# Download M. Manser A2 Level Physics REVISION

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M. Manser A2 Level Physics REVISION FLASHCARDS 1 Newton’s laws of motion Newton’s first law: A body remains at rest or continues in motion with constant velocity unless an externally applied force acts on it. Newton’s second law: Force is proportional to the rate of change of momentum. Force is defined as rate of change of momentum: F = Δ(mv)/Δt When the mass m of a body is constant (at speeds much less than the speed of light), Newton’s second law becomes F = ma where a is acceleration. Newton’s third law: If a force acts on a body then an equal and opposite force of the same type acts on another body. 3 Circular motion 2 Momentum Linear momentum (a vector) = mass × velocity: p = mv Impulse of a force = change in momentum = F Δt Area under a force–time graph = impulse Principle of conservation of momentum: In any collision or explosion, momentum is conserved, provided that no external force acts. In an elastic (or perfectly elastic) collision there is no loss of kinetic energy. Most collisions are inelastic, with some loss of kinetic energy. Intermolecular collisions are perfectly elastic, with no loss of kinetic energy. Angle in radians = arc length/radius. 180° = π rad Angular velocity (or angular frequency) ω is the rate of change of angle. ω = Δθ/Δt = 2π/T = 2πf where T is the time period and f is the frequency. A body moving in a circle at constant speed is changing direction, and therefore changing velocity. It is thus accelerating. The centripetal acceleration and force are directed towards the centre of the circle. For a body moving at speed v in a circle of radius r with period T: v = 2πr/T a = v2/r F = ma = mv2/r 4 Gravitational fields (1) Gravitational field strength g is force per unit mass. g = F/m On the Earth’s surface, the gravitational field strength g = 9.81 N kg−1 is approximately equal to the acceleration of free fall: g = 9.81 m s−2 A gravitational field may be represented by field lines. In a uniform field, the lines are parallel; around the Earth, the lines are radial. Newton’s law of gravitation: The force of attraction F between point masses m1 and m2 at a separation r is F = −Gm1m2/r2 where G = 6.67 × 10−11 N m2 kg−2 is the universal constant of gravitation. 5 Gravitational fields (2) At a distance r from a mass M, the gravitational field strength g = −GM/r2 Equating GMm/r2 = mv2/r for the force on a mass m in orbit round a mass M, and using v = 2πr/T leads to GMT2 = 4π2r3 and if the radius of orbit r and period T are known, M may be calculated. Johannes Kepler stated this result as his third law for planets in orbit round the Sun: T 2 ∝ r 3 A satellite in a geostationary orbit round the Earth has a period of 24 h, so that it remains above one point on the equator. 6 Simple harmonic motion (1) Examples of SHM are the vertical oscillations of a mass on a spiral spring, and the simple pendulum. The horizontal oscillation of a trolley between stretched springs is damped harmonic motion. In SHM the period T of oscillation is independent of amplitude A. The displacement x of a body in SHM from the central position is: x = A cos ωt = A cos 2πft if time t = 0 at an extremity of motion; x = A sin ωt = A sin 2πft if time t = 0 at the centre of the motion. The maximum speed of an oscillator is: vmax = ωA = (2πf)A 7 Simple harmonic motion (2) Definition: SHM occurs when the acceleration a of a body is directed to a fixed point and is proportional to the displacement x from that point. Acceleration a = −ω2x = −(2πf)2x amax = −(2πf)2A The displacement–time, velocity–time and acceleration–time graphs for SHM are all sinusoidal, with ¼ cycle, i.e. π/2 rad, phase differences. The total energy of a body in SHM is constant. The energy–displacement graph for SHM shows zero KE at x = A, maximum KE at x = 0, and maximum PE (gravitational and/or elastic) at x = A 8 Damping and forced oscillations Damping does not change the period of motion, but leads to exponentially decreasing amplitude. Resonance is the maximum amplitude of a forced oscillation when the driving frequency equals the natural frequency of the driven oscillator. When this happens there is maximum energy transfer. Resonance is used in microwave ovens, in radio tuners, and in musical instruments. Resonance is a nuisance in suspension bridges. 