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TESS expert PhysicsTESS expert Physics11 About PHYWEAbout PHYWE 22

22 MechanicsMechanics 2525

33 Oscillations and Mechanical Waves, AcousticsOscillations and Mechanical Waves, Acoustics 5757

44 ThermodynamicsThermodynamics 8181

55 Electricity and MagnetismElectricity and Magnetism 111111

66 Light and OpticsLight and Optics 157157

77 Quantum PhysicsQuantum Physics 189189

88 Atomic PhysicsAtomic Physics 207207

99 Molecule and Solid State PhysicsMolecule and Solid State Physics 217217

1010 Nano PhysicsNano Physics 237237

1111 Nuclear Physics - RadioactivityNuclear Physics - Radioactivity 243243

1212 Particle PhysicsParticle Physics 259259

1313 X-ray PhysicsX-ray Physics 263263

1414 Laser Physics - PhotonicsLaser Physics - Photonics 295295

1515 IndicesIndices 307307

TESS expert PhysicsTESS expert Physics

PHYWE Systeme GmbH & Co. KG www.phywe.comwww.phywe.com

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1 About PHYWE1 About PHYWE

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1 About PHYWE1 About PHYWE1.1 How to use


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1 About PHYWE1 About PHYWE1.2 Computer Assisted Measurement


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1 About PHYWE1 About PHYWE1.3 Curriculum


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11

.FDIBOJDT

2.12.1 Measurement TechniquesMeasurement Techniques

P2110100 Measurement of basic constants: length,weight and time

26

2.22.2 Motion in one DimensionMotion in one Dimension

P2130301 Newton's 2nd law / air track 27

P2130311 Newton's 2nd law/ air track with Cobra3 27

P2130305 Newton's 2nd law/ demonstration track 27

P2130315 Newton's 2nd law/ demonstration trackwith Cobra3

27

P1198860 Uniformly accelerated motion on an in-clined plane, s ~ t with Cobra4 anddemonstration track

27

P6000360 Uniformly accelerated motion caused byan accelerating mass with Cobra4 anddemonstration track

27

P2130711 Free fall Cobra3 29

P2130701 Free fall 29

P2130760 Free fall (interface version with Cobra4)- available 2013

29

P6000460 Free fall with air friction with Cobra4 29

P6000760 Free Fall: determination of the accel-eration of earth (with Cobra 4 Timer-counter)

29

P1199560 Impulse and momentum with Cobra 4 30

P1199660 Conservation of momentum during cent-ral elastic collision with Cobra 4

30

P6000860 Newton's law with Cobra 4 and Timer/Counter sensor

30

2.32.3 Motion in two and three DimensionsMotion in two and three Dimensions

P2131100 Projectile motion 31

P2131200 Ballistic pendulum 32

2.42.4 Linear Momentum and CollisionsLinear Momentum and Collisions

P2130505 Laws of collision/ demonstration trackwith a 4-4 Timer

33

P2130515 Laws of collision/ demonstration trackwith Cobra3

33

P2130501 Laws of collision/ air track 33

P2130511 Laws of collision/ air track with Cobra3 33

P1199560 Impulse and momentum / demonstra-tion track with Cobra4

33

P1199660 Conservation of momentum during cent-ral elastic collision with cobra4

33

P2130560 Laws of collision/ air track with Cobra4 -available 2013

33

2.52.5 Rotational MotionRotational Motion

P2131315 Moment of inertia and angular acceler-ation with Cobra3 with a precision pivotbearing

34

P2131301 Moment of inertia and angular accelera-tion and with an air bearing

34

P2131305 Moment of inertia and angular accelera-tion with a precision pivot bearing

34

P2131311 Moment of inertia and angular accelera-tion with Cobra3 and with an air bearing

34

P2131360 Moment of inertia and angular accelera-tion with Cobra4

34

P2131500 Moment and angular momentum 35

P2131601 Centrifugal force 36

P2131611 Centrifugal force, complete set (interfaceversion)

36

P6000560 Centripetal acceleration with Cobra4 36

P6000660 Centripetal force with Cobra4 36

P2131800 Mechanical conservation of energy /Maxwell's wheel

37

P2131900 Laws of gyroscopes / 3-axis gyroscope 38

P2132000 Laws of gyroscopes / cardanic gyroscope 39

P2132801 Moment of inertia / Steiner's theorem 40

P2132860 Moments of inertia of different bodies /Steiner's theorem with Cobra4

40

2.62.6 Static Equilibrium and ElasticityStatic Equilibrium and Elasticity

P2120100 Moments 41

P1253500 Torque 41

P2120200 Modulus of elasticity 42

P2120300 Mechanical hysteresis 43

P2130111 Hooke's law with Cobra3 44


P2133100 Moments of inertia and torsional vibra-tions

45

P2132801 Moment of inertia / Steiner's theorem 45

2.72.7 Gravity / GravitationGravity / Gravitation

P2130901 Determination of the gravitational con-stant / computerised Cavendish balance

46

P6000460 Free fall with air friction with Cobra4 46

P6000760 Free Fall: determination of the accel-eration of earth (with Cobra 4 Timer-counter)

46

P2130711 Free fall with Cobra3 47

P2132200 Reversible pendulum 47

P2132301 Variable g pendulum 47

2.82.8 Mechanics of Fluids and GasesMechanics of Fluids and Gases

P2140100 Density of liquids 48

P2140200 Surface of rotating liquids 49

Overview TESS expertOverview TESS expert


12

P2140300 Viscosity of Newtonian and non-Newto-nian liquids (rotary viscometer)

50

P2140400 Viscosity measurement with the fallingball viscometer

51

P2140500 Surface tension with the ring method(Du Nouy method)

52

P2140700 Barometric height formula 53

P5140100 Mechanics of flow 54

0TDJMMBUJPOTBOE.FDIBOJDBM8BWFT

"DPVTUJDT

3.13.1 Oscillatory MotionOscillatory Motion

P2132100 Mathematical pendulum 58

P2132200 Reversible pendulum 58

P2132301 Variable g pendulum 59

P2132311 Variable g pendulum with Cobra3 59

P2132360 Variable g pendulum with Cobra4 59

P2132511 Coupled pendula with Cobra3 60

P2132560 Coupled pendula with Cobra4 60

P2132660 Harmonic oscillations of spiral springs -Spring linked in parallel and series withCobra 4

61

P2132701 Forced oscillations - Pohl's pendulum 62

P2132711 Forced oscillations - Pohl's pendulumwith Cobra3

62

P2132760 Forced oscillations - Pohl's pendulumwith Cobra4

62

P2133000 Torsional vibrations and torsion modulus 63

P2150501 Chladni figures 64

3.23.2 Wave MotionWave Motion

P2133200 Propagation of a periodically excitedcontinuous transverse wave

65

P2133400 Wave phenomena in a ripple tank 66

3.33.3 Sound WavesSound Waves

P2133500 Interference and diffraction of waterwaves with the ripple tank

67

P2150305 Velocity of sound in air with UniversalCounter

68

P2133300 Phase velocity of rope waves / waves ofwires

69

P2150405 Acoustic Doppler effect with universalcounter

70

P2150605 Velocity of sound using Kundt's tube anddigital function generator

71

P2150601 Velocity of sound using Kundt's tube 71

P2150702 Wavelengths and frequencies with aQuincke tube with a multimeter

72

P2150811 Resonance frequencies of Helmholtz res-onators with Cobra3

73

P2150860 Resonance frequencies of Helmholtz res-onators with Cobra4

73

P2151000 Optical determination of the velocity ofsound in liquids

74

P2151100 Phase and group velocity of ultrasoundin liquids

75

P2151200 Temperature dependence of the velocityof ultrasound in liquids

75

P2151515 Ultrasonic diffraction at different singleand double slit systems

76

P2151615 Ultrasonic diffraction at different mul-tiple slit systems

76

P2151715 Diffraction of ultrasonic waves at a pinhole and a circular obstacle

76

P2151915 Interference by two identical ultrasonictransmitters

77

P2151300 Stationary ultrasonic waves - determin-ation of wavelength

77

P2151400 Absorption of ultrasound in air 77

P2151800 Ultrasonic diffraction at a Fresnel zoneplate / structure of a Fresnel zone

77

P2152000 Interference of ultrasonic waves by aLloyd mirror

77

P2152115 Determination of the ultrasonic velocity(sonar principle)

77

P2152200 Ultrasonic Michelson interferometer 77

P2152300 Ultrasonic diffraction by a straight edge 77

P2152415 Ultrasonic Doppler effect 78

P2152460 Ultrasonic Doppler effect with Cobra4 78

13900-00 Ultrasound operation unit 78

P5160200 Basic principles of ultrasonic echography(A-Scan)

79

P5160300 Basic principles of ultrasonic echography(B-Scan)

79

P5160700 Frequency dependence of resolutionpower in ultrasonic imaging

79

P5160100 Velocity of ultrasound in solid state ma-terial

80

P5160800 Attenuation of ultrasound in solid statematerials

80

P5160900 Shear waves in solid state materials 80



13

5IFSNPEZOBNJDT

4.14.1 Temperature and the Kinetic Theory ofTemperature and the Kinetic Theory ofGasesGases

P2320115 Equation of state for ideal gases with Co-bra3

82

P1223200 The gas laws of Boyle-Mariotte, Gay-Lus-sac and Charles (Amontons)

