is no air resistance. When air resistance is considered, the acceleration is non-uniform and reduces to zero as the object gains speed (reaches terminal velocity) For an object moving vertically downwards, there are usually just two forces shown: At the beginning, the skydivers speed is zero and hence there is no air resistance. There is a downward resultant created by the weight, therefore there is a downward acceleration of the skydiver. As the skydiver's speed increases, they push downwards on the air molecules with an increasing force. By newton's 3^rd^ law, the air molecules create an equal and opposite force on the skydiver; this is called air resistance, and it increases with speed. Eventually, the air resistance becomes equal to the weight and the terminal velocity is reached. A graph of resultant force (or acceleration, since F=ma) against time would look like this: **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.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 -------------------- ### 1.3.1 - 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. If every force has an associated force that is equal in magnitude but opposite in direction, why don't they cancel each other out? How can anything ever get moving. Consider an F1 car; to accelerate at the start of a race its engine must create a large force. This force is transmitted to the back wheels.  The effect of the force of the road on the wheel is of course to accelerate the car forwards. The effect of the when on the road is to push the earth backwards. **Although the two forces are always equal and opposite, they never 'cancel out' since they act on different objects.** *\[see page 1 of inkodo notes for worked examples\]* ### 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.** The principal deals with a system of particles which is free outside of influences, i.e. it does not gain or lose particles, and it does not subject to forces from the outside. We can also apply it in the case where there is external, but they sum to zero, so there is no resultant force. 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. *\[see page 3 of inkodo notes for worked examples\]* ### 1.3.4 - Elastic and Inelastic Collisions **An elastic collision is one in which E~k~ is conserved (i.e. E~k~ before and after the collision equals E~k~ after the collision).** An example is the collision between molecules of an ideal gas and the walls if its container. **An inelastic collision is one in which the E~k~ is not conserved.** An example is the collisions between trolleys or cars. Some of the initial E~k~ of the system is converted into heat and sound. Collisions in which the bodies stick together are always inelastic. In both types of collisions, **momentum is always conserved.** **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. If units are selected so that k=1, we can simply write: [\$F = \\frac{\\Delta p}{t}\$]{.math.inline}. If we were to plot a graph if momentum against time, it would be a straight line through the origin (showing direct proportion). The gradient would be the change of momentum divided by time, i.e. the force. 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}. \[see inkodo PDF for all worked examples\] Unit 1.4 -- Energy Concepts --------------------------- ### 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 *\[see inkodo Unit 1.4 Class Notes PDF for all examples\]* ### 1.4.2 -- Energy Doing work requires 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} were - 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} were - 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. *\[see inkodo Unit 1.4 Class Noted PDF for examples\]* ### 1.4.3 -- The Work-Energy Relationship Work done is a measure of how much energy is transferred. 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^. *\[see inkodo unit 1.4 PDF for examples\]* ### 1.4.4 -- Dissipative Forces and Energy We have discussed the formulae for various forms of energy by considering the work done against external forces. - 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 will get the percentage efficiency of the system. Efficiency has no units. Unit 1.5 -- Solids Under Stress ------------------------------- ### 1.5.1 Forces on Solid Materials 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 The object is said to be under stress. The forces shown are those applied externally to the object; by Newton's 3^rd^ law the object exerts equal and opposite force on the external objects. The material of Nelson's column is under compression from the weight of the material above. The bungee and cord are subject to tensile forces. The rivet is under shear forces. ### 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) The graph below shows the variation of applied load and extension for a typical metal wire or spring: From (0 ,0) up to the limit of proportionality line is straight. This is the region where the spring obeys Hooke's Law. Beyond the limit of proportionality, the line curves; there is no longer direct proportion between the load and extension. A point is reached where any further load will cause the spring to become permanently stretched. This is the limit of proportionality. Up to this point, if the applied force is removed the spring will return to its original length and it is said to exhibit elastic behaviour. The elastic limit is the maximum force that the spring can experience and still return to its original length when the force is removed. Beyond the elastic limit, the spring no longer returns to its original length when the stretching force is removed. This