Physics data booklet for ib PDF

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Physics data booklet First assessment 2016

Diploma Programme Physics data booklet

Published June 2014 Revised edition published November 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 merchandise and publications c an be purchased through the IB s tore at http://store.ibo.org. Email: [email protected]

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Contents Mathematical equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Metric (SI) multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equations—Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equations—AHL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Equations—Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Physics data booklet

Physics data booklet

Mathematical equations Area of a circle

A = πr 2 , where r is the radius

Circumference of a circle

C = 2πr , where r is the radius

Surface area of a sphere

A = 4πr 2 , where r is the radius

Volume of a sphere

4 V = πr3 , where r is the radius 3

Physics data booklet

1

Fundamental constants Quantity

2

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

σ

5.67 × 10 −8 W m−2 K −4

Coulomb constant

k

8.99 × 109 Nm2 C −2

Permittivity of free space

ε0

8.85 × 10 −12 C 2 N −1 m − 2

Permeability of free space

µ0

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

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

µ

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

Physics data booklet

3

Electrical circuit symbols

cell

battery

ac supply

switch

voltmeter

4

V

ammeter

resistor

variable resistor

lamp

potentiometer

light-dependent resistor (LDR)

thermistor

transformer

heating element

diode

capacitor

A

Physics data booklet

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

Sub-topic 1.3 – Vectors and scalars

If: y = a ± b then: ∆y = ∆a + ∆b

If: y = then:

A

AV

ab c ∆y

y

=

∆ a ∆ b ∆c + + a b c

θ AH A H = A cosθ

If: y = an then:

∆y

y

= n

∆a a

A V = A sinθ

Sub-topic 2.1 – Motion v = u + at s = ut +

F = ma

1 2 at 2

v 2 = u 2 + 2as s=

Sub-topic 2.2 – Forces

Ff ≤ µ sR Ff = µ dR

( v + u) t 2 Sub-topic 2.3 – Work, energy and power

W = Fs cos θ

Sub-topic 2.4 – Momentum and impulse p = mv

EK =

1 mv 2 2

F=

Ep =

1 k∆ x 2 2

EK =

∆E p = mg ∆h

power = Fv efficiency = =

∆p ∆t p2 2m

impulse = F ∆t = ∆p useful work out total work in useful power out total power in

Physics data booklet

5

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

Sub-topic 3.2 – Modelling a gas

p=

F A

n=

N NA

Q = mL

pV = nRT EK =

Sub-topic 4.1 – Oscillations T =

1

f

Sub-topic 4.2 – Travelling waves c = fλ

Sub-topic 4.3 – Wave characteristics

I ∝ A2 I ∝ x−2 I = I 0 cos2 θ

6

3 3 R k BT = T 2 2 NA

Sub-topic 4.4 – Wave behaviour n 1 sinθ 2 v 2 = = n2 sinθ1 v1 s=

λD d

Constructive interference: path difference = nλ Destructive interference: 1

path difference =  n +  λ 2 

Physics data booklet

Sub-topic 5.1 – Electric fields

I=

∆q ∆t

q1q2 r2

F =k

Sub-topic 5.2 – Heating effect of electric currents Kirchhoff’s circuit laws: Σ V = 0 (loop)

Σ I = 0 (junction)

k=

1 4πε 0

R=

V =

W q

P = V I = I2R =

E=

F q

Rtotal = R1 + R2 + ...

I = nAvq

ε = I (R + r )

I V2 R

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

ρ= Sub-topic 5.3 – Electric cells

V

RA L

Sub-topic 5.4 – Magnetic effects of electric currents

F = qvB sin θ F = B IL sin θ Sub-topic 6.2 – Newton’s law of gravitation

Sub-topic 6.1 – Circular motion v =ωr

a=

v 2 4π2r = r T2

g=

F=

mv2 = mω 2r r

g=G

Physics data booklet

Mm r2

F =G F m

M r2

7

Sub-topic 7.1 – Discrete energy and radioactivity

∆E = ∆mc 2

E =hf

λ=

Sub-topic 7.2 – Nuclear reactions

hc E Sub-topic 7.3 – The structure of matter

Charge 2 e 3 1 − e 3

Baryon number

Quarks u

d

c

s

t

1 3

b

1 3

Charge

Leptons

–1

e

µ

τ

0

νe

νµ

ντ

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

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

Particles experiencing Particles mediating

Gravitational

Weak

Electromagnetic

Strong

All

Quarks, leptons

Charged

Quarks, gluons

Graviton

W + , W −, Z 0

γ

Gluons

Sub-topic 8.2 – Thermal energy transfer

Sub-topic 8.1 – Energy sources

power =

energy time

P = eσ AT 4

power =

1 Aρ v 3 2

λmax (metres) = I=

power A

albedo =

8

2.90 × 10 −3 T (kelvin)

total scattered power total incident power

Physics data booklet

Equations—AHL Sub-topic 9.1 – Simple harmonic motion

ω=

2π T

Sub-topic 9.2 – Single-slit diffraction

θ=

λ b

a = −ω 2 x

Sub-topic 9.3 – Interference

x = x 0 sin ω t; x = x 0 cos ω t

nλ = d sinθ

v = ω x0 cos ω t; v = −ω x0 sin ω t

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

v = ± ω ( x 02 − x 2 )