82

P2320160 Equation of state for ideal gases with Co-bra4 - available 2013

82

P1350060 Charles' law 82

P1350160 Amontons law 82

P1350260 Boyle's law 82

P2320300 Maxwellian velocity distribution 83

P2340100 Vapour pressure of water at high tem-perature

84

P2340200 Vapour pressure of water below 100C -molar heat of vaporisation

84

P2140700 Barometric height formula 84

4.24.2 Heat, Work, and the First Law ofHeat, Work, and the First Law ofThermodynamicsThermodynamics

P2320211 Heat capacity of gases with Cobra3 85

P2320201 Heat capacity of gases 85


P2320400 Thermal equation of state and criticalpoint

86

P2320500 Adiabatic coefficient of gases - Flam-mersfeld oscillator

87

P2320600 Joule-Thomson effect 88

P2330111 Heat capacity of metals with Cobra3 89

P2330101 Heat capacity of metals 89


P2330200 Mechanical equivalent of heat 90

P2330260 Mechanical equivalent of heat with Co-bra4

90

P2340300 Boiling point elevation 91

P2340400 Freezing point depression 92

P1500060 Cooling by evacuation 93

P2350101 Stefan-Boltzmann's law of radiationwith an amplifier

94

P2350115 Stefan-Boltzmann's law of radiationwith Cobra3

94

P2350160 Stefan-Boltzmann's law of radiationwith Cobra4

94

P2410800 Peltier heat pump 95


96

P2350200 Thermal and electrical conductivity ofmetals

96

P2360100 Solar ray collector 96

P2360360 Heat insulation / heat conduction 97

P2360415 Stirling engine with Cobra3 97

P2410700 Semiconductor thermogenerator 97

4.34.3 Heat Engines, Entropy, and the SecondHeat Engines, Entropy, and the SecondLaw of ThermodynamicsLaw of Thermodynamics

P2360200 Electric compression heat pump 98

13715-93 Work and power meter 98


P2360401 Stirling engine with an oscilloscope 99



100

P2320400 Thermal equation of state and criticalpoint

100


100

4.44.4 Thermal Properties and ProcessesThermal Properties and Processes

P2310200 Thermal expansion in solids 101

P2310300 Thermal expansion in liquids 102

P2340100 Vapour pressure of water at high tem-perature

103

P2340200 Vapour pressure of water below 100C -molar heat of vaporisation

104

P2350200 Thermal and electrical conductivity ofmetals

105

P2360100 Solar ray collector 106

P2360360 Heat insulation / heat conduction 107

P1500060 Cooling by evacuation 108



108


P2340300 Boiling point elevation 109

P2340400 Freezing point depression 109

4.54.5 LiteratureLiterature

01196-12 Handbook Glass jacket system 110

&MFDUSJDJUZBOE.BHOFUJTN

5.15.1 Electric Charge and Electric FieldElectric Charge and Electric Field

P2420100 Electric fields and potentials in the platecapacitor

112

P2420401 Coulomb's law / image charge 113

P2420500 Coulomb potential and Coulomb field ofmetal spheres

114



14

P2510100 Elementary charge and Millikan experi-ment

115

P2511200 Electron spin resonance 115

5.25.2 Capacitance, Dielectrics, Electric Energy,Capacitance, Dielectrics, Electric Energy,StorageStorage

P2411100 Characteristic curve and efficiency of aPEM fuel cell and a PEM electrolyser

116

P2411200 Faraday's law 117

P2420201 Charging curve of a capacitor / chargingand discharging of a capacitor

118

P2420260 Switch-on behaviour of a capacitor andan inductivity with Cobra4

118

P2420300 Capacitance of metal spheres and of aspherical capacitor

119

P2420600 Dielectric constant of different materials 120

P2420100 Electric fields and potentials in the platecapacitor

120

5.35.3 Electric Current and ResistanceElectric Current and Resistance

P2410101 4 Point Method / Measurement of lowresistances / Ohm's Law

121

P2410115 Ohm's law with Cobra3 122


P2410200 Wheatstone bridge 123

P2410500 Kirchhoff's laws 123

P2410901 Characteristic curves of a solar cell 124

P2410915 Characteristic curves of semiconductorswith Cobra3 and FG module

125

P2410960 Characteristic curves of semicconductorwith Cobra4

125

P2411315 Second order conductors - electrolysiswith the FG module

126

P2411360 Second order conductors. Electrolysiswith Cobra4

126



127

P2420201 Charging curve of a capacitor / chargingand discharging of a capacitor

127

5.45.4 Direct-Current CircuitsDirect-Current Circuits

P2410415 Temperature dependence of differentresistors and diodes with Cobra3

128

P2410401 Temperature dependence of differentresistors and diodes with a multimeter

128

P2410460 Temperature dependance of differentresistors and diodes with Cobra4

128

P2410500 Kirchhoff's laws 129

P2410200 Wheatstone bridge 129

P2410101 4 Point Method / Measurement of lowresistances Ohm's Law

130



P2410915 Characteristic curves of semiconductorswith Cobra3 and FG module

131


131

P2411315 Second order conductors - electrolysiswith Cobra3 and FG module

131

5.55.5 Magnetic Field and Magenetic ForcesMagnetic Field and Magenetic Forces

P2410601 Current balance/ force acting on acurrent-carrying conductor with anamperemeter

132

P2410660 Current balance / Force acting on acurrent-carrying cond. with Cobra4

132

P2430215 Magnetic field of single coils/ Biot-Sav-art's law with Cobra3

133

P2430201 Magnetic field of single coils/ Biot-Sav-art's law with a teslameter

133


133

P2430315 Magnetic field of paired coils in a Helm-holtz arrangement with Cobra3

134

P2430301 Magnetic field of paired coils in a Helm-holtz arrangement with a teslameter

134


134

P2430400 Magnetic moment in the magnetic field 135

P2430605 Magnetic field inside a conductor withdigital function generator

136

P2430600 Magnetic field inside a conductor 136

P2260106 Faraday effect with optical base plate 137

P2430100 Determination of the earth's magneticfield

137

P2430500 Magnetic field outside a straight con-ductor

137

P2430711 Ferromagnetic hysteresis with Cobra3 138

P2430800 Magnetostriction with the Michelson in-terferometer

138

P2530111 Hall effect in p-germanium with Cobra3 138

5.65.6 Sources of Magnetic FieldSources of Magnetic Field

P2430100 Determination of the earth's magneticfield

139

P2430500 Magnetic field outside a straight con-ductor

140


141


141




15

5.75.7 Electromagnetic Induction and FaradaysElectromagnetic Induction and FaradaysLawLaw

P2440100 Transformer 142

P2440201 Magnetic induction 143

P2440215 Magnetic induction with the FG moduleand Cobra3

143

P2440260 Magnetic Induction with Cobra4 143

P2441211 Induction impulse 144

P2441260 Induction impulse with Cobra4 144

5.85.8 Inductance, Electromagnetic Oscillations,Inductance, Electromagnetic Oscillations,AC CircuitsAC Circuits

P2440311 Inductance of solenoids with Cobra3 145

P2440301 Inductance of solenoids 145

P2440360 Inductance of solenoids with Cobra4 145

P2440411 Coil in the AC circuit with Cobra3 and theFG module

146

P2440401 Coil in the AC circuit 146

P2440460 Coil in the AC circuit with Cobra4 146

P2440515 Capacitor in the AC circuit with Cobra3and the FG module

147

P2440501 Capacitor in the AC circuit 147

P2440560 Capacitor in the AC circuit with Cobra4 147

P2440611 RLC circuit with Cobra3 and the FG mod-ule

148

P2440601 RLC circuit 148

P2440660 RLC circuit with Cobra4 148

P2440700 Rectifier circuits 149

P2440801 RC filters 150

P2440905 High-pass and low-pass filters with di-gital function generator

151

P2440915 High-pass and low-pass filters with theFG module

151

P2441101 Resistance, phase shift and power in ACcircuits with digital function generator

152

P2450201 Coupled resonant circuits 153

P2450301 Forced oscillations of a nonlinear elec-trical series resonant circuit - chaotic os-cillation

154

5.95.9 Maxwells Equitations, Magnetism,Maxwells Equitations, Magnetism,Electromagnetic WavesElectromagnetic Waves


P1221300 Ferromagnetism, paramagnetism anddiamagnetism

155



156

-JHIUBOE0QUJDT

6.16.1 Nature and Propagation of LightNature and Propagation of Light

P2210101 Measuring the velocity of light 158

P2210111 Measuring the velocity of light using thesoftware measure

158

P2240211 Photometric inverse-square law - Cobra3

159

P2240201 Photometric inverse-square law 159

P2240260 Photometric invers-square law - Cobra 4 159

P2240405 Lambert's law of radiation on opticalbase plate

160

P2240400 Lambert's law 160

P2210300 Dispersion and resolving power of aprism and a grating spectroscope

161

P2220100 Interference of light 161

P2230405 Diffraction of light through a double slitor by a grid with optical base plate

