16 19 Study Guide. Pocket physics. a handy guide for bright stars

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1 6 9 Study Guide Pocket physics a handy guide for bright stars

2 Miscellaneous Ideal gases Pressure (P) pascal (Pa) : Pa = newton per square metre. P = 3 t c where ρ is the density of the gas and _ c² _ is the mean square speed of the molecules. or n moles of gas PV = nrt. Thermal effects Temperature T (kelvin) = t (Celsius) Heat ΔQ supplied to a mass m of a substance with specific heat capacity c results in a D Q temperature rise D T =. Atoms within a substance at temperature T typically have energy ~ k B T, where mc k B is the Boltzmann constant. In thermal equilibrium, two states and differing in energy by ΔE = E E have relative populations given by a Boltzmann factor D 6 N/ N kt B = e Elastic materials extension, x Stress X v = ( Pa) : Strain f = ( dimensionless) length, L a L E= v cross-sectional area, A The Young Modulus f ( Pa) Strain energy = kx material with Young s Modulus, E force, sample with TIP: compare this formula with that for energy stored in a capacitor. spring constant, k Atomic energy and line spectra Electrons in atoms regarded as matter waves. De Broglie wavelength for a particle of mass m and speed v is where h is the Planck constant. Series of allowed energy levels E, E etc and consequent characteristic spectrum. m = mv h, electron wave function energy E electron wave function energy E potential well for electron in atom + nucleus with positive charge Photoelectric effect Photons incident on a surface may cause electrons to be emitted. Maximum kinetic energy of the emitted electrons is determined by the frequency of incident radiation and the substance being illuminated. photon energy hf maximum electron energy hf W substance with work function W Simple harmonic motion Occurs when the force on an object of mass m is directed towards a point (x = 0) and its magnitude is proportional to the distance from that point. = k x Oscillation frequency, f f = r k m displacement x x = Acos(ωt) 0 velocity v v = Aωsin(ωt) 0 acceleration a a = Aω cos(ωt) = ω x 0 amplitude A maximum speed = ωa time t time t time t Maximum speed = A (A = amplitude) Maximum acceleration = ± A Energy of oscillation, E kinetic energy potential energy

3 Mechanics Mechanical quantities Mass (m) kilogram (kg) Scalar The mass of an object is a measure of its inertia: the difficulty of changing its velocity.* kg is the mass of the international prototype of the kilogram stored at BIPM in Paris. orce () newton (N) Vector An unbalanced force causes a mass to accelerate: a = /m. newton is the force required to accelerate kg at m s. The weight W of an object is the (attractive) gravitational force acting on it: W = mg. On the Earth s surface the gravitational field strength is g = 9.8 N/kg, so kg weighs approximately 9.8 N. Energy (E) joule (J) Scalar joule is the energy change when a force of newton acts through metre. Gravitational potential energy change = weight vertical distance moved = m g h. Kinetic energy (KE) = ½m v. Power (P) watt (W) Scalar Rate of transferring energy watt = J/s Momentum (p) mass velocity (kg m/s) or N s Vector orce = rate of change of momentum: force time (impulse) = momentum change Equations of motion v = u + a t : v u = as : s = u t + ½ a t (for constant acceleration) Conservation laws Always apply providing the entire system is taken into account: energy is conserved, but can transfer from one form to another; momentum is conserved. Circular motion Assume speed is constant (but velocity changing), ~ = angular velocity (v/r) (radian/second), acceleration (toward centre) = v /r = ~ r, T = period = time for rotation T = r/~ mass, m v = rω r

4 Electric circuits Current and circuits Charge (Q) coulomb (C) coulomb is the SI unit of charge. Current (I) ampere (A) ampere is a current of coulomb per second*. Potential difference (V) volt (V) volt is the potential difference (PD) between two points when joule of electrical work is done per coulomb moving between those points. Power (P) watt (W) Energy dissipated per second = IV. Resistance (R) ohm (Ω) ohm is one volt per ampere: R = V/I * In series: R Total = R + R In parallel: = + R R R Total Cells and electromotive force (EM) The EM (ε) = the energy supplied to each coulomb by the cell. Some energy transferred in external resistance R and some in internal resistance r. Electrical work done per coulomb through resistor is V = lr. Electrical work done per coulomb through cell r is v = Ir. So ε = IR + Ir. PD across external resistor V = ε v. EM ε internal resistance r cross-sectional area, A voltage, V V = IR material with resistivity, ρ ρl R = A Capacitors Q is the charge displaced from one plate to the other via the circuit. Capacitance (C) farad (): the number of coulombs displaced per volt. Q C = Q/V energy stored = = QV = CV = TIP: compare with elastic materials. C In series: C = C + C : In parallel: C Total = C + C Total Parallel plate capacitors C = ε r ε 0 A/d (for parallel plates of area A separated by distance d of material with relative permittivity ε r ). Capacitor discharge through resistor TIP: compare with radioactive decay. PD across R: V = Q/C, and I = V/R Thus I = Q/RC so I is proportional to Q So rate of loss of Q (i.e. I ) is proportional to Q Therefore Q = Q 0 e ( t/rc). RC is the time constant = time for Q to fall to /e of original value. 99% discharge after about 5RC seconds. fraction of charge remaining Q 0 Q 0 e 0.0 RC RC 3RC time

