Physics UNIT 3 Study Design
AOS 1: Motion in One and Two Dimensions
· Explain motion in terms of Newton’s model & assumptions
· Apply Newton’s laws to situations with a few forces in one & two dimensions
· Analyse uniform circular motion of an object in a horizontal plane
· Analyse ideal projectile motion of objects near the surface of the Earth
· Analyse relative velocity in two dimensions using Galilean Transformations
· Distinguish between stationary (inertial) frames of reference and frames of reference moving at a constant speed relative to the stationary frame
· Analyse impulse, & momentum transfer, in collisions in one dimension
· Analyse energy transfer from work done by a constant force in one dimension
· Analyse energy transfer involving kinetic & potential & other forms of energy
· Analyse planetary and satellite motion modelled as uniform circular motion in a universal gravitational field, using; a = v2/r = 4p2r/T2, g = GM/r2, & F = GMm/r2
AOS 2: Electronics and Photonics
· Apply the concepts of current, voltage & power to circuits with, diodes, resistors, & photonic transducers; LDRs, photodiodes, & LEDs,
· Simplify circuits with parallel & series resistance & unloaded voltage dividers
· Describe the operation of transistors in terms of the current gain and the effect of biasing the base-emitter voltage on the current-voltage characteristics
· Explain how capacitors act as de-couplers to separate AC DC signals
· Use technical specifications to design circuits to operate for a specific purpose
· Analyse simple electronic transducer circuits that respond to illumination & temperature, including LDRs, photodiodes, phototransistors, & thermistors
· Describe energy transfers & transformations using opto-electronic converters
· Describe information transfer in analogue form using intensity modulated light
DS 2: Investigating Materials and their use in Structures
· Identify different types of external forces (compression, tension & shear)
· Compare compressive & tensile strength & stiffness of different materials under load for their suitability in different structures (columns, beams arches & cables)
· Model the behaviour of materials under load in terms of extension & compression, graphically & algebraically, including Young’s Modulus
· Calculate the stress & strain resulting from forces acting on materials in structures
· Use data to describe and predict brittle or ductile failure under load
· Calculate the potential energy stored in a material under load (strain energy) & the toughness of a material tested to destruction using area under stress-strain graphs
· Describe elastic or plastic behaviour shown by materials under load and the resulting energy lost as heat
· Contrast the performance of a composite material to the performance of the component materials to determine the suitability for use in structures
· Analyse translational and rotational effects of forces in structures (columns, beams & cables) modelled as two dimensional structures in stable equilibrium
· Apply conditions for equilibrium to analyse forces in structures made of combinations of columns, beams & cables
· Use data to describe and predict the performance of a simple structure under load
AOS 1 (40%): Motion in One and Two Dimensions
· Explain motion in terms of Newton’s model & assumptions including;
- Graphical description of motion: displacement-, velocity-, & acceleration-, time graphs.
o For displacement-time (x-t) graphs; velocity (v) = gradient
o For velocity-time (v-t) graphs; displacement (x) = area, acceleration (a) = gradient
o For acceleration-time (a-t) graphs; velocity (v) = area
- Algebraic description of motion: constant acceleration equations of motion.
o v = u + a t x = displacement, v = instantaneous velocity = Dx/Dt
o x = ½(u + v)t u = initial velocity, vav =average velocity = ½(u + v)
o x = ut + ½at2 v = final velocity, Dv = change in velocity = (v – u)
o x = vt – ½at2 a = acceleration = Dv/Dt = vav /t ,
o v2 = u2 + 2ax t = time interval of constant acceleration, Dt = time interval of change
- N1: “A body continues in its state of rest or constant motion unless acted on by a net external force”
Iff SF = 0, Dv=0. If and only if no net external force acts on an object then its velocity will not change
- N2: “The net external force changes the velocity of an object in proportion to its mass”
SF = ma = Dp/Dt. The net force on an object is proportional to its rate of change of momentum
- N3: “Every action has an equal & opposite reaction”
FAB = -FBA. The force of an object on another is equal & opposite to the force of the second onto the first
- Newton’s Laws assume that physical quantities such as mass, time, & distance are absolute quantities. This means that their values did not change whatever the frame of reference.
