Download Understanding Physics

Understanding
Physics
MICHAEL MANSFIELD AND COLM O'SULLIVAN
Physics Department
University College Cork
Ireland
JOHN WILEY & SONS
CHICHESTER . NEW YORK . WEINHEIM . BRISBANE . SINGAPORE . TORONTO
Published in association with
PRAXIS PUBLISHING
CHICHESTER
PR
Contents
Preface
1
Understanding the physical universe
1.1
1.2
1.3
1.4
1.5
1.6
The programme of physics
Building blocks of matter
Matter in bulk
The fundamental interactions
Exploring the physical universe: the scientific method
The role of physics: its scope and applications
2 Using mathematical tools in physics
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
Applying the scientific method
Use of variables to represent displacement and time
Representation of data
Use of differentiation in analysis: velocity and acceleration in
linear motion
Use of integration in analysis
Maximum and minimum values of physical variables: general
linear motion
Angular motion: the radian
Using mathematics in physics
Worked Examples
Problems
3 Causes of motion: dynamics
3.1
3.2
3.3
3.4
3.5
The concept of force
The first law of dynamics (Galileo's principle/Newton's first law)
The fundamental dynamical principle (Newton's second law)
Systems of units: SI
Time-dependent forces: oscillatory motion
xv
1
1
2
6
6
7
10
12
12
12
14
17
21
26
27
30
31
34
36
36
37
38
42
45
vi
Contents
3.6
4
5
48
52
53
Motion in two and three dimensions
55
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
55
59
60
62
64
66
68
69
71
72
73
75
78
Vector physical quantities
Velocity and acceleration vectors
Motion with constant acceleration: projectile motion
Force as a vector quantity: vector form of the laws of dynamics
Constraint forces
Friction
Motion in a circle: centripetal force
Motion in a circle at constant speed
Tangential and radial components of acceleration
Hybrid motion: the simple pendulum
Angular quantities as vectors: the cross product
Worked Examples
Problems
Fields and energy
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
*5.14
*5.15
6
Simple harmonic motion
Worked Examples
Problems
Newton's law of gravitation
General force fields
Mechanical work
Potential energy: conservative fields
Mechanical energy
Power
Plots of potential energy functions
Energy in a constant uniform field
Energy in an inverse square law field
Energy in simple harmonic motion
Damped harmonic motion
Moment of a force: angular momentum
Planetary motion: circular orbits
Planetary motion: elliptical orbits and Kepler's laws
Gravitational forces exerted by shells and spheres
Worked Examples
Problems
81
81
83
85
87
90
92
92
94
95
97
99
102
104
105
109
110
116
Many-body interactions
119
6.1
6.2
6.3
6.4
6.5
119
122
124
124
128
Newton's third law
The principle of conservation of momentum
Mechanical energy of systems of particles
Decays and collisions
The centre of mass of a system
* indicates a more advanced section
Contents vii
6.6
6.7
6.8
The two-body problem: reduced mass
Collisions in LAB and CM coordinate systems
Angular momentum of systems of particles
130
133
139
6.9
Conservation principles in physics
Worked Examples
Problems
141
142
145
7 Rigid-body dynamics
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
Rigid bodies
Rigid bodies in equilibrium: statics
Torque
Dynamics of rigid bodies
Measurement of torque: the torsion balance
Rotation of a rigid body about a fixed axis: moment of inertia
Calculation of moments of inertia: the parallel axes theorem
Conservation of angular momentum of rigid bodies
Conservation of mechanical energy in rigid-body systems
Work done by a torque: torsional oscillations; rotational power
Gyroscopic motion
Summary: the connection between rotational and
translational motions
Worked Examples
Problems
8 Relative motion
8.1
8.2
8.3
8.4
8.5
*8.6
*8.7
8.8
9
Applicability of Newton's laws of motion: inertial reference
frames
The Galilean transformations
The centre of mass (CM) frame
Example of a non-inertial frame: centrifugal force
The Earth as a rotating frame: effective g
The Coriolis force
The Foucault pendulum
Practical criteria for inertial frames: the local view
Worked Examples
Problems
148
148
149
151
152
153
154
155
158
159
162
164
166
167
169
172
172
173
176
178
179
180
183
185
187
191
Special relativity
193
9.1
9.2
9.3
9.4
9.5
9.6
193
194
195
198
201
202
The velocity of light
The Principle of Relativity
Consequences of the Principle of Relativity
The Lorentz transformations
The Fitzgerald-Lorentz contraction
Time dilation
* indicates a more advanced section
viii
Contents
9.7
*9.8
9.9
9.10
9.11
9.12
9.13
9.14
9.15
9.16
10
11
Paradoxes in special relativity
Simultaneity: quantitative analysis of the twin paradox
Relativistic transformation of velocity
Momentum in relativistic mechanics
4-vectors: the energy-momentum 4-vector
Energy-momentum transformations: relativistic energy
conservation
Relativistic energy: mass-energy equivalence
Units in relativistic mechanics
Mass-energy equivalence in practice
General relativity
Worked Examples
Problems
204
205
208
210
212
214
215
219
220
221
222
226
Continuum mechanics: mechanical properties of materials
228
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
10.13
10.14
228
229
233
234
235
236
238
241
243
245
247
250
252
254
256
258
Dynamics of continuous media
Elastic properties of solids
Fluids at rest
Elastic properties of fluids
Pressure in gases
Archimedes' Principle
Fluid dynamics
Viscosity
Surface properties of liquids
Pressure in gases
A microscopic theory of gases
The mole
Interatomic forces: modifications to the kinetic theory of gases