5 The seven SI base units The SI (Système International d Unités) is the standard system of units for scientists worldwide. There are seven base units, from which the other units are derived. Symbol Quantity Unit Definition kg mass kilogram The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. m length metre The metre is the length of the path travelled by light in vacuum during a time interval of / of a second. s time second The second is the duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 33 atom. A electric current ampere The ampere is that constant current that, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed m apart in vacuum, would produce between these conductors a force equal to 0 7 newton per metre of length. K temperature kelvin The kelvin, unit of thermodynamic temperature, is the fraction /73.6 of the thermodynamic temperature of the triple point of water. cd mol Prefixes luminous intensity amount of substance candela mole The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency hertz and that has a radiant intensity in that direction of /683 watt per steradian. The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.0 kg of carbon. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. Greater than unity kilo Mega Giga Tera Peta Exa Zetta Yotta Less than unity milli µ (micro) nano pico femto atto zepto yocto

6 Radioactivity Nuclear structure Atomic (proton) number Z = number of protons in the nucleus. In a neutral atom this is also the number of electrons in the atom (determines the chemical properties). Mass (nucleon) number A = number of protons plus number of neutrons. The strong nuclear force binds neutrons to neutrons, protons to protons and neutrons to protons. Number of neutrons (n) is approximately the same as the number of protons (p). Isotopes. Atoms with same atomic number Z, but different mass number A. Nuclei have the same number of protons but different numbers of neutrons. Nuclear decay Nuclei typically decay by emitting one of two types of particle (α or ß) accompanied by high-frequency electromagnetic radiation known as γ radiation. Alpha (α) decay Beta (ß) minus emission Gamma (γ) radiation p α β n γ A A 4 A A A A Z Z Z Z+ An alpha particle (helium nucleus: 4 He, p + n) is emitted from the nucleus. It is generally followed by a cascade of γ radiation. A beta particle (electron) is emitted from the nucleus along with an antineutrino. It is generally followed by a cascade of γ radiation. dn Probability of decay in a fixed time: N dt When some have decayed, fewer remain so the rate of decay (the activity) falls. N = N 0 e λt TIP: compare with decay of charge on a capacitor. Half-life (T ½ ) Time for half to decay T ½ = ln()/λ = 0.69/λ Radioactivity quantities and units Activity becquerel (Bq) is disintegration per second. Absorbed dose gray (Gy) is the dose when joule is absorbed by kg of tissue. m = 8 B Z Z High-frequency electromagnetic wave (f > 0 7 Hz). Decay constant gradient proportional to number of nuclei undecayed dn activity = = λn dt Dose equivalent sievert (Sv) is related to the biological harm caused by the absorbed dose.* Binding energy If protons and neutrons are bound into a nucleus, nuclear mass is Δm less than the sum of the masses of the constituent protons and neutrons. Binding energy = Δmc, where c is the speed of light in a vacuum. number of undecayed nuclei N N 4 N half life time