1 M. Manser A2 Level Physics REVISION FLASHCARDS 9 Matter Solids, liquids and gases are distinguished by the spacing, ordering and motion of their atoms or molecules. Brownian motion is demonstrated by viewing smoke particles in air under a microscope. The experiment shows that there is much empty space in air, but that the motion of the smoke particles is changed by the random collisions of the much smaller (air) particles moving randomly at very high speed. Pressure p is force F per unit area A: p = F/A The elastic collisions of millions of molecules per second on a surface cause gas pressure. 10 Internal energy; temperature The internal energy of a system is the sum of the random distribution of kinetic and potential energies of the molecules in the system. 11 Specific heat capacity and latent heat The heating of a body leads to an increase in internal energy and to either an increase in temperature or a change of state. The specific heat capacity of a substance is the energy provided by heating to raise the temperature of unit mass by 1 °C or 1 K. If a mass m of a substance of s.h.c. c is raised through a temperature difference Δθ, the energy E transferred is: E = mc Δθ Latent heat (of fusion or of vaporisation) is the energy provided by heating to change the state without changing the temperature. 12 Ideal gases Boyle’s law: For a fixed mass of gas at constant temperature T the pressure p is inversely proportional to the volume V: pV = constant For a fixed mass of gas: pV/T = constant or p1V1/T1 = p2V2/T2 Kinetic theory assumptions: Gases consist of large numbers of indivisible molecules moving at high speeds. Intermolecular collisions are (perfectly) elastic. Volume of molecules ≪ space in which they move. Duration of collisions ≪ time between collisions. Forces between distant molecules are negligible. 13 14 Electric fields (1) Electric field strength E is defined as force F per unit positive charge Q: E = F/Q The equation of state for an ideal gas 1023 mol−1 The Avogadro constant: NA = 6.02 × One mole of any substance contains 6.02 × 1023 particles. The equation of state: The pressure p, volume V and temperature T (in kelvins) of an ideal gas are related by pV = nRT or pV = NkT where n is the amount of substance in moles, R is the molar gas constant, N is the number of particles, and k = R/NA is the Boltzmann constant. The mean translational kinetic energy E of an atom in an ideal gas is directly proportional to the temperature of the gas in kelvins: E = 3⁄2kT 15 Electric fields (2) Coulomb’s law: The force between two point charges Q and q at a separation r in air or space is F = Qq/4πε0r2 where ε0 is the permittivity of free space. The electric field at distance r from a point charge Q is E = Q/4πε0r2. The gravitational field strength around a point mass and the electric field strength around a point charge are both inversely proportional to the square of the distance from the point mass or point charge. Electrostatic forces may be attractive or repulsive, but gravitational forces are only attractive. Absolute zero (zero kelvins, 0 K) is the temperature at which a substance has minimum internal energy. The thermodynamic scale of temperature is an absolute scale that does not depend on the property of any particular substance. Temperatures in kelvins and in degrees Celsius may be converted using: T/K = θ/ºC + 273.15 E is a vector quantity, measured in N C−1 (or V m−1). Between charged parallel plates there is uniform electric field, shown by parallel field lines, of magnitude E = V/d. If a charged particle is moving across a uniform field E, it will follow a parabolic path (similar to a golf ball moving in air under gravity). The electric field lines around a point charge or a charged sphere are in a radial pattern. 