161

P2250305 Fresnel's law - theory of reflection 162

P2261000 Fibre optics 162

6.26.2 Geometric OpticsGeometric Optics

P2210200 Law of lenses and optical instruments 163

6.36.3 Diffraction and InterferenceDiffraction and Interference

P2210300 Dispersion and resolving power of aprism and a grating spectroscope

164

P2220100 Interference of light 165

P2220205 Newton's rings with optical base plate 166

P2220200 Newton's rings with interference filters 166

P2220300 Interference at a mica plate according toPohl

167

P2220400 Structure of a Fresnel zone / zone plate 168

P2220505 Michelson interferometer with opticalbase plate

169

P2220500 Michelson interferometer with opticalprofile bench

169

P2220600 Coherence and width of spectral lineswith the Michelson interferometer withoptical profile bench

170

P2220705 Refraction index of CO2 with the Michel-son interferometer with optical baseplate

171

P2220700 Refraction index of air and CO2 with theMichelson interferometer with opticalprofile bench

171

P2220900 Michelson interferometer - High Resolu-tion with optical base plate

172

P2221100 Refraction index of air with the Mach-Zehnder interferometer with opticalbase plate

173



16

P2221205 Fabry-Perot interferometer - determina-tion of the wavelength of laser light onoptical base plate

174

P2230205 Diffraction of light at a slit and at anedge on optical base plate

175

P2230200 Diffraction of light at a slit and an edgewith optical profile bench

175

P2230300 Intensity of diffractions due to pin holediaphragms and circular obstacles withoptical profile bench

176

P2230405 Diffraction of light through a double slitor by a grid with optical base plate

177

P2230400 Diffraction intensity due to multiple slitsand grids with optical profile bench

177

P2230500 Diffraction intensity at slit and doubleslit systems with optical profile bench

178

P2230605 Diffraction intensity at a slit and at awire - Babinet's theorem with opticalbase plate

179

P2230600 Diffraction intensity at a slit and at awire - Babinet's theorem with opticalprofile bench

179

P2261100 Fourier optics - 2f arrangement 180

P2261200 Fourier optics - 4f arrangement - filter-ing and reconstruction

180

P2220800 Quantum eraser with optical base plate 181

P2221206 Fabry-Perot interferometer - determina-tion of the wavelength of laser light withoptical base plate

181

P2230105 Diffraction at a slit and Heisenberg's un-certainty principle with optical baseplate

181

P2430800 Magnetostriction with the Michelson in-terferometer with optical base plate

182

P2541301 Examination of the structure of NaClmonocrystals with different orientations

182

P2541601 X-ray investigation of crystal structures /Laue method

182

6.46.4 PolarizationPolarization

P2250105 Polarisation through quarter-waveplates with optical base plate

183

P2250100 Polarisation through quarter-waveplates with optical profile bench

183

P2250200 Polarimetry 183

P2250305 Fresnel's law - theory of reflection withoptical base plate

184

P2250300 Fresnel's equations - theory of reflectionwith optical profile bench

184

P2250400 Malus' law 185

P2250505 Polarimetry with optical base plate 186


P2260100 Faraday effect with optical profile bench 187

2VBOUVN1IZTJDT

7.17.1 Quantum eraserQuantum eraser

P2220800 Quantum eraser 190

7.27.2 Heisenberg's uncertainty principleHeisenberg's uncertainty principle

P2230105 Diffraction at a slit and Heisenberg's un-certainty principle with optical baseplate

191

P2230100 Diffraction at a slit and Heisenberg's un-certainty principle with optical bench

191

7.37.3 Millikan experimentMillikan experiment

P2510100 Elementary charge and Millikan experi-ment

192

7.47.4 Specific charge of the electronSpecific charge of the electron

P2510200 Specific charge of the electron e/m 193

7.57.5 Franck-Hertz experimentFranck-Hertz experiment

P2510311 Franck-Hertz experiment with a Hg tube 194

P2510315 Franck-Hertz experiment with a Ne tube 195

7.67.6 Planck's "quantum of action" andPlanck's "quantum of action" andphotoelectric effectphotoelectric effect

P2510402 Planck's "quantum of action" and pho-toelectric effect (line separation by in-terference filters)

196

P2510502 Planck's "quantum of action" and externphotoelectric effec effect (line separa-tion by a diffraction grating)

196

7.77.7 Stern-Gerlach experimentStern-Gerlach experiment

P2511111 Stern-Gerlach experiment with a steppermotor and interface

197

P2511101 Stern-Gerlach experiment (classical ver-sion)

197

7.87.8 Zeeman effectZeeman effect

P2511001 Zeeman effect with an electromagnetand optical bench

198

P2511005 Zeeman effect with an electromagnetand CCD camera including the measure-ment software

198

P2511006 Zeeman effect with a variable magneticsystem

199

P2511007 Zeeman effect with a variable magneticsystem and a CCD camera including themeasurement software

199

7.97.9 Nuclear Magnetic Resonance (NMR, MRT) -Nuclear Magnetic Resonance (NMR, MRT) -Electron spin resonance (ESR)Electron spin resonance (ESR)

P5942100 Basic principles in Nuclear Magnetic Res-onance (NMR)

200

P5942200 Relaxation times in Nuclear MagneticResonance

200



17

P5942300 Spatial encoding in Nuclear MagneticResonance

200

P5942400 Magnetic Resonance Imaging (MRI) I 200

09500-99 Compact magnetic resonance tomograph(MRT), incl. sample set, software andhandbook on USB stick , in a sturdy car-rying case

201


7.107.10 Electron diffractionElectron diffraction

P2511300 Electron diffraction 203

7.117.11 Compton effectCompton effect

P2524415 Compton effect with the multi-channelanalyser

204

P2546001 Compton effect - energy-dispersive dir-ect measurement

205

P2541701 Compton scattering of X-rays 205

7.127.12 Duane-Hunt displacement lawDuane-Hunt displacement law

P2540901 Duane-Hunt displacement law andPlanck's "quantum of action"

206

"UPNJD1IZTJDT

8.18.1 One and two electron spectraOne and two electron spectra

P2510600 Fine structure: one and two electronspectra

208

8.28.2 Balmer series/ determination of Rydberg'sBalmer series/ determination of Rydberg'sconstantconstant

P2510700 Balmer series/ determination of Ry-dberg's constant

209

P2510800 Atomic spectra of two-electron system:He, Hg

209

8.38.3 X-ray fluorescence and Moseley's lawX-ray fluorescence and Moseley's law

P2524715 X-ray fluorescence and Moseley's lawwith the multi channel analyser

210

P2541001 Characteristic X-ray lines of different an-ode materials / Moseley's law

211

P2541201 K and L absorption edges of X-rays /Moseley's law and the Rydberg constant

212

8.48.4 Characteristic X-raysCharacteristic X-rays

P2540101 Characteristic X-rays of copper 213

P2540201 Characteristic X-rays of molybdenum 213

P2540301 Characteristic X-rays of iron 213

P2542801 Characteristic X-rays of tungsten 213

8.58.5 K alpha double splitting of molybdenumK alpha double splitting of molybdenumX-raysX-rays

P2540701 K alpha double splitting of molybdenumX-rays/ fine structure

214

P2540801 K alpha doublet splitting of iron X-rays /fine structure

214

8.68.6 Related ExperimentsRelated Experiments

P2260701 Helium neon laser, basic set 215

P2260800 Optical pumping 215

P2511001 Zeeman effect with an electromagnet 215

P2511111 Stern-Gerlach experiment with a steppermotor and interface

216


P2522115 Rutherford experiment with MCA 216

.PMFDVMFBOE4PMJE4UBUF1IZTJDT

9.19.1 MagnetostrictionMagnetostriction


218

9.29.2 Semiconductor thermogeneratorSemiconductor thermogenerator


9.39.3 Beta spectroscopyBeta spectroscopy

P2523200 Beta spectroscopy 220

9.49.4 Hall effectHall effect

P2530111 Hall effect in p-germanium with Cobra3 221

P2530101 Hall effect in p-germanium (with theteslameter)

221

P2530201 Hall effect in n-germanium (with theteslameter)

221

P2530211 Hall effect in n-germanium (with Co-bra3)

221

P2530401 Band gap of germanium 221

P2530411 Band gap of germanium (with Cobra3) 221

P2530160 Hall effect in p-germanium (with Co-bra4)

221

9.59.5 Examination of the structure ofExamination of the structure ofmonocrystalsmonocrystals

P2541301 Examination of the structure of NaClmonocrystals with dif-ferent orienta-tions

222

9.69.6 Investigation of cubic crystal structuresInvestigation of cubic crystal structures

P2541401 X-ray investigation of cubic crystal struc-tures / Debye- Scherrer powder method

223

9.79.7 Laue methodLaue method

P2541601 X-ray investigation of crystal structures /Laue method

224

P2541501 X-ray investigation of hexagonal crystalstructures / Debye-Scherrer powdermethod

224



18

9.89.8 Debye-Scherrer diffraction patternsDebye-Scherrer diffraction patterns

P2542101 Debye-Scherrer diffraction patterns ofpowder samples with three cubic Bravaislattices (Bragg-Brentano-geometry)

225

P2542201 Debye-Scherrer diffractions pattern ofpowder samples with a diamond struc-ture (according to Bragg-Brentano)

225

P2542301 Debye-Scherrer diffraction patterns ofpowder samples with a hexagonal latticestructure (according to Bragg-Brentano)

