Annotated Physics Data Booklet 2016 PDF

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ib physics 2016 annotated databook for reference...

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Physics data booklet First assessment 2016 Annotated by Boaz V.

Diploma Programme Physics data booklet

Published June 2014 Revised edition published January 2016 Published on behalf of the International Baccalaureate Organization, a not-for-profit educational foundation of 15 Route des Morillons, 1218 Le Grand-Saconnex, Geneva, Switzerland by the International Baccalaureate Organization (UK) Ltd Peterson House, Malthouse Avenue, Cardiff Gate Cardiff, Wales CF23 8GL United Kingdom Website: www.ibo.org © International Baccalaureate Organization 2014 The International Baccalaureate Organization (known as the IB) offers four high-quality and challenging educational programmes for a worldwide community of schools, aiming to create a better, more peaceful world. This publication is one of a range of materials produced to support these programmes. The IB may use a variety of sources in its work and checks information to verify accuracy and authenticity, particularly when using community-based knowledge sources such as Wikipedia. The IB respects the principles of intellectual property and makes strenuous efforts to identify and obtain permission before publication from rights holders of all copyright material used. The IB is grateful for permissions received for material used in this publication and will be pleased to correct any errors or omissions at the earliest opportunity. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior written permission of the IB, or as expressly permitted by law or by the IB’s own rules and policy. See http://www.ibo.org/copyright. IB mer chandise and publicat ions can be purchased t hr ough the IB st or e at http://store.ibo.org. Email: [email protected]

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Contents Fundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Metric (SI) multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Equations—Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Equations—AHL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Equations—Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Physics data booklet

Physics data booklet

Fundamental constants Quantity

Symbol

Approximate value

Acceleration of free fall (Earth’s surface)

g

9.81m s2

Gravitational constant

G

6 .67 ×10 −11 Nm2 kg−2

Avogadro’s constant

NA

6 .02 ×1023 mol −1

Gas constant

R

8.31JK 1 mol1

Boltzmann’s constant

kB

1 .38 ×10 −23 JK −1

Stefan–Boltzmann constant

V

5.67 × 10 −8 W m−2 K −4

Coulomb constant

k

8.99 × 109 Nm2 C −2

Permittivity of free space

H0

8.85 × 10 −12 C 2 N −1 m − 2

Permeability of free space

P0

4π × 10−7 T m A −1

Speed of light in vacuum

c

3.00 × 108 m s −1

Planck’s constant

h

6.63 × 10 −34 Js

Elementary charge

e

1 .60 ×10 −19 C

Electron rest mass

me

9.110 × 10−31 kg = 0 .000549 u = 0 .511 MeV c−2

Proton rest mass

mp

1 .673 ×10 − 27 kg = 1 .007276 u = 938 MeV c− 2

Neutron rest mass

mn

1 .675 ×10 − 27 kg =1 .008665 u =940 MeV c − 2

Unified atomic mass unit

u

1 .661 ×10 −27 kg =931 .5 MeV c −2

Solar constant

S

1 .36 ×103 W m −2

Fermi radius

R0

1 .20 ×10 −15 m

Physics data booklet

1

Metric (SI) multipliers Prefix

Abbreviation

Value

peta

P

1015

tera

T

1012

giga

G

109

mega

M

106

kilo

k

103

hecto

h

102

deca

da

101

deci

d

10 –1

centi

c

10 –2

milli

m

10 –3

micro

P

10 –6

nano

n

10 –9

pico

p

10 –12

femto

f

10 –15

Unit conversions 1 radian (rad) ≡

180 ° π

Temperature (K) = temperature (°C ) + 273 1 light year (ly) = 9 .46 ×1015 m

1 parsec (pc) 3 .26 ly 1 astronomical unit (AU) = 1. 50 × 1011 m

1 kilowatt-hour (kWh) = 3 .60 ×10 6 J

hc = 1 .99 × 10 − 25 Jm = 1 .24 × 10−6 eV m

2

Physics data booklet

Electrical circuit symbols

cell

battery

ac supply

switch

voltmeter

V

ammeter

resistor

variable resistor

lamp

potentiometer

light-dependent resistor (LDR)

thermistor

transformer

heating element

diode

capacitor

Physics data booklet

A

3

Equations—Core Note: All equations relate to the magnitude of the quantities only. Vector notation has not been used. Sub-topic 1.2 – Uncertainties and errors Adding/subtracting quantities: uncertainty in result will be sum ∆a + ∆b of uncertainties of quantities.

Sub-topic 1.3 – Vectors and scalars

If: y = a ± b then: ∆y =

A

AV

y = Result.

AH = Horizontal component.

a, b, c = Quantities.

If: y

Δ = Uncertainty.

then:

Multiplying/dividing quantities: % uncertainties of quantities are added together to obtain % uncertainty in result.

ab c ∆y

=

y

AV = Vertical component.

∆ a ∆ b ∆c + + a b c

T AH

If: y

an

then:

∆y

Powers of quantities: % uncertainty of quantity is multiplied by power to obtain % uncertainty in result.

= n

y

v = Final velocity.

∆a a

A H = A cosθ A V = A sinθ

F = Resultant force.