Destructive interference: 2dn = mλ

EK =

1 mω 2 ( x02 − x2 ) 2

ET =

1 mω 2 x0 2 2

pendulum: T = 2π

l g

mass-spring:T = 2π

m k

Sub-topic 9.4 – Resolution

θ = 1.22

R=

λ ∆λ

λ b = mN

Sub-topic 9.5 – Doppler effect  v  Moving source: f ′ = f    v ± us   v ± uo  Moving observer: f ′ = f    v  ∆f

f

Physics data booklet

=

∆λ

λ

≈

v c

9

Sub-topic 10.1 – Describing fields W = q ∆V e

W = m∆Vg

Sub-topic 10.2 – Fields at work

Vg = − g=−

GM r

∆Vg

10

GMm r2

v esc =

2GM r

v orbit =

GM r

kQ r

E=−

∆r

Ep = mVg = − Fg =

Ve =

∆Ve ∆r

GMm kQq E p = qV e = r r Fe =

kQq r2

Physics data booklet

Sub-topic 11.1 – Electromagnetic induction

Φ = BA cos θ ∆ ε = −N Φ ∆t

ε = Bv l

Sub-topic 11.3 – Capacitance C=

q V

C parallel = C 1 + C 2 + ... 1

ε = Bv lN

Cseries

Sub-topic 11.2 – Power generation and transmission

C= ε

I0

I rms = Vrms =

E=

2 V0

1 1 + + ... C1 C2

= A d

1 CV 2 2

τ = RC

2 t

V0

V R = = rms I0 I rms

q = q0 e

Pmax = I 0V0

I = I 0e

−

τ

t

P =

1 I 0V 0 2

−

τ

t −

V = V0e τ

ε p Np Is = = ε s Ns I p Sub-topic 12.1 – The interaction of matter with radiation

Sub-topic 12.2 – Nuclear physics 1

E =hf

R = R0 A 3

E max = h f − Φ

N = N 0e − λt

E=−

13 .6 eV n2

mvr =

nh 2π

A = λN 0e −λt

sinθ ≈

λ D

2

P (r ) = ψ ∆V ∆ x∆p ≥

h 4π

∆E ∆t ≥

h 4π

Physics data booklet

11

Equations—Options Sub-topic A.1 – The beginnings of relativity

x′ = x − v t

Sub-topic A.2 – Lorentz transformations 1

γ=

1−

u′ = u − v Sub-topic A.3 – Spacetime diagrams v θ = tan− 1   c 

v2 c2

x′ = γ ( x − vt ); ∆ x′ = γ ( ∆ x − v ∆t ) 

vx   ; ∆t′ = γ c2 

t′ = γ  t − 

u′ =

v ∆x    ∆t − 2  c  

u −v uv 1− 2 c

∆t = γ ∆t0 L=

L0

γ

( ct′ )2 − (x ′)2 = ( ct )2 − (x )2 Sub-topic A.4 – Relativistic mechanics (HL only) E = γ m0 c 2 E 0 = m0c 2 E K = (γ − 1) m 0c 2 p = γ m 0v E 2 = p2 c 2 + m0 2c 4

Sub-topic A.5 – General relativity (HL only) ∆f

=

g ∆h c2

Rs =

2GM c2

f

∆t =

∆t 0 1−

Rs r

qV = ∆EK

12

Physics data booklet

Sub-topic B.1 – Rigid bodies and rotational dynamics

Γ = Fr sin θ

Sub-topic B.2 – Thermodynamics Q = ∆U + W

I = ∑ mr 2

3 nRT 2

U=

Γ = Iα ω = 2πf

∆S =

ωf = ωi + α t ωf2 = ωi2 + 2αθ 1 θ = ω it + α t 2 2 L = Iω EKrot =

1 Iω 2 2

Sub-topic B.3 – Fluids and fluid dynamics (HL only)

∆Q T

5

pV 3 = constant (for monatomic gases) W = p∆V

η=

useful work done energy input

η Carnot = 1 −

Tcold Thot

Sub-topic B.4 – Forced vibrations and resonance (HL only) energy stored energy dissipated per cycle

B = ρfVf g

Q = 2π

P = P0 + ρ f gd

Q = 2π × resonant frequency×

energy stored power loss

Av = constant 1 ρv 2 + ρgz + p = constant 2

FD = 6πηrv R=

vr ρ

η

Physics data booklet

13

Sub-topic C.1 – Introduction to imaging 1

f

=

P=

1 1 + v u

Sub-topic C.2 – Imaging instrumentation

fo fe

M=

1

Sub-topic C.3 – Fibre optics

f n=

h v m = i =− ho u

1 sin c

attenuation = 10 log

θ M= i θo

Mnear point =

D

f

+ 1; M infinity =

I I0

Sub-topic C.4 – Medical imaging (HL only)

D

f LI = 10 log

I1 I0

I = I 0 e − µx

µ x 1 = In2 2

Z = ρc

Sub-topic D.1 – Stellar quantities

d (parsec) = L = σ AT b=

1 p (arc-second)

4

Sub-topic D.2 – Stellar characteristics and stellar evolution

λmaxT = 2.9 × 10 −3 mK L ∝ M 3.5

L 4π d 2 Sub-topic D.3 – Cosmology

Sub-topic D.5 – Further cosmology (HL only)

z=

∆λ v ≈ λ0 c

v=

z=

R −1 R0

ρc =

4πG ρ r 3 3H 2 8 πG

v = H 0d T ≈

14

1 H0

Physics data booklet...