225

P2542401 Debye-Scherrer diffraction patterns ofpowder samples with a tetragonal latticestructure (according to Bragg-Brentano)

225

P2542501 Debye-Scherrer diffraction patterns witha cubic powder sample (according toBragg-Brentano)

225

9.99.9 Energy-dispersive measurementsEnergy-dispersive measurements

P2546101 Energy-dispersive measurements of K-and L-absorption edges

226

9.109.10 Lattice constants of a monocrystalLattice constants of a monocrystal

P2546201 Determination of the lattice constants ofa monocrystal

227

9.119.11 Duane-Hunt displacement lawDuane-Hunt displacement law

P2546301 Duane-Hunt displacement law 228

9.129.12 Velocity of ultrasound in solid stateVelocity of ultrasound in solid statematerialmaterial

P5160100 Velocity of ultrasound in solid state ma-terial

229

9.139.13 Attenuation of ultrasound in solid stateAttenuation of ultrasound in solid statematerialsmaterials

P5160800 Attenuation of ultrasound in solid statematerials

230

9.149.14 Shear waves in solid state materialsShear waves in solid state materials

P5160900 Shear waves in solid state materials 231



P2120200 Modulus of elasticity 233

P2120300 Mechanical hysteresis 233


P2260900 Nd:YAG laser 234

P2410800 Peltier heat pump 234


P2410915 Characteristic curves of semiconductorswith the FG module

235

P2420600 Dielectric constant of different materials 235



236

P2532000 Atomic Resolution of the graphite sur-face by STM (scanning tunnelling micro-scope)

236

/BOP1IZTJDT

10.110.1 Atomic Resolution by STM (ScanningAtomic Resolution by STM (ScanningTunnelling Microscope)Tunnelling Microscope)

09600-99 Compact-Scanning Tunneling Microscope(STM)

238

P2532000 Atomic Resolution of the graphite sur-face by STM (Scanning Tunnelling Micro-scope)

239

P2532500 Investigate in surface atomic structuresand defects of diffrent samples by STM(Scanning Tunneling Microscopy)

239

P2533000 Nanoscale workfunction measurementsby STS (Scanning Tunneling Spectroscopy

239

10.210.2 Nanoscale electrical charakteristics byNanoscale electrical charakteristics bySTMSTM

P2533500 Nanoscale electrical charakteristics ofdifferent samples by STS (Scanning Tun-nelling Spectroscopy)

240

10.310.3 Quantum mechanics by STM / AFMQuantum mechanics by STM / AFM

P2535000 Quantum Mechanics by STM - TunnelingEffect and Charge Density Waves

241

P2537000 Roughness and nanomorhology of differ-ent metal samples using by STM

241

09700-99 Compact-Atomic Force Microscope (AFM) 242

/VDMFBS1IZTJDT3BEJPBDUJWJUZ

11.111.1 Half-life and radioactive equilibriumHalf-life and radioactive equilibrium

P2520101 Half-life and radioactive equilibrium 244

P2520111 Half-life and radioactive equilibriumwith Cobra3

244

P2520160 Half-life and radioactive equilibriumwith Cobra4

244

11.211.2 Poisson's and Gaussian distribution ofPoisson's and Gaussian distribution ofradioactive decayradioactive decay

P2520311 Poisson's and Gaussian distribution ofradioactive decay (Influence of the deadtime of the counter tube)

245

P2520360 Poisson's and Gaussian distribution ofradioactive decay with Cobra4 (Influenceof the dead time of the counter tube)

245



19

11.311.3 Alpha Particles - Energy - RutherfordAlpha Particles - Energy - RutherfordExperimentExperiment

P2522015 Alpha energies of different sources withMulti Channel Analyser (MCA)

246

P2522115 Rutherford experiment with Multi Chan-nel Analyser (MCA)

247

P2522101 Rutherford experiment with the digitalcounter

247

P2522215 Fine structure of the alpha spectrum ofAm-241 with Multi Channel Analyser(MCA) / alpha spectroscopy

248

P2522315 Study of the alpha energies of Ra-226with Multi Channel Analyser (MCA)

249

P2522415 Energy loss of alpha particles in gaseswith Multi Channel Analyser (MCA)

250

11.411.4 Beta Particles - Electron AbsorptionBeta Particles - Electron Absorption

P2523100 Electron absorption 251

P2523200 Beta spectroscopy 252

11.511.5 Gamma Particles - Energy - ComptonGamma Particles - Energy - ComptonEffectEffect

P2524101 Inverse-square law and absorption ofgamma or beta rays with the Geiger-Mller counter

253

P2524215 Energy dependence of the gamma ab-sorption coefficient with Multi ChannelAnalyser (MCA) / Gamma spectroscopy

254

P2524515 Internal conversion in 137m Ba withMulti Channel Analyser (MCA)

255

P2524615 Photonuclear cross-section/ Comptonscattering cross-section with Multi Chan-nel Analyser (MCA)

256

11.611.6 Counter tube characteristicsCounter tube characteristics

P2540010 Counter tube characteristics with XR 4.0X-ray expert unit

257

11.711.7 X-ray dosimetryX-ray dosimetry

P2541801 X-ray dosimetry with XR 4.0 X-ray expertunit

258

1BSUJDMF1IZTJDT

12.112.1 Visualisation of radioactive particlesVisualisation of radioactive particles

P2520400 Visualisation of radioactive particleswith the diffusion cloud chamber PJ45

261

12.212.2 Cosmic Muon Lifetime - KamiocanCosmic Muon Lifetime - Kamiocan

P2520800 Cosmic Muon Lifetime measurement -Kamiocan -

262

9SBZ1IZTJDT

13.113.1 Characteristic of X-raysCharacteristic of X-rays

P2540101 Characteristic X-rays of copper 267

P2540201 Characteristic X-rays of molybdenum 267

P2540301 Characteristic X-rays of iron 267

P2542801 Characteristic X-rays of tungsten 267

P2540401 The intensity of characteristic X-rays as afunction of anode current and voltage

268

P2540501 Monochromatisation of molybdenum 269

P2540601 Monochromatisation of copper X-rays 269

P2540701 K alpha double splitting of molybdenumX-rays/ fine structure

270

P2540801 K alpha doublet splitting of iron X-rays /fine structure

270

P2540901 Duane-Hunt displacement law andPlanck's "quantum of action"

270

P2541001 Characteristic X-ray lines of different an-ode materials / Moseley's law

270

13.213.2 RadiographyRadiography

P2540020 Radiographic examination of objects 271

P2541901 Contrast medium experiment with ablood vessel model

272

P2542001 Determination of length and position ofan object which can not be seen

273

13.313.3 Absorption of X-rays - DosimetryAbsorption of X-rays - Dosimetry

P2540030 Qualitative examination of absorption 274

P2541101 Absorption of X-rays 275

P2541201 K and L absorption edges of X-rays /Moseley's law and the Rydberg constant

276

P2541801 X-ray dosimetry 277

P2540040 Ionizing effect of X-radiation 277

13.413.4 Debye-Scherrer diffractionDebye-Scherrer diffraction

P2541401 X-ray of cubic crystal structures / Debye-Scherrer powder method

278

P2541501 X-ray of hexagonal crystal structures /Debye-Scherrer powder method

278

P2542601 Diffraction measurements to determinethe intensity of Debye-Scherrer reflexesusing a cubic powder sample

279

P2542101 Debye-Scherrer diffraction pattern ofpowder samples, cubic Bravais lattices

279

P2542201 Debye-Scherrer diffractions pattern ofpowder samples, diamond structure

279

P2542301 Debye-Scherrer diffraction pattern ofpowder samples, hexagonal latticestructure

279



20

P2542401 Debye-Scherrer diffraction pattern ofpowder samples, tetragonal latticestructure

279

P2542501 Debye-Scherrer diffraction pattern ofpowder samples, cubic lattice structure

279

P2542701 Debye-Scherrer diffraction measure-ments for the examination of the textureof rolled sheets

280

13.513.5 Laue diffractionLaue diffraction

P2541602 X-ray of crystal structures/Laue methodwith digital X-ray image sensor (XRIS)

281

P2541601 X-ray investigation of crystal structures /Laue method with X-ray film

281

13.613.6 X-ray fluorescence spectroscopyX-ray fluorescence spectroscopy

P2544001 X-ray energy spectroscopy - calibrationof the X-ray energy detector

282

P2544101 Energy resolution of the X-ray energy de-tector

283

P2544201 Inherent fluorescence radiation of the X-ray energy detector

284

P2544501 Qualitative X-ray fluorescence spectro-scopy of metals - Moseley's law

285

P2544601 Qualitative X-ray fluorescence analysis ofalloyed materials

285

P2544701 Qualitative X-ray fluorescence analysis ofpowder samples

285

P2544801 Qualitative X-ray fluorescence analysis ofsolutions

285

P2544901 Qualitative X-ray fluorescence analysis ofore samples

285

P2545001 Quantitative X-ray fluorescence analysisof alloyed materials

286

P2545101 Quantitative X-ray fluorescence analysisof solutions

286

P2545201 X-ray fluorescence spectroscopy / layerthickness determination

287

P2546001 Compton effect - energy-dispersive dir-ect measurement

288

P2541701 Compton scattering of X-rays 288

P2546101 Energy-dispersive measurements of K-and L-absorption edges

289

P2546201 Determination of the lattice constants 289

P2546301 Duane-Hunt displacement law 289

13.713.7 Computed TomographyComputed Tomography

P2550100 Computed tomography 290

P2541602 X-ray of crystal structures/Laue methodwith digital X-ray image sensor (XRIS)