Sub-topic 2.1 – Motion

u = Initial velocity.

v = u + at

Sub-topic 2.2 – Forces

F

a = Acceleration (‘g’ for gravitational).

s = ut +

s = Displacement.

v 2 = u2 + 2as

t = Time elapsed.

s=

1 2 at 2

Equations applied to uniform motion (known as ‘suvat’ equations).

s = Displacement.

EK

EK = Kinetic energy.

Frictional force on a static object.

Ff = µ dR

Frictional force on a dynamic object.

1 mv 2 2

v = Velocity.

∆E p = mg ∆h

EP = Potential energy.

power

efficiency

x = Extension.

Work done.

Kinetic energy.

m = Mass.

Fv

Sub-topic 2.4 – Momentum and impulse p

∆p F= ∆t

Elastic potential energy (in a spring).

EK Gravitational potential energy. Power.

mv

μs = Coefficient of static friction. μd = “ dynamic “.

p2 2m

R = Normal reaction force.

p = Momentum.

Resultant force due to momentum. m = Mass. v = Velocity.

Kinetic energy.

F = Force. t = Time.

impulse = F ∆t = ∆p

useful work out total work in

EK = Kinetic energy.

h = Height.

4

a = Acceleration.

Momentum.

useful power out total power in

g = Earth’s gravity.

m = Mass.

Ff = Frictional force.

1 Ep = k∆ x 2 2

k = Spring constant

Acceleration due to resultant force (Newton’s 2nd law of motion).

( v + u) t 2

W = Fs cos θ

F = Force.

ma

Ff ≤ µ sR

Sub-topic 2.3 – Work, energy and power

W = Work done.

Trigonometric rules of triangles are applied when taking components of vector quantities.

Physics data booklet

p = Pressure. F = Force. A = Area. n = Number of moles.

Q = Energy/heat. m = Mass. c = Specific heat capacity.

Sub-topic 3.1 – Thermal concepts Q = mc ∆T Q

mL

Energy/heat given/received in changing an object’s temperature.

n

L = Specific latent heat.

f = Frequency. λ = Wavelength.

T

1

f

Period (time taken to complete 1 oscillation).

Sub-topic 4.2 – Travelling waves c = fλ

N NA

N = Number of atoms.

Pressure.

NA = Avogadro’s constant. Number of moles of a substance. V = Volume.

nRT

EK

3 kBT 2

R = Gas constant.

Ideal gas law.

3 R T 2 NA

T = Temperature.

Average kinetic energy per molecule of a gas.

EK = Kinetic energy. kb = Boltzmann’s constant.

Sub-topic 4.4 – Wave behaviour n1 sinθ 2 v 2 = = n2 sinθ1 v1 s=

λD

Refraction when a wave crosses a boundary between 2 media (Snell’s law).

n1/n2 = Index of refraction. θ = Angle of incidence/refraction.

Fringe spacing in double slit diffraction.

d

Speed of a wave.

Sub-topic 4.3 – Wave characteristics

I v A2

Intensity of a wave vs. amplitude.

A = Amplitude.

I ∝ x−2

Intensity of a wave’s radiation at a certain distance from the source.

x = Distance from source.

I = I0 cos2 T

I = Intensity.

F A

pV

Sub-topic 4.1 – Oscillations

T = Period.

c = Velocity.

p

Energy/heat given/received in changing an object’s phase.

T = Temperature.

f = Frequency.

Sub-topic 3.2 – Modelling a gas

Transmitted intensity of light incident on a polariser (Malus’s law).

v = Wave velocity.

Constructive interference: path difference = n λ Destructive interference: 

s = Fringe spacing.

Maxima/minima on screen in double slit diffraction.

λ = Wavelength.

1

D = Distance to screen.

path difference =  n +  λ 2 

d = Slit spacing.

I0 = Original intensity.

n = Any integer (order of minimum/ maximum).

θ = Angle of polarizer.

Physics data booklet

5

I = Current. q = Charge. t = Time.

Sub-topic 5.2 – Heating effect of electric currents

Sub-topic 5.1 – Electric fields

F = Force. k = Coulomb constant.

Kirchhoff’s circuit laws: Σ V = 0 (loop)

I=

∆q ∆t

r = Separation distance.

F

qq k 12 2 r

Force experienced by 2 charges (Coulomb’s law).

ε0 = Permittivity of free space.

k

1 4S H0

Coulomb constant.

V

W q

Potential difference.

E

F q

Electric field strength.

Rtotal = R1 + R2 + ...

Current in a wire.

1 1 1 = + + ... Rtotal R1 R2

V = Potential. W = Work done. E = Electric field strength. n = Number of charges per unit volume.

I

Current.

nAvq

V

V2 I 2R R

RA L

R = Resistance.

Power supplied/dissipated.

Total resistance of resistors in series. Total resistance of resistors in parallel.

F = Force.

F = qvB sin θ

Force on a charge moving through a magnetic field.

F = B IL sin θ

Force on a current-carrying wire in a magnetic field.

Sub-topic 6.2 – Newton’s law of gravitation

Sub-topic 6.1 – Circular motion

v = Velocity.

v =ωr

Velocity of body travelling in circle.

