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Transcript
Waves, Fields & Nuclear Energy Contents Oscillations & Waves Capacitance Gravitational & Electric Fields Magnetic Effects of Currents Nuclear Applications Circular Motion Consider an object going round in a circle of radius r: - speed is constant - velocity changes s=r - angular velocity ω = 2f = r/v - centripetal acceleration a = v2/r = ω2r - centripetal force f = ma = mv2/r = mω2r Oscillations Natural frequency: an object will swing freely at this frequency Free oscillation: an object oscillates independently Forced oscillation: a force causes an object to oscillate Resonant frequency: where maximum amplitude is attained (car suspensions, bridges swaying, bells ringing) Damping: amplitude of oscillations exponentially decreases - light damping reduces oscillations slowly - heavy damping reduces oscillations quickly - critical damping stops the oscillation within one cycle SHM max. a and max. v: origin V = 0 at –A and +A max. PE at –A and +A max. KE at origin a = - (2f )2x a = - ω2x v = 2f (A2 – x2) s = A cos 2ft T = 2(l/g) Etot = PE + KE SHM Mass on a spring: Fup = k(l + x) – mg a = -kx/m = - (2f )2x T = 2(m/k) Progressive Waves Wave Equation: v = fλ v = velocity (m/s) f = frequency (Hz) or (1/s) λ = wavelength (m) λ Polarisation: Superposition of Waves Superposition can only be applied to waves of the same kind The diagram shows a green wave added to a red wave. The result is the black wave, whose wavelength and amplitude reflects the sum of the two waves Wave Behaviour Interference: When two waves collide, they superimpose Superposition affects the waveform and interference results Path difference: difference in distance between two sources. It is measured in half wavelengths Waves in phase interfere constructively (increased amplitude) Waves out of phase interfere destructively (cancellation) Constructive: even number of ½ λs Destructive: odd number of ½ λs Wave Behaviour Diffraction Grating: - Light is split by travelling through very thin slits called a diffraction grating - Light is split because it is composed of different wavelengths - Each of these wavelengths diffracts at a different angle d sin = mλ d = slit width = angle m = spectrum order number (1st: m= 1, 2nd: m = 2 etc.) λ = wavelength NB: “m” is sometimes denoted as “n” instead Wave Behaviour The more slits, the more defined the diffractions The more slits, the greater the intensity The more slits, the greater the angle (easier to measure!) There is a limited number of orders, as sin has a maximum value of 1 - therefore at maximum, d = mλ Capacitors Capacitors: store charge for a short time - consists of two metal plates separated by a layer of insulating material dielectric Electrons are pumped onto the –ve plate Electrons are repelled off the +ve plate A potential difference is formed thus a charge Capacitance: charge required to produce 1V of potential difference in a conductor capacitance (F) = charge (C) /voltage (V) C = Q / V Capacitors Energy in a Capacitor: When a capacitor is charged up, a certain amount of charge moves through a certain voltage. Work is done on the charge to build up the electric field in the capacitor energy = charge x voltage capacitance = charge / voltage Thus: E = ½CV2 Discharge of a Capacitor: Charge decreases by the same fraction for each time interval, so that if it takes time, t, for the charge to decay to 50 % of its original level, the charge after 2t seconds is 25 % of the original Capacitors Q = Q0e–t/RC V = V0e–t/RC I = I0e–t/RC RC = time constant t½ = 0.693 RC t½ = half life Gravity Fields Newton’s Square Law of Gravitation: - Every particle of matter in the Universe attracts every other particle with a gravitational force that is proportional to the products of the masses and inversely proportional to the square of the distance between them Thus: F = -GMm/r2 G = 6.67x10-11Nm2kg-2 a = F/m where a = gravity: g = F/m Thus: g = -GM/r2 r = radius from centre of orbit! Gravity Fields Heading towards the centre of the Earth… At centre: g = 0 as matter is pulled in all directions equally Gravity Fields Gravitational Potential: - Work done on a unit mass in moving it to that point from a point remote from all other masses Always negative, because this involves a closed system - the zero point of gravitational potential is at infinity Vg = -GM/r Vg = gravitational potential Vg is the area under the curve on the previous slide Potential Energy in space: Ep = -GMm/r Electric Fields Electric field: region of force around a point charge F = kQ1Q2/r2 k= 0 = 8.8510-12 C2N-1m-2 (F/m) Electric Field Strength: force per unit charge E = F/Q This is radial for point charges: Electric Fields Electric Field Strength: is inversely proportional to the square of the radius - uniform field: E = V/d Electric Potential: energy per unit charge Magnetic Fields A current (I) has a magnetic field (B) around it A wire has a circular magnetic field around it If the current changes