290


P2540010 Counter tube characteristics 292

P2541301 Examination of NaCl monocrystals 293

-BTFS1IZTJDT1IPUPOJDT

14.114.1 Doppler effect with the MichelsonDoppler effect with the Michelsoninterferometerinterferometer

P2221000 Doppler effect with the Michelson inter-ferometer with optical base plate

296

14.214.2 Determination of the wavelength of laserDetermination of the wavelength of laserlightlight

P2221206 Fabry-Perot interferometer - wavelengthof laser light with optical base plate

297

14.314.3 HolographyHolography

P2260300 Recording and reconstruction of holo-grams with optical base plate

298

P2260305 Transfer hologram - master hologram 298

P2260306 Holography - Real time procedure 298

14.414.4 LDA - Laser Doppler AnemometryLDA - Laser Doppler Anemometry

P2260511 LDA - laser Doppler anemometry withoptical base plate

299

14.514.5 Helium neon laserHelium neon laser

P2260701 Helium neon laser, basic set 300

P2260705 Helium neon laser, advanced set 300

14.614.6 Optical pumpingOptical pumping

P2260800 Optical pumping 301

14.714.7 Nd:YAG laserNd:YAG laser

P2260900 Nd:YAG laser 302

14.814.8 Fibre opticsFibre optics

P2261000 Fibre optics 303


P2220600 Coherence, width of spectral lines,Michelson interferometer, optical base-plate

304

P2220705 Refraction index of CO2, Michelson inter-ferometer with optical base plate

304

P2220800 Quantum eraser with optical base plate 304

P2220900 Michelson interferometer - High Resolu-tion with optical base plate

305

P2221100 Refraction index of air, Mach-Zehnderinterferometer with optical base plate

305

P2221205 Fabry-Perot interferometer - wavelengthof laser light with optical base plate

305

P2250105 Polarisation through quarter-waveplates with optical base plate

306

P2261100 Fourier optics - 2f arrangement with op-tical base plate

306


306



21

1 About PHYWE1 About PHYWE1.5 Nobel Prize Experiments


22

1 About PHYWE1 About PHYWE1.5 Nobel Prize Experiments


23

1 About PHYWE1 About PHYWE1.6 Cooperations


24

262627273131333334344141464648485555

MechanicsMechanics2.12.1 Measurement TechniquesMeasurement Techniques2.22.2 Motion in one DimensionMotion in one Dimension2.32.3 Motion in two and three DimensionsMotion in two and three Dimensions2.42.4 Linear Momentum and CollisionsLinear Momentum and Collisions2.52.5 Rotational MotionRotational Motion2.62.6 Static Equilibrium and ElasticityStatic Equilibrium and Elasticity2.72.7 Gravity / GravitationGravity / Gravitation2.82.8 Mechanics of Fluids and GasesMechanics of Fluids and Gases2.92.9 Literature and SoftwareLiterature and Software

2 Mechanics2 Mechanics


25

PrinciplePrinciple

Caliper gauges, micrometers and spherometers are used for theaccurate measurement of lengths, thicknesses, diameters andcurvatures. A mechanical balance is used for weight determina-tions, a decade counter is used for accurate time measurements.Measuring procedures, accuracy of measurement and reading ac-curacy are demonstrated.

TasksTasks

1. Determination of the volume of tubes with the caliper gauge.2. Determination of the thickness of wires, cubes and plates

with the micrometer.3. Determination of the thickness of plates and the radius of

curvature of watch glasses with the spherometer.

What you can learn aboutWhat you can learn about

Length Diameter Inside diameter thickness Curvature Vernier Weight resolution Time measurement

Main articlesMain articles

Universal Counter 13601-99 1

Spherometer 03017-00 1

Precision balance,2 pans,500g 44011-50 1

Set of precision weights,1mg-200g 44070-20 1

Light barrier, compact 11207-20 1

Micrometer 03012-00 1

Vernier caliper 03010-00 1

Aluminium foil, set of 4 sheets 06270-00 1

Cubes, set of 8 02214-00 1

Universal CounterUniversal Counter

Function and ApplicationsFunction and Applications

The universal counter is used for measuring time, frequency, pulserates, pulse counting, periodic times, speeds and velocities.

BenefitsBenefits

The device has all the qualities that are expected of a modernuniversal counter and is also equipped with a number of tech-nical specifics of how it specifically arise from the require-ments of science teaching practice.

For the scientifically correct representation of each measure-ment is shown in principle with the associated unit. With theoverflow of the display is automatically switched into the nextarea.

Before the measurement starts it can be manually adjusted toa maximum of 6 decades defined range, eg to suppress is notphysically meaningful digits on the display.

A special jack for direct connection of a GM counter tube isavailable for radioactivity experiments. The required voltagecan be changed manually to determine the characteristics ofa counter tubes to.

13601-9913601-99

P2110100P2110100 Measurement of basic constants: length, weight and timeMeasurement of basic constants: length, weight and time

Vernier caliper

2 Mechanics2 Mechanics2.1 Measurement Techniques


26

PrinciplePrinciple

The distance-time law, the velocity time law, and the relationshipbetween mass, acceleration and force are determined with the aidof the air track rail for uniformly accelerated motion in a straightline.

TasksTasks

Determination of:

1. Distance travelled as a function of time2. Velocity as a function of time3. Acceleration as a function of the accelerated mass4. Acceleration as a function of force.


Velocity, Acceleration Force, Acceleration of gravity


Air track rail, 2 meters 11202-17 1

Timer 4-4 13604-99 1

Blower 230V/50Hz 13770-97 1

Starter system for air track 11202-13 1

Precision pulley 11201-02 1


Portable Balance, OHAUS CS2000 - AC adapterincluded 48917-93 1

Stop, adjustable 11202-19 1

Barrel base PHYWE 02006-55 4

Glider f.air track 11202-02 1

Related ExperimentsRelated Experiments

Cobra4 Experiments -available 2013Cobra4 Experiments -available 2013

P2130301P2130301Newton's 2nd law / air trackNewton's 2nd law / air track

The distance travelled s plotted as a function ofthe time t.

Newton's 2nd law/ air track with Cobra3Newton's 2nd law/ air track with Cobra3

P2130311P2130311

Newton's 2nd law/ demonstration trackNewton's 2nd law/ demonstration track

P2130305P2130305

Newton's 2nd law/ demonstration track with Cobra3Newton's 2nd law/ demonstration track with Cobra3

P2130315P2130315

Newton's 2nd law/ demonstration track with Cobra4Newton's 2nd law/ demonstration track with Cobra4

P2130360P2130360

Uniformly accelerated motion on an inclined plane, s ~ tUniformly accelerated motion on an inclined plane, s ~ twith Cobra4 and demonstration trackwith Cobra4 and demonstration track

P1198860P1198860

Uniformly accelerated motion caused by an acceleratingUniformly accelerated motion caused by an acceleratingmass with Cobra4 and demonstration trackmass with Cobra4 and demonstration track

P6000360P6000360

2 Mechanics2 Mechanics2.2 Motion in one Dimension


27

Air track rail, 2 metersAir track rail, 2 meters


Air track rail

BenefitsBenefits

Square Aluminium profile tube adjusted and mounted with 7screws on a U-shape extrusion profilebeam.

Measuring scale on bothsides with mm division in both direc-tions, opening for pressure hose/tube.

Equipment and technical dataEquipment and technical data

Incl. 2 end holders and 4 knurled screws. Track length: 2 m Square profile: 63 x 63 mm Diameter hose connection: 40 mm

11202-1711202-17

Demonstration Track, Aluminium, 1.5Demonstration Track, Aluminium, 1.5metersmeters


Aluminium track for demonstration experiments with scale, level-ling with adjustable feeds, with quick lock system for accessories.

BenefitsBenefits

Usable on small desks due to free positioning of feeds.


Length: 1.53 m. Width of track: 105 mm. Width: 240 mm. Depth: 100 mm. Mass: 4.1 kg

11305-0011305-00

Demo advanced Physics Manual LinearDemo advanced Physics Manual LinearMotion (LMT)Motion (LMT)

Article no. 16001-02Article no. 16001-02

DescriptionDescription

Instructions for 17 experiments on linear motion.

TopicsTopics

Uniform and uniformly accelerated motion (5 experiments) Free fall (1 experiment) Newton's laws (3 experiments) Inertia and weight (2 experiments) Friction (1 experiment) Elastic and inelastic collisions (5 experiments)

Almost all experiments can be performed either with the 2 m longair track 11202-17 or with the 1.5 m long demonstration track11305-00.

For the measurements and data recording you can use an inter-face or the 4-4 Timer 13604-99.

16001-0216001-02

Laws of collision/ air track with Cobra3 - P2130511Laws of collision/ air track with Cobra3 - P2130511



28

PrinciplePrinciple

The fall times t are measured for different heights of fall h. h isrepresented as the function of t or t2, so the distance-time law ofthe free fall results as h = 1/2 g t2. Then the measured valuesare taken to determine the acceleration due to gravity g.