F

G

g

F m

g

G

Mm r2

Force experienced by 2 masses (Newton’s law of gravitation).

r = Radius of circle.

v 2 4π 2 r a= = 2 r T

a = Acceleration. T = Period of rotation.

F=

F = Force.

q = Charge. v = Velocity of charge. B = Magnitude of magnetic field. θ = Angle with field.

r = Internal resistance.

ω = Angular velocity.

L = Length.

Resistivity of material of a wire.

ε = Emf. I = Current.

ρ = Resistivity.

Sub-topic 5.4 – Magnetic effects of electric currents

Sub-topic 5.3 – Electric cells Emf of a cell.

P = Power.

A = X-sectional area.

VI

P

v = Drift velocity.

ε = I (R + r )

R = Resistance.

Resistance.

I

ρ=

A = X-sectional area.

I = Current.

Σ I = 0 (junction) R

V = Potential.

mv2 = m ω 2r r

Centripetal acceleration.

Centripetal force.

Field strength as experienced by a mass in the field.

M r2

Field strength at a certain distance from body.

F = Force. G = Gravitational constant. M = Mass of body. m = Mass of body (in a field). r = Separation distance of bodies. g = Gravitational field strength

m = Mass.

6

Physics data booklet

E = Energy. h = Planck’s constant. f = Frequency. λ = Wavelength. c = Speed of light.

Sub-topic 7.1 – Discrete energy and radioactivity hf

E

λ=

∆E = ∆mc 2

Energy of a photon.

E = Energy.

Sub-topic 7.2 – Nuclear reactions

m = Mass.

Energy released when nucleons are assembled into nucleus.

c = Speed of light.

Wavelength of a photon.

hc E

Sub-topic 7.3 – The structure of matter e = Elementary charge. u = Up.

Charge 2 e 3

Baryon number

Quarks u

c

t

Charge

e = Electron.

s = Strange. t = Top.

1  e 3

d

s

b

–1

e

P

W

0

Qe

νµ

ντ

u = Muon.

1 3

d = Down. c = Charm.

Leptons

τ = Tau.

All leptons have a lepton number of 1 and antileptons have a lepton number of –1

1 3

ν = Neutrino.

All quarks have a strangeness number of 0 except the strange quark that has a strangeness number of –1

b = Bottom.

Particles experiencing Particles mediating

Gravitational

Weak

Electromagnetic

Strong

All

Quarks, leptons

Charged

Quarks, gluons

Graviton

W + , W −, Z 0

J

Gluons

Sub-topic 8.2 – Thermal energy transfer

Sub-topic 8.1 – Energy sources A = Area swept out by turbine blades. ρ = Air density. v = Wind speed.

power

energy time

1 power = Aρ v3 2

P = eσ AT Power available from a wind turbine.

4

Power radiated by a body.

λ max(metres) = I

power A

P = Power.

2.90 × 10 −3 T (kelvin)

e = Emissivity.

Wavelength at which intensity of radiation is at a maximum.

σ = Stefan-Boltzmann constant. A = Area.

Intensity of radiation.

T = Temperature. λ = Wavelength.

albedo

Physics data booklet

total scattered power total incident power

I = Intensity.

7

Equations—AHL Sub-topic 9.1 – Simple harmonic motion

ω = Angular frequency.

ω=

T = Period.

2π T

Angular frequency of oscillation

a = −ω 2 x

a = Acceleration.

θ=

Acceleration of object in SHM. Displacement of object in SHM.

x = Displacement from equilibrium.

x = x 0 sin ωt ; x = x 0 cos ωt

x0 = Maximum displacement.

v = ω x 0 cos ω t; v = −ω x 0 sin ω t

t = Time elapsed.

Sub-topic 9.2 – Single-slit diffraction

v = ±ω ( x 02 − x 2 )

Velocity of object in SHM.

Velocity of object in SHM.

λ b

Angle at which first minimum occurs in single-slit diffraction.

EK =

1 mω 2 ( x02 − x2 ) 2

ET =

1 mω 2 x0 2 2

l = Length of pendulum. g = Gravitational field strength.

Sub-topic 9.3 – Interference nλ = d sin θ

Path difference between slits for a diffraction grating (constructive/ destructive interference).

1   Constructive interference: 2 dn =  m +  λ 2 

Destructive interference: 2dn = mλ

l g

θ = 1.22

b = Slit width/ diameter. R = Resolvance

R=

Δλ = Smallest possible resolvable wavelength difference.

λ b

d = Slit spacing (for diffraction grating). θ = Angle. d = Thickness of medium (for TFI).

Period of oscillation of a mass on a spring in SHM.

First minimum for diffraction in a circular aperture.

λ = mN ∆λ

λ = Wavelength.

m = Any integer (for TFI).

Sub-topic 9.4 – Resolution

λ = Wavelength.

n = Any integer (for diffraction grating).

n = Refractive index of medium (for TFI).

Period of oscillation of a pendulum in SHM.

m mass-spring:T = 2π k θ = Angle.

Interference patterns for thin-film interference.

Total energy of object in SHM.

pendulum: T ...