· Apply Newton’s laws to situations with a few forces in one & two dimensions
- SF = F1 + F2 , for two forces acting on an object (or system)
- Use N1 to determine if an object is in equilibrium (SF = 0), if so a=0, & e.g., F1 = -F2., if not use N2
- Use N2 to relate force, mass, acceleration (changes in velocity), changes in momentum and time
- Use N3 only to find the forces of one object on another given the forces of the other object on the first
- Use vector addition and trigonometry to resolve forces along two dimensions
- Inclined Planes: when an object is on a slope, the net external force is often along the angle of the slope
- Forces should be resolved into components that are parallel & perpendicular to the inclined plane:
o FW┴ = mg·cosq, perpendicular component of weight force
o FW|| = mg·sinq, parallel component of weight force
o SF = FW|| + FD + FF, at an angle of q from horizontal, up the slope (parallel).
o FN + FW┴ = 0, at an angle of q from vertical, up from the face of the slope (perpendicular)
- FW = Weight = mg, g= gravitational field = g(Earth’s Surface) ≈ 10 Nkg-1 or ms-2,
- FN = Normal Reaction Force = - FW┴, FW┴ = perpendicular component of weight force
- FD = Driving Force (parallel to incline) FF = Friction Force (opposes direction of motion)
· Analyse uniform circular motion of an object in a horizontal plane
- Centripetal acceleration, aC, is a centre-directed acceleration of an object moving in a circle:
o aC = v2/r = 4p2r/T2, {from a= Dv/t and Dv:v=u::x=vt:r},
- v = velocity with a constant magnitude (speed) & direction at a tangent to the circle at any instant
- r = radius of the circle of motion
- T = period of motion around a circle, time of one revolution around the circle of motion = 2pr/v
- A centripetal (centre-seeking) force, FC, is any force that acts perpendicular to the direction of velocity
o FC = maC = mv2/r = m4p2r/T2,
- m = mass of the object in motion around a circle or part of a circle
- In a horizontal plane, gravitational forces act perpendicular to the centripetal force and can be ignored
- In a vertical plane, gravitational forces act parallel to the centripetal force (not uniform circular motion)
· Analyse ideal projectile motion of objects near the surface of the Earth
- Ideal projectile motion is the motion of objects vertically & horizontally where weight is the only force
- Air resistance acts opposite to the direction of motion: it is often negligible & can be ignored.
- Ideal projectile motion situations should be resolved into vertical & horizontal components
- u = initial velocity at an angle q; vertical uV = u•sinq, & horizontal uH = u•cosq,
- Vertically: xV = uVt + ½aVt2, aV = g = 10 ms-2 or Nkg-1.
- Horizontally: xH = uHt, aH = 0.
- You may also need to calculate the upward and downward arcs (paths) separately.
- Maximum Height: at xVmax, vV = 0 .: xVmax= ½gt2.
- Total time: Calculated from the vertical component (time to ground).
- Range: The total horizontal displacement calculated from the total time.
· Analyse relative velocity in two dimensions using Galilean Transformations
- Galilean Transformations: vB:A = vB – vA (velocity of B relative to A is the vector difference of A from B).
- Not valid for very-very large or very-very small objects or objects travelling near the speed of light
· Distinguish between stationary (inertial) frames of reference and frames of reference moving at a constant speed relative to the stationary frame
- An inertial frame of reference is one that is at rest or that moves with a constant velocity
- Newton’s Laws & the Galilean Transformations are only valid in inertial frames of reference
· Analyse impulse, & momentum transfer, in collisions in one dimension
- p = momentum = mv = mass times velocity
- SFDt = impulse = Dp = change in momentum = pf – pi = mv – mu.= area under F-t graph
- Isolated System: A system of objects in which the only forces acting on the objects are the action-reaction forces between the objects in the system (i.e., no external forces acting on the system)
- Conservation of momentum: In an isolated system the total momentum of all objects in the system remains constant: DpT(iso) = SpTf – SpTi = 0 .: mAuA + mBuB = mAvA + mBvB.