TasksTasks

Determination of

1. Distance time law for the free fall.2. Velocity-time law for the free fall.3. Precise measurement of the acceleration due to gravity for

the free fall.


Linear motion due to constant acceleration Laws governing falling bodies Acceleration due to gravity


Cobra3 BASIC-UNIT, USB 12150-50 1

Release unit 02502-00 1

Impact switch 02503-00 1

Tripod base PHYWE 02002-55 1

Power supply 12V / 2A 12151-99 1

Software Cobra3 Timer/Counter 14511-61 1

Support rod PHYWE, square, l = 1000 mm 02028-55 1

Right angle clamp PHYWE 02040-55 2

Related ExperimentRelated Experiment

Cobra4 ExperimentsCobra4 Experiments

P2130711P2130711Free fall Cobra3Free fall Cobra3

Height of fall as a function of falling time.

Free fallFree fall

P2130701P2130701

Free fall (interface version with Cobra4) - available 2013Free fall (interface version with Cobra4) - available 2013

P2130760P2130760

Free fall with air friction with Cobra4Free fall with air friction with Cobra4

P6000460P6000460

Free Fall: determination of the acceleration of earth (withFree Fall: determination of the acceleration of earth (withCobra 4 Timer-counter)Cobra 4 Timer-counter)

P6000760P6000760



29

P1199560P1199560

PrinciplePrinciple

An impulse is described as the change in momentum by a forceapplied upon a body for a small interval of time. The momentumis defined here as the product of force and time and is conservedif no friction loss occurs. This means that in a closed system ofdifferent bodies the latter can transfer or receive momentum,however the total momentum of the system remains temporallyand quantitatively constant.

Impulse and momentum with Cobra 4Impulse and momentum with Cobra 4

For more details refer to www.phywe.comFor more details refer to www.phywe.com

P1199660P1199660

PrinciplePrinciple

An impulse is a change in momentum caused by a force F in ashort amount of time. The momentum p is defined here as theproduct of force F and time t and is conserved if no friction lossoccurs and the collision is elastic. This means that in a closedsystem of different bodies the latter can transfer or receive mo-mentum, however the total momentum of the system remainstemporally and quantitatively constant and the energy is there-fore a conserved quantity.

Conservation of momentum during central elastic collision with Cobra 4Conservation of momentum during central elastic collision with Cobra 4


P6000860P6000860

PrinciplePrincipleIn this experiment, the distance-time law and the velocity-timelaw are examined in addition to Newton's second law whichgives a connection between mass, acceleration and force. A rollertrack is hereby used on which a cart is subjected to uniformly ac-celerated motion.

Newton's law with Cobra 4 and Timer/Counter sensorNewton's law with Cobra 4 and Timer/Counter sensor




30

PrinciplePrinciple

A steel ball is fired by a spring at different velocities and at differ-ent angles to the horizontal. The relationships between the range,the height of projection, the angle of inclination,and the firing ve-locity are determined.TasksTasks

1. To determine the range as a function of the angle of inclina-tion.

2. To determine the maximum height of projection as a func-tion of the angle of inclination.

3. To determine the (maximum) range as a function of the ini-tial velocity.


Trajectory parabola Motion involving uniform acceleration Ballistics


Ballistic Unit 11229-10 1Two-tier platform support 02076-03 1Speed measuring attachment 11229-30 1Power supply 5 VDC/2.4 A withDC-socket 2.1mm 13900-99 1Barrel base PHYWE 02006-55 1Meter scale, demo. l=1000mm 03001-00 1Recording paper, 1 roll,25 m 11221-01 1Steel ball, d = 19 mm 02502-01 2

Ballistic UnitBallistic Unit


For demonstrating projectile motion and for quantitative invest-igation of the laws of projection, in particular for determining therange of a projectile as a function of the projectile angle and theinitial velocity of the projectile.BenefitsBenefits

The catapult included in the extent of delivery can be used to: achieve reproducible projectile ranges up to 3 m (scatter of the

projectile ranges approx. 1%) set a continuously variable projection angle between 0 and

90- to select three projection speeds use two balls with different masses but with the same dia-

meterEquipment and technical dataEquipment and technical data

with catapult and fixed storage for two balls d = 19 mm(wooden ball with iron core and steel ball 02502.01),

dimensions 60 cm38 cm

11229-1011229-10

P2131100P2131100Projectile motionProjectile motion

Maximum range as a function of the angle ofinclination for different initial velocity v0:

Curve 1 v0 = 5.3 m/sCurve 2 v0 = 4.1 m/sCurve 3 v0 = 3.1 m/s

2 Mechanics2 Mechanics2.3 Motion in two and three Dimensions


31

PrinciplePrinciple

A classic method of determining the velocity of a projectile is toshoot the projectile into a resting mass which is large comparedto the projectile's mass and hung as a pendulum. In the process,the projectile remains in the pendulum mass and oscillates withit. This is an inelastic collision in which the momentum remainsunchanged. If the pendulum's mechanical data are known, onecan infer the velocity of the pendulum's mass (including the pro-jectile's mass) at the lowest point of the pendulum's oscillationfrom the amplitude of the pendulum's oscillation. The momentumof the two masses in this phase of the oscillation must thus beequal to the impulse of the projectile before it struck the pendu-lum. If one knows the masses of the pendulum and the projectile,one can calculate the projectile's velocity. In order to be able touse this measuring principle without danger, the following set-up is used here: A steel ball is shot at the mass of a pendulumwith the aid of a spring catapult. The pendulum mass has a hol-low space in which the steel ball is held. If, additionally, two lightbarriers and a time measuring device are available, an independ-ent, direct measurement of the initial velocity of the ball can bemade.

TasksTasks

1. Measurement of the oscillation amplitudes of the ballisticpendulum after capturing the steel ball for the three possibletension energies of the throwing device.

2. Calculation of the initial velocities of the ball from the meas-ured oscillation amplitudes and the mechanical data of thependulum is performed using the approximation formula (3).

3. Plotting of the velocity v of the steel ball as a function of themaximum deflection; (0.90) of the pendulum according toformula (3), taking into consideration the special mechanicaldata of the experiment.

4. Determination of the correction factor for the utilised pen-dulum for the conversion of the velocities determined by us-ing the approximation formula into the values obtained fromthe exact theory. Correction of the velocity values from Tasks2.5. If the supplementary devices for the direct measurementof the initial velocity are available, measure the initial velo-cities corresponding to the three tension steps of the throw-ing device by performing 10 measurements each with sub-sequent mean value calculation. Plot the measured points inthe diagram fromTask 3. Give reasons for contingent system-atic deviations from the theoretical curve.


Potential and kinetic energy Rotational energy Moment of inertia Inelastic collision Principle of conservation of momentum Angular momentum Measurement of projectile velocities


Ballistic Unit 11229-10 1

Speed measuring attachment 11229-30 1

Ballistic Pendulum,f.Ballist.Unit 11229-20 1

Power supply 5 VDC/2.4 A withDC-socket 2.1mm 13900-99 1

Steel ball, d = 19 mm 02502-01 2

P2131200P2131200 Ballistic pendulumBallistic pendulum

Diagram on the theory of the ballistic pendu-lum.

2 Mechanics2 Mechanics2.3 Motion in two and three Dimensions


32

PrinciplePrinciple

The volocities of two gliders, moving without friction on a demon-stration track, are measured before and after collision, for bothelastic and inelastic collision.

TasksTasks

1. Elastic collision1. Elastic collision

1. The impulses of the two gliders as well as their sum after thecollision. For comparison the mean value of the impulses ofthe first glider is entered as a horizontal line in the graph.

2. Their energies, in a manner analogous to Task 1.1

2. Inelastic collision2. Inelastic collision

1. The impulse values are plotted as in Task 1.1. The energy val-ues are plotted as in Task 1.2.


Conservation of momentum, Conservation of energy Linear motion, Velocity, Elastic loss, Elastic collision


Timer 4-4 13604-99 1

Starter system for demonstration track 11309-00 1

Demonstration Track, Aluminium, Length:1.5 m 11305-00 1

Cart, low friction sapphire bearings 11306-00 2




P2130505P2130505Laws of collision/ demonstration track with a 4-4 TimerLaws of collision/ demonstration track with a 4-4 Timer

Elastic collision: calculated energies after thecollision as functions of the mass ratio of thegliders.

Laws of collision/ demonstration track with Cobra3Laws of collision/ demonstration track with Cobra3

P2130515P2130515

Laws of collision/ air trackLaws of collision/ air track

P2130501P2130501

Laws of collision/ air track with Cobra3Laws of collision/ air track with Cobra3

P2130511P2130511

Impulse and momentum / demonstration track withImpulse and momentum / demonstration track withCobra4Cobra4

P1199560P1199560

Conservation of momentum during central elastic collisionConservation of momentum during central elastic collisionwith cobra4with cobra4

P1199660P1199660

Laws of collision/ air track with Cobra4 - available 2013Laws of collision/ air track with Cobra4 - available 2013

P2130560P2130560

2 Mechanics2 Mechanics2.4 Linear Momentum and Collisions


33

PrinciplePrinciple

If a constant torque is applied to a body that rotates without fric-tion arounda fixed axis, the changing angle of rotation increasesproportionally to thesquare of the time and the angular velocityproportional to the time.