is described as plastic behaviour. The spring has now became permanently stretched or deformed. It is very important not to get length and extension confused whenever carrying out a Hooke's Law calculation. ### 1.5.3 - Springs in series and parallel ***\[see inkodo 1.5 class nots pdf for all examples\]*** ### 1.5.4 -- Work of deformation and Strain Energy When a material is stretched by a force, the work done by the stretching force is stored as strain energy or elastic potential energy in the material. Up to the elastic limit, the strain energy stored will equal the work done in the stretching material. If the material being stretched obeys Hooke's law, the graph will be a straight line as shown above. Up to the limit of proportionality, the force and extension are proportional and the strain energy, E, can be calculated by finding the area between the graph and the x-axis. \ [\$\$E = work\\ done = \\frac{1}{2}\\text{Fx}\$\$]{.math.display}\ Since Hooke's law is obeyed and [*F* = *kx*]{.math.inline}, we can also say: \ [\$\$E = \\frac{1}{2}kx\^{2}\$\$]{.math.display}\ ### 1.5.5 -- Stress, Strain and Youngs Modulus Stress is defined as the applied force per unit of cross section. This can be expressed as [\$\\sigma = \\frac{F}{A}\$]{.math.inline} where: - [*σ*]{.math.inline} = stress (Pa or Nm^-2^) - [*F*]{.math.inline} = force (N) - [*A*]{.math.inline}= cross sectional area (m^2^) Strain is defined as the ratio of the change in the length of the specimen to its original length. This can be expressed as [\$\\epsilon = \\frac{\\Delta L}{L\_{o}}\$]{.math.inline} where: - [*ϵ*]{.math.inline}= strain (no unit as it's a ratio) - [*ΔL*]{.math.inline} = change in length (m) - [*L*~*o*~]{.math.inline}= original length (m) Generally, applying a tensile stress to a material produces a corresponding strain. Provided 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 defined as the young modulus. This can be expressed as [\$E\_{Y} = \\frac{\\sigma}{\\epsilon} = \\frac{F \\bullet L\_{o}}{A \\bullet \\Delta L}\$]{.math.inline} where: - E~Y~ = Young's modulus (Pa or Nm^-2^) If stress and strain of a were measured to breaking point a graph like this one shown below could be plotted. Point A represents the limit of proportionality. Point B represents the elastic limit. Point C represents the position of ultimate tensile stress. The ultimate tensile stress (UTS) of a material is defined as the maximum stress which can be applied to it without it breaking. The gradient of the straight line is the Young Modulus. Young Modulus is a property of the material and does not depend on the dimensions of the sample. It is a measure of the stiffness of the material -- the larger the value of the young modulus, the stiffer the material. ### 1.5.6 -- Types of Solid 1. **Crystalline**: These solids have short- and long-range order, i.e. there is a regular pattern of atoms (or sometimes molecules) over a distance of at least 100 atomic diameters. Almost all metals are examples of polycrystalline solids, as well as many minerals, e.g. salt, where there are many small crystals called grains. Each grain has a different orientation. This makes the structure very strong. The line between each grain is known as the grain boundary. 2. **Amorphous**: The term amorphous (meaning 'without shape or form') is used to describe solid substances which there is little to no long-range order in the arrangement of the particles. It can be linked to an instantaneous or frozen' picture of the internal structure of a liquid. In practice there are a few examples of solids with such totally random structures, however, glass or brick are given as examples in which there may be ordered clusters of atoms (much smaller than the 'small' crystals found in polycrystalline materials like metals). 3. **Polymetric**: Polymers consist of very long chains of carbon atoms (commonly in excess of 1,000 atoms) bonded to hydrogen and other atoms. Polymers can be natural (e.g. cellulose, nylon, etc.). The bonds in most polymers are strong and can rotate. Therefore, most polymers are strong and flexible. Cross links (where chains are tied together) can be added to polymer chains to make them stiffer. ### 1.5.7 -- Stress-Strain Graphs for Metals  [Analysis] 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 [\ ] [Explanation ] Metals (and minerals like salt) have regular atomic pattern. Any force exerted on a crystalline material will therefore be transmitted equally to each other because of the long-range order. So, for mall extensions, behaviour of a single bond where [*F* ∝ *x*]{.math.inline}, and hence the graph is straight from O to P Plastic behaviour occurs when a solid is extended beyond its elastic limit. The atoms in one plane can slip over the atoms in the other plane if the forces are great enough. A more detailed look at the 'slipping planes brings in the idea of dislocations to explain the relative ease with which ductile material extends in the plastic region. Sometimes, as molten metal cools down when it is smelted, mistakes happen as the metal ions join the crystal. A frequent mistake (1/1,000,000 atomic planes) is that half a plane is misses out. This is known as edge dislocation. Edge dislocations are the key to plastic deformation. The secret is in the bonds around the ion X. These bonds are all under strain (they're longer than usual), so they are places of weakness. Suppose the structure in the diagram above is put under tension. If the forces, F, are small\< the horizontal bonds are stretched reversibly (if the force is removed, they contract again) and the material behaves elastically. If