16 Magnetic fields The magnetic field pattern around a long currentcarrying conductor is of concentric circles. The magnetic field pattern around a long solenoid is similar to that around a bar magnet; within the solenoid the field is uniform. The direction of the force on a current-carrying conductor placed at right angles to a magnetic field is found using Fleming’s left-hand rule: first finger = field second finger = current thumb = motion 2 M. Manser A2 Level Physics REVISION FLASHCARDS 17 Magnetic flux density The force on a conductor of length L carrying current I at an angle θ to a field of flux density B is F = BIL sin θ Magnetic flux density B is the force per unit length per unit current on a conductor placed at right angles to the field: B = F/IL A field has flux density of 1 tesla (1 T) if the force on a conductor of length 1 m carrying a current of 1 A at right angles to the field is 1 N. A particle of charge Q moving at speed v at right angles to a magnetic field of flux density B experiences a force F = BQv. 19 Magnetic flux The magnetic flux through an area A inclined at an angle θ to a magnetic field of flux density B is Φ = BA sin θ. If an area of 1 m2 is perpendicular to a magnetic field of flux density 1 T then the magnetic flux through the area is 1 weber (1 Wb). The magnetic flux linkage through a coil is the magnetic flux times the number of turns N on the coil: magnetic flux linkage = NΦ = BAN sin θ 18 Motion of charged particles in magnetic fields The force F on a charge Q moving at speed v across a magnetic field B causes it to move in a circular path of radius R because the force is always perpendicular to the field and to the motion. The force on the moving charged particle is the centripetal force. Therefore BQv = mv2/R and so: BQR = mv A charged particle moving across electric and magnetic fields at right angles has an undeflected path if FB = FE, i.e. if BQv = EQ. This is a velocity selector for speed v = E/B and is used in a mass spectrometer. 20 Electromagnetic induction Faraday’s law of electromagnetic induction: The induced e.m.f. is proportional to the rate of change of flux linkage. Lenz’s law: The induced e.m.f. acts in such a direction as to oppose the change causing it. This follows from the conservation of energy. Faraday’s and Lenz’s laws become: induced e.m.f. = - (rate of change of flux linkage); e = −Δ(NΦ)/Δt Alternating current (a.c.) can be generated using a coil rotating in a magnetic field or a magnet rotating inside a coil. 21 Transformers A transformer is made using two separate coils of wire wound on a laminated iron ring or core. Transformers work only on a.c., not d.c. In an ideal transformer with a primary coil of NP turns and a secondary coil of NS turns, the ratio of the secondary and primary voltages is: VS/VP = NS/NP Step-up and step-down transformers are used to transmit electrical energy over long distances. In a high-voltage power line the low current wastes little energy as heat in the resistance of the wires. 22 Capacitors The capacitance C of a capacitor is the charge Q stored per unit potential difference V: C = Q/V. 23 Discharging capacitors When a capacitor discharges through a resistor R the p.d. V across it, charge Q on it, and current I through R all fall exponentially with time. In an exponential decay each quantity (V, Q or I) falls by a constant factor in each successive time interval. The time constant for a capacitance C discharging through a resistance R is T = RC. The p.d., charge and current all fall with time t according to the same pattern: V = V0e−t/CR Q = Q0e−t/CR I = I0e−t/CR 24 The nuclear atom (1) Rutherford’s alpha-scattering experiment shows that each atom has a tiny massive positively charged nucleus and much empty space. The nucleus of an atom comprises protons and neutrons and is surrounded by orbiting electrons. A capacitor has a capacitance 1 farad (1 F – a very large unit) if it stores 1 coulomb of charge when the p.d. across it is 1 volt. For three capacitors in parallel: CP = C1 + C2 + C3 For three capacitors in series: 1/CS = 1/C1 + 1/C2 + 1/C3 The energy stored in a capacitor is given by W = ½QV = ½CV 2 and is represented by the area under a graph of p.d. against charge. Nuclear diameters are measured in fm (10−15 m); atomic diameters are of the order of 10−10 m. The density of a proton of diameter 1.2 fm is of the order of 1017 kg m−3. Nucleons are tightly packed, thus all nuclei have similar densities. 