TasksTasks

1. Measurement of the laws of angle andangular velocity ac-cording to time for auniform rotation movement.

2. Measurement of the laws of angle andangular velocity ac-cording to time for auniformly accelerated rotational move-ment.

3. Rotation angle; is proportional to the time t required for therotation.


Angular velocity Rotation Moment Torque Moment of inertia Rotational energy



Precision pivot bearing 02419-00 1

Inertia rod 02417-03 1

Holding device w. cable release 02417-04 1

Turntable with angle scale 02417-02 1




Bench clamp PHYWE 02010-00 2

Softw. Cobra3 translat./rotation 14512-61 1


Cobra4 Experiment - available 2013Cobra4 Experiment - available 2013

P2131315P2131315 Moment of inertia and angular acceleration with Cobra3 with aMoment of inertia and angular acceleration with Cobra3 with aprecision pivot bearingprecision pivot bearing

Angle vs. square of time for one turntable.

Moment of inertia and angular acceleration and with anMoment of inertia and angular acceleration and with anair bearingair bearing

P2131301P2131301

Moment of inertia and angular acceleration with aMoment of inertia and angular acceleration with aprecision pivot bearingprecision pivot bearing

P2131305P2131305

Moment of inertia and angular acceleration with Cobra3Moment of inertia and angular acceleration with Cobra3and with an air bearingand with an air bearing

P2131311P2131311

Moment of inertia and angular acceleration with Cobra4Moment of inertia and angular acceleration with Cobra4

P2131360P2131360

2 Mechanics2 Mechanics2.5 Rotational Motion


34

PrinciplePrinciple

The angle of rotation and angular velocity are measured as a func-tion of time on a body which is pivoted so as to rotate withoutfriction and which is acted on by a moment. The angular acceler-ation is determined as a function of the moment.

TasksTasks

With uniformly accelerated rotary motion, the following will bedetermined:

1. the angle of rotation as a function of time,2. the angular velocity as a function of time.3. the angular acceleration as a function of time,4. the angular acceleration as a function of the lever arm.


Circular motion Angular velocity Angular acceleration Moment of inertia Newton's laws Rotation


Blower 230V/50Hz 13770-97 1

Air bearing 02417-01 1

Light barrier with counter 11207-30 1


Turntable with angle scale 02417-02 1

Precision pulley 11201-02 1


Power supply 5 V DC/2.4 A with 4 mm plugs 11076-99 1

Light barrier with counterLight barrier with counter


With the function of an electronic time measuring and countingdevice.

BenefitsBenefits

4 figureluminous display, selection switch for 4 operatingmodes

RESET key BNC jack for exterior starting and/ or stopping of time meas-

urement TTL output to control peripheral devices power supply connector (4 mm jacks)


Fork width: 70 mm Usable barrier depth: 65 mm Sensitivity adjustable LED-Display: 4digits, 8 mm Time measurement: 0...9,999 s Counting: 0...9999 Supply voltage: 5 V DC Max. working frequency: 25 kHz External dimensions (mm): 160 x 25 x 105M6 Threaded holes in casing: 7 Stem included: 100 mm, M6 thread

11207-3011207-30

P2131500P2131500Moment and angular momentumMoment and angular momentum

Angle of rotation as a function of time withuniformly accelerated rotary motion for m =0.01 kg, r = 0.015 m.



35

PrinciplePrinciple

A body with variable mass moves on a circular path with ad-justable radius and variable angular velocity. The centrifugal forceof the body will be measured as a function of these parameters.

TasksTasks

Determination of the centrifugal force as a function

1. of the mass,2. of the angular velocity,3. of the distance from the axis of rotation to the centre of

gravity of the car.


Centripetal force Rotary motion Angular velocity Apparent force


Laboratory motor, 220 V AC 11030-93 1

Gearing 30/1, for 11030.93 11029-00 1


Centrifugal force apparatus 11008-00 1

Bearing unit 02845-00 1


Cart for measurements and experiments 11060-00 1



P2131601P2131601 Centrifugal forceCentrifugal force

Centrifugal force as a function of the angularvelocity v.

Centrifugal force, complete set (interface version)Centrifugal force, complete set (interface version)

P2131611P2131611

Centripetal acceleration with Cobra4Centripetal acceleration with Cobra4

P6000560P6000560

Centripetal force with Cobra4Centripetal force with Cobra4

P6000660P6000660



36

PrinciplePrinciple

A disc, which can unroll with its axis on two cords, moves in thegravitational field. Potential energy, energy of translation and en-ergy of rotation are converted into one another and are determ-ined as a function of time.

TasksTasks

The moment of inertia of the Maxwell disc is determined. Usingthe Maxwell disc,

1. the potential energy,2. the energy of translation,3. the energy of rotation,

are determined as a function of time.


Maxwell disc Energy of translation, Energy of rotation Potential energy Moment of inertia Angular velocity, Angular acceleration Instantaneous velocity Gyroscope



Maxwell wheel 02425-00 1



Meter scale, demo. l=1000mm 03001-00 1

Capacitor 100 nF/250V, G1 39105-18 1

Maxwell wheelMaxwell wheel


Apparatus for conversion of potential to kinetic energy and vice-versa (translation and rotation). Two aperatures at ends of axleskeep wheel from running off its trajectory and are used, togetherwith a light barrier, to measure translation velocity.


Metal wheel with support rod and adjustable suspension. Wheel diameter: 130 mm, Mass of wheel: 470g. Moment of inertia: 10 kg cm. Cord length: 800 mm, Diameter

of shutter: 20 mm.

02425-0002425-00

P2131800P2131800Mechanical conservation of energy / Maxwell's wheelMechanical conservation of energy / Maxwell's wheel

Distance travelled by the centre of gravity of theMaxwell disk as a function of time.



37

PrinciplePrinciple

The momentum of inertia of the gyroscope is investigated bymeasuring the angular acceleration caused by torques of differentknown values. In this experiment, two of the axes of the gyroscopeare fixed. The relationship between the precession frequency andthe gyro-frequency of the gyroscope with 3 free axes is examinedfor torques of different values applied to the axis of rotation. Ifthe axis of rotation of the force free gyroscope is slightly displaced,a nutation is induced. The nutation frequency will be investigatedas a function of gyro frequency.

TasksTasks

1. Determination of the momentum of inertia of the gyroscopeby measurement of the angular acceleration.

2. Determination of the momentum of inertia by measurementof the gyro-frequency and precession frequency.

3. Investigation of the relationship between precession andgyro-frequency and its dependence from torque.

4. Investigation of the relationship between nutation frequencyand gyro-frequency.


Momentum of inertia, Angular momentum Torque Precession, Nutation


Gyroscope with 3 axes 02555-00 1


Additional gyro-disk w. c-weight 02556-00 1


Gyroscope with 3 axesGyroscope with 3 axes


Demonstration and practical set for working up the gyroscopelaws.

BenefitsBenefits

The following relationships can be produced:

Precession (influence of torque and rotational frequency) Nutation (influence of the speed of the disc on the nutational

frequency) Measurement of the moment of inertia of the gyroscope disc

from the angular acceleration for a known torque Investigation of the relationship between the duration of a

precession rotation and the rotational frequency of the gyro-scope disc, Investigation of the relationship between the pre-cession frequency and the turning moment exerted on thegyroscope axis for constant rotational frequency of the disc

Determination of the relationship between the rotational andnutational frequency of the gyroscope disc

Gyroscope disc with double ball bearings, balanced and freelymovable via 3 axes, which is wound up by hand with the aidof a thread

Mounted on a metal stand, Sliding counterweight for calibrat-ing the gyro disc


Disc diameter: 245 mm, Disc thickness: 25 mm Disc weight: approx. 1317 g, Counterweight: approx. 925 g

02555-0002555-00

P2131900P2131900 Laws of gyroscopes / 3-axis gyroscopeLaws of gyroscopes / 3-axis gyroscope

Determination of the momentum of inertiafrom the slope of straight line tR -1 = f(tP).



38

PrinciplePrinciple

If the axis of rotation of the force-free gyroscope is displacedslightly, a nutation is produced. The relationship between preces-sion frequency or nutation frequency and gyro-frequency is ex-amined for different moments of inertia. Additional weights areapplied to a gyroscope mounted on gimbals, so causing a preces-sion.

TasksTasks

1. To determine the precession frequency as a function of thetorque and the angular velocity of the gyroscope.

2. To determine the nutational frequency as a function of theangular velocity and the moment of inertia.


Moment of inertia Torque Angular momentum Nutation Precession


Gyro,Magnus type, incl. Handb. 02550-00 1

Digital stroboscope 21809-93 1

Stopwatch, digital, 1/100 s 03071-01 1

Gyro, Magnus type, incl. Handb.Gyro, Magnus type, incl. Handb.


Gyro, Magnus type, universal gyro for demonstration and quantit-ative evaluation of gyro laws and their application.