the forces become larger, the already strained bonds below and to the right of X are stretched even more and at some point (the Yield Point of the material) they snap, making the dislocation migrate to the right. If the same force that causes this movement continues to be applied, the dislocation carries on moving through the snapping and reformation of bonds, until it reaches the edge of the crystal. In this way, the dislocation has moved from left to right through the crystal. It appears as if plane A and plane B have slipped over each other. However, it has been achieved more easily since only one (short) line of bonds, rather than a whole plane, has been broken at a time. Metals can therefore be strengthened (by making plastic deformation less likely) by: - Having smaller 'grains '-- this restricts the movement of dislocations. - Introducing foreign atoms. In effect this creates a point of dislocation that inhibits the movement of dislocations as described above. ### 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 main factor that dictates the behaviour of a polymer is the cross-links. These are strong (covalent) bonds that form between adjacent/overlapping molecules, or even between different parts of the same molecule. If the molecules don't have many cross-links, then they can slide over each other quite easily i.e. the polymer is stretchy, like rubber. If you increase the number of cross-links by adding impurities like sulfur to the latex, the polymer then becomes more rigid. The 'latex' is then given a different name -- "vulcanite." Region OA Blow hard ----------- -------------- Region AB Much easier Region BC Harder again Point C BANG We need to take a closer look at a typical stress-strain curve for rubber. You must be able to explain, on the molecular level, why it has three distinct sections. Rubber molecules are long and thin, resembling rods with swivel joints at periodic intervals. The cross-links are strong covalent bonds (in addition to the strong covalent bonds in between each molecule) but as already mentioned, are quite scarce in natural rubber (latex) Hence, there aren't enough cross-links to keep the molecules in a tangled, knotted mess. Weaker bonds are formed in the tangled mess known as van der Waals forces. Every time one part of a molecule comes very close to another molecule (or a different part of the same molecule) a van der Waals force can occur. \[Think of van der Waals forces as a weak bond that acts only over very short distances\] Many of these are produced between the rubber molecules and tend to keep the molecules stuck together. This explains the section of OA of the graph, i.e. the initial stiffness of the material. The strength of these van der Waals forces decrease very rapidly with distance, and hence suddenly (at point A) the molecules begin untangling from themselves and from each other. This is why section AB of the graph is quite 'flat,' i.e. there is a larger extension of the rubber material without much extra effort. Once the molecule has been straightened out (point B), stretching the rubber any further requires that the strong covalent bonds in between each molecule are lengthened, as well as lengthening or breaking the strong covalent cross-links. This is much more difficult than simply unravelling the molecules, and so the graph becomes much steeper from this point on. The rubber behaves much like any other covalently bonded solid in section BC of the graph, i.e. its stiff and strong. ### 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 ------------------------------------------------ ### 1.6.1 -- Stellar Spectra and Black Bodies Almost all the information we have about the universe comes from electromagnetic radiation. Photographs of constellations are taken using visible radiation, i.e. with wavelength ([*λ*]{.math.inline}) in the range 400-700nm (400x10^-9^-700x10^-9^m). Until recently, this was the only wavelength range available to us because earths atmosphere is opaque to most the EM spectrum. Space telescopes have allowed us to observe the universe across the complete range from radio to gamma rays. Multi-wavelength astronomy gives us a much more complete understanding of the processes in the universe. The light from the stars is analysed by separating out the wavelengths, e.g. by passing the light through a prism or a diffraction grating, and then either making an image or plotting the energy density at different wavelengths. Stars don't have a definite surface; the light we see from a star comes from a layer of gas several hundreds of kilometres thick, known as the **photosphere**. When light is emitted by a hot object like a star, we expect the light to have a wide range of wavelengths. Similar to the spectrum of a black body. **[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. Although stars are obviously not black, they are almost perfect 'emitters,' and so when we look at the light emitted by a star, we should get a continuous spectrum as shown to the right (i.e. all colours, all wavelengths). However, some specific colours/wavelengths can be absorbed by the atoms in a star's atmosphere (and upper photosphere) and so what arrives at our telescope is an absorption spectrum. These spectra contain a huge quantity of information about the star, in particular the temperature of its outer layer and its chemical composition. Using the shape of the continuous spectrum and the positions of the dark lines (the Fraunhofer lines), astronomers can compare stars and also obtain evidence about their motion and even the age of the universe. The intensity of the