7 ields ields due to an isolated spherical charge or mass Inverse square law of force due to an isolated charge (Q) or mass (M), +Q r +q M r m kqq GMm = (where k = in a vacuum) : (where G is gravitational constant). r 4rf = - 0 r ield strength Vector. Examples are force per unit charge E, or force per unit mass g. kq orce on coulomb E = + : orce on kilogram. r g = GM r or fields within a substance of relative permittivity ε r electric fields are reduced by factor ε r. There is no known type of gravitational permittivity. ield strength = negative potential gradient = dv -. dr ield potential ield potential (V) Scalar. Potential energy of unit electric charge (or unit mass). Energy required to bring unit electric charge (or mass) from infinity to the point in question. Electrical (repulsive force for positive Q): V elec = kq/r Gravitation (attractive force for positive M): V grav = GM/r. Potential energy of charge q (or mass m ) in the field: qv elec (or mv grav ). Uniform fields. ield lines are parallel; field strength is given by the negative of potential gradient E = V/d. Magnetic fields Magnetic field strength (B) tesla (T) Vector. tesla is the magnetic field strength that gives rise to a force of newton per metre on a wire carrying ampere. Density of field lines in diagrams is proportional to field strength. Magnetic flux (Φ) weber ( Wb ) Through an area A : Φ = BA (field lines perpendicular to A). orces in a magnetic field orce on a wire length l carrying current I N S perpendicular to field B has magnitude = BIl, which acts I perpendicular to B and I as given by a left-hand rule. N B S orce on a charge q travelling with speed v perpendicular to magnetic field B has magnitude = Bqv, which acts perpendicular to B and v as given by a left-hand rule. Charge moves in arc of circle of radius r = mv/qb. Induced EM in a magnetic field dz dz or a loop of wire threaded by flux Φ, f =. or a coil of N loops each with flux Φ, f = N. dt dt

8 θ { Waves Energy transfer by waves Transfer of energy without the transfer of matter. Speed of waves or both transverse and longitudinal v = f m : v = speed: f = frequency: m = wavelength Interference Diffraction pattern from single slit Diffraction results from interruption of part of the wavefront. An explanation can be given using Huygen s construction. Electrons and other particles can be diffracted to show their wave properties. or first minimum sin θ = m b or small angles sin θ θ (rads) Radiation wavelength m Slit width b single slit intensity diffraction angle θ 0 θ b λ Double slit Assume that waves at each slit are coherent and in-phase. or constructive interference on the screen, the path difference = n m. sin θ = nm m s ; = (for small angles) d d L d S S path difference θ L L>>d A s B θ intensity Diffraction grating (multiple slits) Different wavelengths produce constructive interference at different angles given by n λ = d sin i. Same formula as two slits, but grating forms narrow distinct lines. d usually small, so i large. d θ direction for constructive interference 0 θ n = n = 0 n = Electromagnetic radiation Speed of light in a vacuum: c = fn 0 0 Refractive index measures the reduction in the speed of light within a medium. A refractive index of.5 means light travels at /.5 times the speed of light in a vacuum. Energy of a photon is E = h f (h is the Planck constant). intensity

9 Data Acceleration of free fall (in UK) g 9.8 m s Gravitational field strength (in UK) g 9.8 N kg Gravitational constant G Nm kg Electric force constant k = 4rf Nm C Speed of light in a vacuum c m s Permeability of free space µ o 4r 0 7 N A Permittivity of free space ε o m Planck constant h J s Elementary electron charge e C Electron rest mass m kg Electronvolt ev J Unified atomic mass constant u kg Proton rest mass m p kg Neutron rest mass m n kg Molar gas constant R 8.3 J K mol Boltzmann constant k B J K Avogadro constant N A mol Standard temperature and pressure STP 73.5 K and Pa Molar volume at STP V m m 3 mol myphysicscourse.org inding the right degree Everything from physics with mathematics to physics with music, across the UK and Ireland.

10 SI derived units Derived quantity SI derived unit Base units Acceleration metre per second squared m s orce newton (N) kg m s Work joule (J) kg m s Pressure/stress pascal (Pa) kg m s Charge coulomb (C) A s EM/potential difference volt (V) A kg m s 3 Electric field strength newton per coulomb (NC ) or volt per metre (Vm ) A kg m s 3 Capacitance farad () A kg m s 4 Magnetic field strength tesla (T) A kg s Concentration (of amount of substance) mole per cubic metre mol m 3 Useful websites National Physical Laboratory outreach: npl.co.uk/educate-explore Institute of Physics: iop.org/careers Physical and chemical constants reference: kayelaby.npl.co.uk Author s notes This is intended as a quick revision guide and not a definitive reference. * indicates an equation is correct but not the definition. QUBIT Aged between 6 and 9 and studying physics? Want to know about what s new in physics? Sign up to Qubit and receive regular updates from the IOP. iop.org/6-9

16 19 Study Guide. Pocket physics. a handy guide for bright stars

16 19 Study Guide. Pocket physics. a handy guide for bright stars 6 9 Study Guide Pocket physics a handy guide for bright stars Miscellaneous Ideal gases Pressure (P) pascal (Pa) : Pa = newton per square metre. P = 3 t c where ρ is the density of the gas and _ c² _ is