BenefitsBenefits

Rich accessories to demonstrate the following topics:

symmetrical and asymmetrical elonged and flattened gyro force free, driven and captive gyro, navigational gyro compass


steel gyro disc with reinforced edge suspended in gimbols withbolt bearings, springs and clamps for restriction

variation of moments of inertia by supplementary steel-weights

Disk diameter: 128 mm, Storage box (mm): 355 x 380 x 385 Including manual of 124 pages.

02550-0002550-00

P2132000P2132000Laws of gyroscopes / cardanic gyroscopeLaws of gyroscopes / cardanic gyroscope

Precession frequency as a function of the gyrofrequency for different additional masses.



39

PrinciplePrinciple

The period of vibration of a circular disc which performs torsionalvibrations about various parallel axes, is measured. The momentof inertia of the disc is determined as a function of the perpen-dicular distance of the axis of rotation from the centre of gravity.

TasksTasks

1. Determination of the angular restoring constant of the spiralspring.

2. Determination of the moment of inertia of a circular disc as afunction of the perpendicular distance of the axis of rotationfrom the centre of gravity


Rigid body Moment of inertia Centre of gravity Axis of rotation Torsional vibration Spring constant Angular restoring force



Rotation axle 02415-01 1

Disk, w. diametrical holes 02415-07 1




Spring balance, transparent, 2 N 03065-03 1

Ruler, plastic, 200 mm 09937-01 1


Light barrier with counterLight barrier with counter


With the function of an electronic time measuring and countingdevice.

BenefitsBenefits

4 figureluminous display, selection switch for 4 operatingmodes

RESET key; BNC jack for exterior starting and/ or stopping oftime measurement

TTL output to control peripheral devices;power supply con-nector (4 mm jacks)


Fork width: 70 mm, Usable barrier depth: 65 mm Sensitivity adjustable, LED-Display: 4digits, 8 mm, Time meas-

urement: 0...9,999 s, Counting: 0...9999 Supply voltage: 5 V DC, Max. working frequency: 25 kHz External dimensions (mm): 160 x 25 x 105M6, Threaded holes

in casing: 7, Stem included: 100 mm, M6 thread

11207-3011207-30

P2132801P2132801 Moment of inertia / Steiner's theoremMoment of inertia / Steiner's theorem

Moment (torque) of a spiral spring as a functionof the angle of rotation.

Moments of inertia of different bodies / Steiner's theoremMoments of inertia of different bodies / Steiner's theoremwith Cobra4with Cobra4

P2132860P2132860



40

PrinciplePrinciple

Coplanar forces (weight, spring balance) act on the moments discon either side of the pivot. In equilibrium, the moments are de-termined as a function of the magnitude and direction of theforces and of the reference point.

TasksTasks

1. Moment as a function of the distance between the origin ofthe coordinates and the point of action of the force

2. Moment as a function of the angle between the force and theposition vector to the point of action of the force

3. Moment as a function of the force.


Moments Couple Equilibrium Statics Lever Coplanar forces


Moments disk 02270-00 1


Spring Balance 1 N 03060-01 2


Bolt with pin 02052-00 1

Fish line, l. 100m 02090-00 1

Support rod PHYWE,square,l 400mm 02026-55 2

Right angle clamp PHYWE 02040-55 1

Bosshead, turnable 02048-04 1


Moments diskMoments disk


Disk to investigate general equilibrium conditions of a body sub-mitted to forces and supported at its centre of gravity so that itcan rotate.


Metallic disk, white on both sides with a central hole for lowfriction support on rod with pin.

One side with auxiliary circles with angular scales. Disk diameter: 270 mm. Number of holes: 64. Grid constant (mm): 30 x 30.

02270-0002270-00

P2120100P2120100MomentsMoments

Moment as a function of the distance betweenthe origin of the coordinates and the point ofaction of the force.

TorqueTorque

P1253500P1253500

2 Mechanics2 Mechanics2.6 Static Equilibrium and Elasticity


41

PrinciplePrinciple

A flat bar is supported at two points. It is bent by the action of aforce acting at its centre. The modulus of elasticity is determinedfrom the bending and the geometric data of the bar.

TasksTasks

1. Determination of the characteristic curve of the dial gauge.2. Determination the bending of flatbars as a function of the

force; at constant force: of the thickness, of the width and ofthe distance between the support points.

3. Determination the modulus of elasticity of steel, aluminiumand brass.


Young's modulus Modulus of elasticity Stress Deformation Poisson's ratio Hooke's law


Flat bars, set 17570-00 1

Dial gauge 10/0.01 mm 03013-00 1


Holder for dial gauge 03013-01 1

Knife-edge with stirrup 03015-00 1


Vernier caliper 03010-00 1

Bolt with knife-edge 02049-00 2

Support rod PHYWE, square, l 630mm 02027-55 1

P2120200P2120200 Modulus of elasticityModulus of elasticity

Table 1: The modulus of elasticity for differentmaterials.



42

PrinciplePrinciple

The relationship between torque and angle of rotation is determ-ined when metal bars are twisted. The hysteresis curve is recor-ded.

TasksTasks

1. Record the hysteresis curve of steel and copper rods.2. Record the stress-relaxation curve with various relaxation

times of different materials.


Mechanical hysteresis Elasticity Plasticity Relaxation Torsion modulus Plastic flow Torque Hooke's law


Torsion apparatus 02421-00 1


Spring balance 2,5 N 03060-02 1

Torsion rod, Al, l = 500 mm, d = 4 mm 02421-06 1


Torsion rod, Cu, l = 500 mm, d = 2 mm 02421-08 1

Torsion rod, steel, l = 500 mm, d = 2 mm 02421-01 1



Torsion apparatus, completeTorsion apparatus, complete


To investigate deformations due to torques. For demonstration ofthe combined effects of force and lever.

02421-8802421-88

P2120300P2120300Mechanical hysteresisMechanical hysteresis

Mechanical hysteresis curve for the torsion of acopper rod of 2 mm dia meter and 0.5 m long.



43

PrinciplePrinciple

The validity of Hooke's Law is proven using various helical springswith different spring constants. In comparison, the behaviour of astretched rubber band is examined, for which there is no propor-tionality between acting force and resulting extension.

TasksTasks

1. Calibration of the system (movement sensor and forcesensor).

2. Measurement of the tensile force as a function of the pathfor three different helical springs and a rubber band.

3. Determination of the spring constant and evaluation of ahysteresis curve.

4. Verification of Hooke's law.


Spring constant Limit of elasticity Extension and compression



Newton sensor 12110-01 1

Movement sensor with cable 12004-10 1

Measuring module Newton 12110-00 1



Bench clamp PHYWE 02010-00 1

Plate holder 02062-00 1

Stand tube 02060-00 1

Software Cobra3-Force/ Tesla 14515-61 1


P2130111P2130111 Hooke's law with Cobra3Hooke's law with Cobra3

Characteristic elongation curve for a helicalspring with D = 20 N/m.

Hooke's law with Cobra4Hooke's law with Cobra4

P2130160P2130160



44

PrinciplePrinciple

Various bodies perform torsional vibrations about axes throughtheir centres of gravity. The vibration period is measured and themoment of inertia determined from this.

TasksTasks

The following will be determined:

1. The angular restoring moment of the spiral spring.2. The moment of inertia a) of a disc, two cylinder, a sphere and

a bar, b) of two point masses, as a function of the perpen-dicular distance to the axis of rotation. The centre of gravitylies in the axis of rotation.


Rigid body, Moment of inertia, Angular restoring moment Axis of rotation, Torsional vibration, Spring constant Moment of inertia of a sphere, a disc, a cylinder, a long bar

and 2 point masses



Rotation axle 02415-01 1

Sphere 02415-02 1

Rod with movable masses 02415-06 1

Hollow cylinder 02415-04 1

Disk 02415-03 1

Solid cylinder 02415-05 1



Spring balance 2,5 N 03060-02 1


P2133100P2133100Moments of inertia and torsional vibrationsMoments of inertia and torsional vibrations

Moment of inertia of two equal masses, of0.214 kg each, as a function of the distancebetween them.

Moment of inertia / Steiner's theoremMoment of inertia / Steiner's theorem

P2132801P2132801



45

PrinciplePrinciple

Two small lead spheres are positioned on a beam, which is freelysuspended on a thin metal wire. At the beginning the large leadspheres are positioned symmetrically opposite to the small spheresin that way that the attractive forces are eliminated. There after,the large spheres are swung so that they are close to the smallspheres. As a consequence of the gravitational attracting force thebeam with the small spheres now moves in a new equilibrium po-sition, where the attractive forces are equivalent to the force ofthe torsion of the wire. The gravitational constant can be determ-ined from the new equilibrium position.

TasksTasks

1. Calibration of an angular detector.2. Determination of the oscillation time of a free and damped

oscillating torsion pendulum.3. Determination of the gravitational constant.


Law of gravitation Free, damped, forced and torsional oscillations Moment of inertia of spheres and rods Steiner's theorem Shear modulus


Cavendish balance/computerized 02540-00 1

Circular level, d = 36 mm 02123-00 1


Cavendish balance / computerizedCavendish balance / computerized


For the demonstration of the mass attraction of two bodies andfor the determination of the gravitational constant.

BenefitsBenefits

Complete and compact system with control unit, only a re-cording system (e.g. aninterface-system ) or a multimeter is tobe used to get 2%

Accurate results in a single lab period Short oscillation periods of 2-4 mi

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