3 M. Manser A2 Level Physics REVISION FLASHCARDS 25 The nuclear atom (2) Two protons in a nucleus have a strong electrostatic repulsion (Coulomb’s law) and a weak gravitational attraction (Newton’s law of gravitation). There must therefore be a very strong short-range attractive force (the strong nuclear interaction) between nucleons. For a nuclide is the nucleon number or mass number, the number of nucleons in the nucleus; Z is the proton number or atomic number of the element, the number of protons in the nucleus. For isotopes of an element, Z is the same, but A is different. 26 Fundamental particles Baryons, massive particles such as protons and neutrons, are not fundamental and are made up of charged particles called quarks. The six types of quark are: up, down, strange, charm, top and bottom. The quarks in a proton are u, u, d; in a neutron, u, d, d. Weak nuclear interaction: a quark may change its flavour causing β decay of the nucleus. In β− decay the emissions are an electron and an antineutrino; in β+ decay, a positron and a neutrino. Electrons and neutrinos are leptons, which are fundamental particles. 27 Radioactivity The activity A of a radioactive source is its rate of decay in becquerels (Bq). Decay constant λ is probability of decay per unit time. If there are N undecayed nuclei present, then the activity A = λN. The half-life t1/2 of a decay process is the time for the number of undecayed nuclei or the activity to fall to half of its original value. Half-life and activity are related: λt1/2 = ln 2 = 0.693. The activity A and number of undecayed nuclei N fall exponentially with time according to: A = A0e−λt N = N0e−λt 28 Nuclear fission Einstein’s equation: If an object is given energy ΔE, its mass increases by Δm = ΔE/c2 where.c is the speed of light in vacuo. A thermal neutron may cause the fission of a large, neutron-rich nucleus such as U-235 into two large fragments and more neutrons. Fission reactors, with fuel rods, control rods and moderators, are energy sources, but produce longlived radioactive waste. The binding energy of a nucleus is the energy needed to break the nucleus into its separate protons and neutrons. 29 30 Medical diagnosis A gamma camera detects γ-rays emitted by the Tc-99m radioisotope absorbed by parts of the body. A positron emission tomography (PET) scanner is used to scan the brain and map changes in the blood flow. Carbon-11, absorbed into the blood, decays by positron emission and produces γ-ray photons. In magnetic resonance imaging (MRI) a patient is placed in a strong magnetic field. A radiofrequency pulse of e-m radiation produces precession of nuclei at the Larmor frequency. X-rays (~10−10 m) X-rays are short-wavelength electromagnetic waves produced when high-energy electrons hit a metal surface. When they interact with matter, X-rays may be scattered by the Compton effect, and may cause the photoelectric effect or produce an electron–positron pair and then two photons. The intensity of an X-ray beam is the power per unit cross-sectional area. The intensity I of a collimated X-ray beam varies with the thickness x of the medium according to I = I0e−μx where μ is the linear attenuation coefficient. 31 The universe (1) 1 astronomical unit (AU) = 1.5 × 1 light-year (ly) = 9.5 × 1015 m 1 parsec (pc) = 3.1 × 1016 m = 2.1 × 105 AU = 3.3 ly Doppler effect: For an e-m wave source moving at a speed v relative to an observer, the apparent change in wavelength Δλ is given by Δλ = (v/c)λ. Hubble’s law: The recession velocity v of a distant galaxy is proportional to its distance d: v = H0d. 1011 m H0 = 70 km s−1 Mpc−1 = 70 000/(106 × 3.1 × 1016) = 2.26 × 10−18 s−1 The age of the universe = 1/H0 = 1.4 × 1010 y = 14 billion years 32 The universe (2) Olbers' paradox: An infinite universe full of stars should mean that the light reaching us from all directions would give a bright night sky. This theory fails as the universe is not static: stars are evolving. The cosmological principle: The universe is homogeneous. The 3 K microwave background radiation is evidence of radiation from the matter and antimatter annihilation following the big bang. The universe may be ‘open’, ‘flat’ or ‘closed’, depending on its density. The critical density of the universe is: ρ0 = 3H02/8πG 4