Microscopic models of condensed matter systems
Worked Examples
Problems
Thermal physics
260
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
260
262
265
267
268
269
270
272
274
276
Friction and heating
Temperature scales
Heat capacities of thermal systems
Comparison of specific heat capacities: calorimetry
Thermal conductivity
Convection
Thermal radiation
Thermal expansion
The first law of thermodynamics
Change of phase: latent heat
* indicates a more advanced section
Contents
11.11
11.12
11.13
11.14
11.15
11.16
11.17
11.18
11.19
11.20
11.21
11.22
12
The equation of state of an ideal gas
Isothermal, isobaric and adiabatic processes
The Carnot cycle
Entropy and the second law of thermodynamics
Helmholz and Gibbs functions
Microscopic interpretation of temperature
Polyatomic molecules: principle of equipartition of energy
Ideal gas in a gravitational field: the'law of atmospheres'
Ensemble averages and distribution functions
Distribution of molecular velocities in an ideal gas
Distribution of molecular speeds, momenta and energies
Microscopic interpretation of temperature and heat capacity
in solids
Worked Examples
Problems
277
278
281
283
286
287
291
293
294
296
298
300
301
304
Wave motion
307
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
12.10
12.11
12.12
12.13
12.14
12.15
12.16
12.17
12.18
12.19
307
310
312
313
315
318
322
325
329
331
335
336
338
341
343
344
345
346
Characteristics of wave motion
Representation of a wave travelling in one dimension
Energy and power in a wave motion
Plane and spherical waves: the concept of flux
Huygens'principle: the laws of reflection and refraction
Geometrical optics
Interference between waves
Diffraction: resolving power
Two-slit interference and diffraction: Young's double slits
Multiple slit interference: the diffraction grating
X-ray diffraction: Bragg scattering
Standing waves
The Doppler effect
Coherence: the laser
The wave equation
Waves along a string
Waves in elastic media: longitudinal waves in a solid rod
Waves in elastic media: sound waves
Superposition of two waves of slightly different frequencies:
wave and group velocities
12.20 Other waveforms: Fourier analysis
Worked Examples
Problems
13 Introduction to quantum mechanics
13.1
13.2
13.3
Physics at the beginning of the twentieth century
Blackbody radiation
The photoelectric effect
"
347
349
352
355
358
358
359
362
ix
x Contents
13.4
13.5
13.6
13.7
13.8
13.9
13.10
13.11
13.12
13.13
13.14
13.15
*13.16
13.17
14
15
The X-ray continuum
The Compton effect: the photon model
The de Broglie hypothesis: electron diffraction
Interpretation of wave-particle duality
The Heisenberg uncertainty principle
The wavefunction: expectation values
The Schrodinger (wave mechanical) method
The free particle
The time-independent Shrodinger equation: eigenfunctions
and eigenvalues
The infinite square potential well
The potential step
Other potential wells and barriers
The simple harmonic oscillator
Further implications of quantum mechanics
Worked Examples
Problems
365
367
370
371
373
376
378
379
383
385
388
394
398
401
402
404
Electric currents
407
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
14.10
14.11
14.12
14.13
14.14
14.15
407
409
411
411
414
415
416
417
419
420
422
423
424
426
426
427
430
Electric currents
Force between currents
The unit of electric current
Heating effect revisited: electrical resistance
Strength of a power supply: emf
Resistance of a circuit
Potential difference
Effect of internal resistance
Comparison of emfs: the potentiometer
Resistivity
Variation of resistance with temperature
Multiloop circuits
Kirchhoff's rules
Comparison of resistances: Wheatstone bridge
Power supplies connected in parallel
Worked Examples
Problems
j
Electric fields
432
15.1
15.2
15.3
15.4
15.5
432
434
436
440
443
The electric charge model
Interpretation of electric current in terms of charge
Electric field strength and electric flux density
Electric fields due to point charges
Forces between point charges: Coulomb's law
* indicates a more advanced section
Contents
15.6
15.7
15.8
15.9
15.10
15.11
Potential difference in electric fields
Electric potential
Capacitors
Capacitors in series and in parallel
Charge and discharge of a capacitor through a resistance
Dielectric materials
Worked Examples
Problems
16 Magnetic fields
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
16.10
16.11
16.12
16.13
16.14
16.15
16.16
16.17
16.18
*16.19
17.6
17.7
17.8
470
Magnetism
Work of Ampere, Biot and Savart
Magnetic pole strength
Magnetic field strength
Ampere's law
The Biot-Savart law
Applications of the Biot-Savart law
Magnetic flux and magnetic flux density
Magnetic fields due to systems of poles
Forces between magnets
Forces between currents and magnets
The permeability of vacuum
Current loop in a magnetic field
Magnetic dipoles and magnetic materials
Moving coil meters and electric motors
Magnetic fields due to moving charges
Force on a charge in a magnetic field
Magnetic dipole moments of charged particles in closed orbits
Electric and magnetic fields in moving reference frames
470
473
474
475
476
479
481
482
484
485
486
487
488
490
495
496
497
500
501
Worked Examples
Problems
505
508
17 Electromagnetic induction: time-varying emfs
17.1
17.2
17.3
17.4
17.5
446
450
455
459
460
463
464
468
The principle of electromagnetic induction
Simple applications of electromagnetic induction
Self-inductance
Series L-R circuit
Discharge of a capacitor through an inductance and a
resistance
Time-varying emfs: mutual inductance, transformers
Alternating current (a.c.)