radiation emitted from a black body varies with the wavelengths. The curves below shoes how the intensity varies with wavelength 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 wavelength, i.e. the peak is shifted to the left at higher temperatures. - The lower the temperature, the longer the 'flat' section is before the curve 'lifts off.' ### 1.6.2 -- 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) ### 1.6.4 -- Luminosity, Intensity and Distance The luminosity of a star is the total energy it emits per unit time in the form of electromagnetic radiation. The unit for luminosity is the watt, W. Therefore, luminosity is equivalent to the power of a star. Thos means we could have used luminosity instead of power in Stefan's law. The diagram below shows how radiation from a small source, such as a star, spreads out. The further from the star, the bigger the area the same quantity of radiation has to cover, so the lower 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 inversely proportional to the distance from the star squared. This can be written 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 various regions of the electromagnetic spectrum gives us information about different processes in the universe. Most of the power of the sun is emitted in the form of near infrared, visible and near ultraviolet radiation. This is because the temperature of the photosphere is approximately 5800K. The higher the temperature of an object, the shorter the wavelengths of the continuous spectrum the object emits. 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.  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 ------------------------------------------- ### 1.7.1 - A Brief History of Our Understanding of the Atom - The atom was regarded as an elementary particle in the late 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 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 identified and were initially thought the be elementary. This brings us up to your understanding of the structure of the atom from GCSE. But there's more: - Collison experiments, known as deep inelastic scattering, in the 1960's and 1970's showed that nucleons (protons and neutrons) are [not] elementary particles. They are composed of 3 particles called quarks, bound together by the "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... *Definition: An elementary (or fundamental) particle is a subatomic particle that is not composed of other particles.* ### 1.7.2 -- Quarks and Leptons The image below shoes the standard practice modle whereby the different quarks and leptons can be seen. Note they are grouped into generations. You are expected to recognise that there are 3 generations of quarks and leptons, but questions will only be set involving the firs three generations. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- **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. This means when a particle encounters its antiparticles (e.g. an electron and a positron), all the mass is converted into energy. In electron-positron annihilation this releases two photons of gamma energy travelling in opposite directions. Leptons are the lightest of the subatomic particles and they always exist separately; they do not combine to form composite subatomic 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 commonly known baryons are the proton and neutron: ---------------------------------------------------------------------- **PROTON** **NEUTRON** ------------------- --------------------------- ---------------------- Charge \ \ [ + *e*]{.math.display}\ {.math.display}\ Baryon number 1 1 Quark composition UUD UDD ---------------------------------------------------------------------- You need to use your knowledge of leptons and quarks to suggest the quark make-up of less known baryons and of charged pions. 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 combines 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}\ --------------------------------------------------------------------------------------------------- Note there are two possible quark compositions that make up the neutral pion. ### 1.7.4 -- Interactions (Forces) Between Particles There are four interactions, or force, experienced by particles as summarised in the table below: **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. Strong interactions (lifetime 10^-24^s) - Only hadrons involved. - There is no change in quark flavour. - These are typically involved in collisions between particles. Electromagnetic interactions (lifetime 10^-12^ - 10^-18^s): - The particles must be charged or have 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 (lifetime 10^-8^s) - Neutral leptons (neutrinos) as 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 wich 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}.  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 wich 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}. ### 1.7.5 -- Conservation Laws In addition to the conservation of energy and momentum laws discussed previously, reactions involving subatomic particles must obey the conservation of charge, lepton number and baryon number. 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}\ ----------------------------------------------------------------------------------------------- Similarly to lepton number, we define a baryon number, B. Each baryon (e.g. a proton) has a baryon number of 1, anti-baryons have a baryon number of -1 and leptons and mesons have a baryon number of 0. Baryon number is always conserved. 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.