· Analyse energy transfer from work done by a constant force in one dimension
- Energy cannot be created or destroyed it can only be transferred or transformed
- Work is done to transform energy from one type into another: W = F||x = Fx·cosq = DE,
- W= Work done on an object is the net force applied to it across a distance to change its energy
- F|| =component of force parallel to direction of motion, q = angle of applied force
- DE =change in energy of the object, x = displacement of the object while the force was applied
· Analyse energy transfer involving kinetic & potential & other forms of energy
- Kinetic Energy, EK, is the energy of an object associated with its motion: EK = ½mv2.
- In an elastic collision both momentum & kinetic energy are conserved.
- In an inelastic collision momentum is conserved but the kinetic energy is transformed into another form.
- Potential Energy is available to do work due to position/configuration of an object & its surroundings.
- Gravitational Potential Energy, EGP, is the potential energy stored in an object, m, due to its position, h, within a gravitational field (gravitational field strength = g): EGP = mgh.
- When an object moves through a changing gravitational field the Gravitational Potential Energy can be calculated from the area under force-distance or field distance graphs
- Elastic Potential Energy, EEP, is the potential energy stored in a stiff spring, k, due to its compression, Dx: EEP = ½kx2, for springs that obey Hooke’s Law: F= k(–Dx), an elastic object exerts a restoring force proportional to its compression, k = the proportionality (spring) constant
- The Elastic Potential Energy stored in a spring can be calculated from the area under force-compression graphs
· Analyse planetary and satellite motion modelled as uniform circular motion in a universal gravitational field, using; a = v2/r = 4p2r/T2, g = GM/r2, & F = GMm/r2
- Newton’s Law of Universal Gravitation: a gravitational force of attraction acts between two objects in proportion to the product of their masses, M & m, and inversely proportional to the square of the distance between their centres of mass, r: FG= Mm/r2.
- The Gravitational Field Strength, g, at a distance from the centre of mass of an object is the gravitational force, FG, or weight, FW = mg, experienced by objects of mass, m, near larger objects of mass, M, with a distance, r, between their centres of mass: g = FG/m = M/r2.
- An orbital system (involving planets or satellites) can be modelled as uniform circular motion where the centripetal force, FC, is due to the gravitational force, FG, between the orbiting object, m, and the orbited object, M:
o FG = FC = maC .: GMm/r2 = mv2/r .: v2 = GM/r,
o FG = FC = maC .: GMm/r2 = m4p2r/T2, .: GM/4p2 = r3/T2,
- For any objects, m, in the same gravitational system (orbiting the same M) r3/T2 & v2r are constants.
AOS 2 (30%): Electronics and Photonics
· Apply the concepts of current, voltage & power to circuits with, diodes, resistors, & photonic transducers; LDRs, photodiodes, & LEDs,
- q = electric charge [C = coulombs]: relative distribution (concentration) of electrons
o e = electron charge (smallest possible charge)= –1.6 x10-19 C
- U = electrical energy [J = joules]: potential work done by/on an electric charge
- I = current [A = amperes]: the rate of flow of electric charge: I = q/t.
- V =voltage [V = volts]: the electrical energy carried by a moving charge: V = U/q.
o e = Emf = electromotive force: the voltage gain of an electrical energy source
o pd = potential difference (drop): the voltage loss of an electrical energy load
- P = power [W = watts]: the rate of energy transfer/transformation: P = U/t = IV.
- R = resistance [W = ohms]: opposition to the flow of current for a given voltage:
o Ohmic devices: follow Ohm’s Law: V = IR, where R is constant for the device
o Non-ohmic devices: do not obey Ohm’s Law: see I-V characteristics.
- Diodes: semiconductor devices that generally allow a large current to flow in only one direction
o Forward-bias: with a voltage large enough to allow a large current to flow through a diode
§ Acts like a small backward emf (voltage source) or closed switch