Alternating current transformers
* indicates a more advanced section
510
510
514
516
518
520
522
524
527
xi
xii
Contents
18
17.9
Resistance, capacitance and inductance in a.c. circuits
17.10 Series L-C-R circuit: phasor diagrams
17.11 Power in an a.c. circuit
17.12 Faraday's law revisited
Worked Examples
Problems
529
531
535
536
536
539
Maxwell's equations: electromagnetic radiation
541
18.1
Reconsideration of the laws of electromagnetism: Maxwell's
equations
^
18.2
Plane electromagnetic waves
18.3 . Experimental observation of electromagnetic radiation
18.4 The electromagnetic spectrum
18.5
Energy in electromagnetic waves
18.6
Momentum in electromagnetic waves
18.7
Polarisation of electromagnetic waves
18.8 The photon model revisited
*18.9
Invariance of electromagnetism under the Lorentz
transformation
Worked Examples
Problems
19 Atomic physics
19.1
19.2
19.3
19.4
19.5
*19.6
19.7
19.8
19.9
19.10
19.11
19.12
19.13
19.14
19.15
19.16
Atomic models
The hydrogen spectrum: the Rydberg formula
"
The Bohr postulates
The Bohr theory of the hydrogen atom
The quantum mechanical (Schrodinger) solution of the
one-electron atom
The radial solutions of the lower energy states of hydrogen
Interpretation of the one-electron atom eigenfunctions
Intensities of spectral lines: selection rules
Space quantisation: quantisation of angular momentum
Magnetic effects in one-electron atoms: the Zeeman effect
The Stern-Gerlach experiment: electron spin
The spin-orbit interaction
Identical particles in quantum mechanics: the Pauli exclusion
principle
The periodic table: multielectron atoms
The theory of multielectron atoms
Further uses of the solutions of the one-electron atom
Worked Examples
Problems
* indicates a more advanced section
541
544
548
549
551
553
555
561
563
564
566
569
569
572
573
574
579
584
587
591
593
594
596
599
600
603
608
609
610
612
Contents
20
Electrons in solids: quantum statistics
615
20.1
20.2
20.3
615
620
20.4
20.5
20.6
20.7
20.8
20.9
20.10
20.11
20.12
20.13
Bonding in molecules and solids
The classical free electron model of solids
The quantum mechanical free electron model: the Fermi
energy
The electron energy distribution at OK
Electron energy distributions at T > 0 K
Specific heat capacity and conductivity in the quantum free
electron model
The band model of solids
Semiconductors
Junctions in conductors and semiconductors: the p-n
junctions
Transistors
The Hall effect
Quantum statistics: systems of bosons
Superconductivity
Worked Examples
Problems
21 Nuclear physics, particle physics and astrophysics
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8
21.9
21.10
21.11
21.12
21.13
21.14
Properties of atomic nuclei
Nuclear binding energies
Nuclear models
Radioactivity
a- 0- and y-decay
Detection of radiation: units of radioactivity
Nuclear reactions
Nuclear fission and nuclear fusion
Fission reactors
Thermonuclear fusion
Sub-nuclear particles
The quark model
Physics of stars
The orig i n of the U n iverse
Worked Examples
Problems
Answers to problems
Appendix A Mathematical rules and formulas
Appendix B Some fundamental physical constants
Appendix C Some astrophysical and geophysical data
Appendix D The periodic table of the elements
Bibliography
Index
623
626
629
630
632
634
637
643
646
647
649
651
653
656
656
659
660
666
667
672
674
676
678
680
684
690
695
704
708
710
712
717
738
740
741
743
744
xiii