THE UNIVERSITY OF MALTA MATSEC SUPPORT UNIT PHYSICS FORMULAE AND DATA BOOKLET This booklet is not to be removed from the examination room or marked in any way.
THE UNIVERSITY OF MALTA MATSEC SUPPORT UNIT PHYSICS FORMULAE AND DATA BOOKLET The following equations and formulae may be useful in answering some of the questions in the examination.
Table of Contents Uniformly accelerated motion... 3 Mechanics... 3 Circular motion and rotational dynamics... 3 Simple harmonic motion... 4 Ray optics... 4 Current electricity... 5 Alternating current... 5 Stationary waves... 6 Wave motion... 6 Fields... 6 Capacitance... 7 Inductance... 7 Electromagnetism... 8 Temperature... 8 First and second laws of thermodynamics... 9 Gases... 9 Materials... 9 Heat transfer... 10 Quantum phenomena... 10 Radioactivity... 10 Mathematical Formulae... 11 Physical Constants... 12 2
Uniformly accelerated motion Equations of motion: v = u + at v 2 = u 2 + 2as u + v s = ( 2 ) t s = ut + 1 2 at2 Mechanics Newton s second law: Kinetic Energy: Potential Energy: Mechanical Work Done: Power: Momentum: F = ma = d(mv) dt KE = 1 2 mv2 PE = Δ(mgh) W = FΔd P = Fv p = mv Circular motion and rotational dynamics Angular speed: Angular acceleration: Centripetal acceleration: ω = dθ dt = v r α = dω dt = a r a = v2 r 3
Centripetal force: Period: Torque: F = mv2 r T = 2π r v τ = Iα Work done in rotation: τθ = Δ ( 1 2 Iω2 ) Simple harmonic motion Displacement: Velocity: x = x 0 sin(ωt + φ) v = ωx 0 cos(ωt + φ) v = ±ω x 0 2 x 2 Acceleration: Period: Mass on a light spring: a = kx = ω 2 x T = 1 f = 2π k = 2π ω T = 2π m k Ray optics Refractive index: n 1 sin θ 1 = n 2 sin θ 2 1n2 = sin θ 1 = v 1 sin θ 2 v 2 1n3 = 1 n 2 2 n 3 Thin lenses: 1 f = 1 u + 1 v 4 (real is positive)
Magnification: 1 f = 1 v 1 u m = v u = h i h o m = v u = h i h o (Cartesian) (real is positive) (Cartesian) Current electricity Ohm s Law: Current: Resistors in series: Resistors in parallel: Power: Resistivity: V = IR I = nave R TOTAL = R 1 + R 2 + 1 = 1 + 1 + R TOTAL R 1 R 2 P = IV = I 2 R = V2 R ρ = RA l Temperature coefficient: α = R θ R 0 R 0 θ Alternating current For sinusoidal alternating current: Root mean square for sinusoidal alternating current and voltage: I = I 0 sin 2πft I rms = I 0 2 5 V rms = V 0 2
Reactance: X L = 2πfL X C = 1 Stationary waves 2πfC Speed of waves on strings: v = T μ Wave motion Velocity of a wave: Two slit interference: Diffraction grating: Single slit diffraction: Diffraction of circular aperture: v = fλ s = λd d d sin θ = nλ θ = λ a sin θ θ = 1.22 λ a Fields Electric field strength: E = F +q = dv dr Uniform field: Force between point charges: Electric field strength of a point charge: E = F +q = V d Q 1 Q 2 F = 4πε o r 2 Q E = 4πε o r 2 6
Force between point masses: F = G M 1M 2 r 2 Electric potential: V = Q 4πε 0 r Gravitational potential: V G = GM r Work: W = QV = Δ ( 1 2 mv2 ) Capacitance Charge on a capacitor: Capacitance of parallel plates: Capacitors in parallel: Capacitors in series: Energy stored: Charging: Discharging: Q = CV C = ε 0ε r A d C TOTAL = C 1 + C 2 + 1 = 1 + 1 + C TOTAL C 1 C 2 W = 1 2 CV2 Q = Q 0 (1 e t RC) Q = Q 0 e t RC Inductance Mutual inductance: M = E di dt 7
Self-inductance: L = E di dt Energy stored: W = 1 2 LI2 Electromagnetism Force on wire: Torque on a rectangular coil: Force on moving charge: Magnetic flux: Field inside a solenoid: Field near a long straight wire: Induced emf: Emf induced in a moving conductor: Simple alternator emf: Hall voltage: F = BIl τ = BANI F = BQv Φ = BA B = μ 0 μ r ni I B = μ 0 2πr E = N d dt E = Blv V = V 0 sin (ωt + φ) V H = BI nqt Temperature Temperature (K): T = 273.16 P P tr K 8
Celsius scale: θ( C) = T(K) 273.15 K First and second laws of thermodynamics First law of thermodynamics: Ideal heat engine: ΔU = ΔQ + ΔW η = 1 T c T h Gases Ideal gas equation: Kinetic theory of an ideal gas: Boltzmann s constant: Principal molar heat capacities of an ideal gas: Adiabatic process: PV = nrt PV = 1 3 Nm c2 k = R N A γ = C P C V PV γ = constant C P C V = R Materials Hooke s law: Stress: Strain: Young s modulus: F = kδx σ = F A ε = Δl l Y = σ ε 9
Energy stored in a stretched wire: Heat transfer Thermal conduction: E = 1 2 k( l)2 dq dt = ka dθ dx Quantum phenomena Quantum energy: E = hf Mass-energy: E = mc 2 Photoelectric effect: hf = φ + ( 1 2 mv2 ) max Energy levels: ΔE = E 2 E 1 = hf = hc λ De Broglie wavelength: λ = h mv Radioactivity Decay rate: Half-life: Absorption law for gamma radiation: dn dt = λn A = λn N = N 0 e λt T1 = ln 2 2 λ I = I 0 e μd 10
Mathematical Formulae Surface area of a sphere: S = 4πr 2 Volume of a sphere: V = 4 3 πr3 Surface area of a cylinder: S = 2πrh + 2πr 2 Volume of a cylinder: Logarithms: V = πr 2 h ln(x n ) = nlnx ln(e kx ) = kx Equation of a straight line: y = mx + c Relationship between cosine and sine: Small angles: sin(90 θ) = cos θ sin θ tan θ θ(in radians) 11
Physical Constants Acceleration of free fall on and near the Earth s surface Gravitational field strength on and near the Earth s surface Mass of the Earth Radius of the Earth Boltzmann constant Molar gas constant Avogadro s constant g = 9.81 m s 2 g = 9.81 N kg 1 M E = 6.00 10 24 kg r E = 6.37 10 6 m k = 1.38 10 23 J K 1 R = 8.31 J K 1 mol 1 N A = 6.02 10 23 mol 1 Coulomb s law constant k = 1 4πε 0 = 8.99 10 9 N m 2 C 2 Charge of an electron Rest mass of an electron Rest mass of a proton Rest mass of a neutron Electronvolt Gravitational constant Permittivity of free space Permeability of free space Planck constant Speed of light in a vacuum e = 1.60 10 19 C m e = 9.11 10 31 kg m p = 1.67(3) 10 27 kg m n = 1.67(5) 10 27 kg 1 ev = 1.60 10 19 J G = 6.67 10 11 N m 2 kg 2 ε 0 = 8.85 10 12 F m 1 μ 0 = 4π 10 7 H m 1 h = 6.63 10 34 J s c = 3.00 10 8 m s 1 12
Unified atomic mass unit 1 u = 1.66 10 27 kg 13