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TitleProblems in Physics
Author
TagsPhysics
LanguageEnglish
File Size21.5 MB
Total Pages342
Table of Contents
                            Front Cover
PREFACE
CONTENTS
SOME PRACTICAL HINTS
PROBLEMS
	1. MOTION AND FORCES
		1. Kinematics of a Particle
		2. Force
		3. Particle Dynamics
		4. Gravitation. Electrical Forces
		6. Theory of Relativity
	2. CONSERVATION LAWS
		7. The Law of Conservation of Momentum. Centre of Mass
		8. Total and Kinetic Energy
		9. Uncertainty Relation
		10. Elementary Theory of Collisions
		11. Potential Energy. Potential
		12. The Law of Conservation of Energy in Newtonian Mechanics
		13. The Law of Conservation of Energy
		14. Rotational Dynamics of a Rigid Body
		15. Non-inertial Frames of Reference and Gravitation
	3. MOLECULAR-KINETIC THEORY OF GASES
		16. An Ideal Gas
		17. The First Law of Thermodynamics
		18. The Second Law of Thermodynamics
		19. Fundamentals of Fluid Dynamics
	4. MOLECULAR FORCES AND STATES OF AGGREGATION OF MATTER
		20. Solids
		21. Liquids
		22. Vapours
		23. Phase Transitions
	5. ELECTRODYNAMICS
		24. A Field of Fixed Charges in a Vacuum
		25. Dielectrics
		26. Direct Current
		27. A Magnetic Field in a Vacuum
		28. Charges and Currents in a Magnetic Field
		29. Magnetic Materials
		30. Electromagnetic Induction
		31. Classical Electron Theory
		32. Electric Conductivity of Electrolytes
		33. Electric Current in a Vacuum and in Gases
	6. VIBRATIONS AND WAVES
		34. Harmonic Vibrations
		35. Free Vibrations
		36. Forced Vibrations. Alternating Current
		37. Elastic Waves
		38. Interference and Diffraction
		39. Electromagnetic Waves
		40. Interference and Diffraction of Light
		41. Dispersion and Absorption of Light
		42. Polarization of Light
		43. Geometrical Optics
		44. Optical Instruments
	7. FUNDAMENTALS OF QUANTUM PHYSICS
		45. Photons
		46. Elementary Quantum Mechanics
		47. Atomic and Molecular Structure
		48. Quantum Properties of Metals and of Semiconductors
	8. NUCLEAR AND ELEMENTARY PARTICLE PHYSICS
		49. Nuclear Structure
		50. Nuclear Reactions
SOLUTIONS
ANSWERS AND HINTS
TABLES
Back Cover
                        
Document Text Contents
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Page 171




HenceConservationLaws167N=mg(3cOSa-2+2:)Inthe
highestpointoftheloopa=n,soNtop=mg(-5+2:)Theminimumheightisfoundfrom
theconditionNtop=0,foreHmIn=R.Inthiscase.ex.N=3mg(1+QOsa)==6mgcos2T12.9.The
objectthrownataninitialspeedVoatanangle
atothe
zontalmustflythroughtheairadistanceAB
==L=2RsinCL.Weknow(see
§8.2)thatL=206sinexcosex.g2gRsoVo=cosaTofind
thespeedVoapplythelawofconservationofenergy1mgH==mgR(1-1-cosa)+2mV5fromwhichk==1+cosa+1+2cosa·Forthecomputationofcos
ex.Fig.12.6.
weobtainanequation2cos2a-2(k-1)cosa+1=0Hence1cosa=T(k-1±Y(k-1)2_2)Sincethenumberundertherootsignmustbenon-negative,weobtaink-1Y2:i.e.k1+y2:Onthe
otherhand,0<cosa1,i.e.k-1+Y(k-1)2-
22and
k2.5.Thus
1+Y2k2.5,I.e,(1+Y2)RH2.5RForthe
limitingvaluesofthecosineswehave
Y2cosa=T'Le.a1==45°cosa=={1.5±0.5)/2,cos(X2=0.5,cos(1.3==1


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168SolutionsObviouslythesolutioncosa3=1does
notsatisfytheconditionoftheproblem,sincefor
as=0therewillbenocut.So'theremainingsolutioniscosa2=0.5,a2=60°.Accordingly,fortheheightsintherange
(1+V2)RH2.5R,correspondingsuitablecutsarethose
withanglesof
45°ex60°chosenso
astosatit5fythecondition1eosex=T(k-1-Vk2-2k-1)12.10.Denote
theradiusofcurvatureintheperihelionbyRo,thekineticenergyofthe
planetinperihelionby'K0=mV6/2,anditshiIt---------I/JIIF:.««II/
",1/"-Cl/f3/VFig.12.7.
Fig.12.8.
potentialenergyU0=-ymM1ro'Tofindthe
radiusofcurvatureintheperihelionapplyNewton'ssecondlaw
ymMfromwhichRo==mvar3=_
2roKotc::,yMmu,Theradiusofcurvatureatthe
aphelionisthesameasinthehelionsincetheellipseisa
symmetricalfigure.We
have,accordingtoNewton'ssecondlaw,
"lmMThetotalmechanicalenergyofthe
planet,accordingtothelaw
ofconservationofenergyisWymMymM==EliminatingthevelocityweobtainVmMRoymMVmMRoymMror«


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