direction, so does the field Magnetic Fields Magnets attract magnetic materials using a magnetic field The magnetic field surrounds the magnet, and gets weaker as the distance from the magnet increases Magnets should be called permanent magnets the magnetism is always there Electricity makes a magnet much stronger This can be turned on and off Magnetic Fields Magnets pick up paper clips etc. strong weak Electromagnets pick up cars etc. Magnetic Fields The magnetic field around a coil electromagnet can be increased by: - Increasing the current flowing through the wire - Adding loops on the coil (loops are long lengths of wire) - Placing an iron or steel core inside the coil Basic electromagnet Magnetic Fields The Motor Effect: - When two magnets are placed close to each other, they the fields affect each other produce a force If a wire carrying a current is placed inside this magnetic field, a force is produced. This is called the motor effect The direction of the force will depend on the direction of the magnetic field and the direction of the current in the field Magnetic Fields Fleming’s Left Hand Rule: - When creating a force, use Fleming’s LH Rule to determine in which way the motor will spin - Magnetic Fields We can increase the force produced by: - increasing the current - increasing the number of coils - increasing the magnetic field strength (stronger magnet) Magnetic Fields • When a magnet is moved into a coil, an electrical current is induced • When the magnet stops, the induced current stops • When the magnet reverses, the electrical current reverses Magnetic Fields Increase the voltage? … 3 ways… 1. Stronger magnet 2. Speed of magnet 3. Number of coils Magnetic Fields To work out the force on a wire: use Fleming’s LH Rule Force is proportional to: - current - magnetic field strength - length of wire inside magnetic field F = BIl B = magnetic field strength or flux density (Tesla) When a wire is at an angle to the magnetic field… F = BIl sin Magnetic Fields To work out the force on a charge: use Fleming’s LH Rule Force is proportional to: - current (flow of charge) - magnetic field strength - velocity of charged particle F = BqV B = magnetic field strength or flux density (Tesla) When a charge is at an angle to the magnetic field… F = BqV sin F = mv2/r BqV = mv2/r V = Bqr/m Magnetic Fields Magnetic Flux: Product between the magnetic flux density and the area when the field is at right angles to the area Ф = BA Flux Linkage: Ф multiplied by number of turns on a wire Ф = NBA It can be changed by: - changing the strength of the magnetic field - move the coil so it enters the field at an angle Lenz’s Law: direction of an induced current opposes the flux change that caused it Mass & Energy 1 atomic mass unit (u) = 1.661 10-27 kg Atomic mass: mass of an atom Nuclear mass: mass of atom’s nucleus E = mc2 (J) = (kgm2/s2) c = 3x108m/s 1eV = 1.6x10-19J 1u = 931.3MeV Binding Energy per Nucleon: Energy required to remove a nucleon. Higher numbers more stable nuclei Mass & Energy Fission: splitting up of a large nucleus which is rarely spontaneous The strong nuclear force acts between neighbouring nucleons The forces are now weak in this shape/formation Nucleus splits (rarely spontaneously) Induce fission: add thermal neutron whose kinetic energy: 1) isn’t too low (will bounce off nucleus) 2) isn’t too high (will go through nucleus) 3) is correct to be captured by the attractive force in between nucleons - this can result in a chain reaction Mass & Energy Fusion: when light nuclei bind together which increases the binding energy per nucleon energy is released Each nucleus has to have sufficient energy to: - overcome electrostatic repulsion from the protons - overcome the repulsive strong force which is found outside the region of the strong force High temperatures are required (gas plasma) If it could be made to work, has advantages over fission: - greater power per kilogram of fuel used - raw materials are cheap and readily available - reaction is not radioactive Nuclear Power Although the fission products are not easily predictable, three more neutrons are produced An uncontrolled chain reaction causes a violent explosion Minimum mass before chain reaction occurs: critical mass Nuclear power station: Reactor is housed in a concrete to prevent radiation from leaking Expensive to build Costly to run Very clean, no pollution Need very little fuel Produce dangerous waste Nuclear power France vs. England = 80% vs. 20% Nuclear Power Safety: - Strict regulations - Serious accidents involving radiation leaks have occurred - Disposal of radioactive waste must be carried out carefully Transmutation: - Definition: changing the nuclei of elements by exposing them to particles - Particles have to travel slow enough to be captured by the nucleus - used in medicine Summary Circular Motion Oscillations SHM Progressive Waves Superposition of Waves Wave Behaviour Capacitors Gravity Fields Electric Fields Magnetic Fields Mass & Energy Nuclear Power