Physics Experiment Calculations

7/30/2019 Physics Experiment Calculations

1/43

This Excel package was created as a teacher's aid in the school laboratory / clas

1 A teachers demonstration tool to illustrate data handling

2 A tool for the plotting of graphs both for the experiments themselves or

3 It may also be used to check and plot student data before leaving the la

Created By: James Frawley

Revision: B

Date: 1/7/2009

Helpf l Hints

Copyright James FFor non-commercial

Please leave feedbacSecond Level Suppor


2/43

Helpful Hints:

room / computer room. It can be used as:

past exam questions

oratory

awleyurposes only !

k / suggestions on the PhysicsService Homepage Forum


3/43

To Measure the Focal Length of a Concave Mirror

Measurement Object Image Focal All data here is measured in units of cm

Distance Distance 1 1 1 Length

u v u v f f Remember:

cm cm cm

1 15.00 60.50 0.067 0.017 0.083 12.02

2 20.00 30.00 0.050 0.033 0.083 12.00 1 + 1 = 1

3 25.00 23.00 0.040 0.043 0.083 11.98 u v f

4 30.00 20.50 0.033 0.049 0.082 12.18

5 35.00 18.00 0.029 0.056 0.084 11.89

6 40.00 17.00 0.025 0.059 0.084 11.93

7 45.00 16.50 0.022 0.061 0.083 12.07

8 50.00 15.90 0.020 0.063 0.083 12.06

9 55.00 15.50 0.018 0.065 0.083 12.09

10 60.00 15.10 0.017 0.066 0.083 12.06

Average Focal Length (cm) 12.03

All data above is measured in units of cm From the Graph we see:

Intercept = 1/f = 0.083 cm^-1

Intercept = 1/f = 0.083

Focal Length = f = 12.05 cm


cm-1 cm-1 cm-1

cm-1

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

0.090

f(x) = -0.994x + 0.083

Focal Length of Concave Mirror

1/v


4/43

0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090

0.000

1/u


5/43

To Measure the Focal Length of a Convex Lens

Measurement Object Image Focal

Distance Distance 1 1 1 Length

u v u v f f

cm cm cm

1 20.00 66.40 0.050 0.015 0.065 15.37

2 25.00 40.60 0.040 0.025 0.065 15.47

3 35.00 27.60 0.029 0.036 0.065 15.43

4 45.00 23.20 0.022 0.043 0.065 15.31

5 55.00 21.50 0.018 0.047 0.065 15.46

6 65.00 20.10 0.015 0.050 0.065 15.35

7 75.00 19.20 0.013 0.052 0.065 15.29

8 85.00 18.80 0.012 0.053 0.065 15.39

9 95.00 18.40 0.011 0.054 0.065 15.41

10 100.00 18.20 0.010 0.055 0.065 15.40

Average Focal Length 15.39

All data above is measured in units of cm

Intercept = 1/f = 0.065


cm-1 cm-1 cm-1

cm-1

0.000 0.010 0.020 0 .030 0.040 0.050 0.060 0 .070 0.080

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

f(x) = -1.004x + 0.065

Focal Length of Convex Lens

1/u

1/v


6/43

Refractive Index of a Glass Block:

Measurement Angle of Angle of Angle of Angle of sin i sin r Refractive

Incidence Refraction Incidence Refraction Index

i (Degrees) r (Degrees) i (Radians) r (Radians) n

1 25.0 16.0 0.436 0.279 0.423 0.276 1.53

2 30.0 19.0 0.524 0.332 0.500 0.326 1.54

3 35.0 22.0 0.611 0.384 0.574 0.375 1.53

4 40.0 25.0 0.698 0.436 0.643 0.423 1.52

5 45.0 28.0 0.785 0.489 0.707 0.469 1.51

6 50.0 30.0 0.873 0.524 0.766 0.500 1.53

7 55.0 33.0 0.960 0.576 0.819 0.545 1.50

Average Refractive Index (n) 1.52

n = sin i

sin r

From the Graph:

Slope = n = 1.52

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

f(x) = 1.48x + 0.02

Snells Law - Glass Block

Sin r

Sini


7/43


8/43

Measurement of the Refractive Index of a Liquid (Water is used here)

Measurement Real Apparent Refractive

Depth Depth Index

cm cm n

Beaker 1 10.70 8.00 1.34

Beaker 2 8.10 6.20 1.31

Beaker 3 7.30 5.50 1.33

Beaker 4 6.10 4.50 1.36

Beaker 5 4.90 3.90 1.26

Average Refractive Index 1.32

Units of cm are used in the experiment above

Slope of Graph = n = 1.32

n = Real Depth

Apparent Depth

Ideal Value for the Refractive Index of Water = 1.330.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

f(x) = 1.37x - 0.29

Refractive Index of a Liquid

Apparent Depth (cm)

R

ealDepth(cm)


9/43

To Measure the Wavelength of Monochromatic Light (Sodium Vapour Lamp):

Diffraction Grating has: 600 lines/mm

==> Grating Constant (d): d = 1.67E-06 m REMEMBER 1

(lines/mm) x 1000

Spectrometer Zero Error Reading ==> 0.3 Degrees to RHS

n.A = d.sin(Theta)

Order of Angle (Theta) Corrected Angle for Sin Theta Wavelength

Image for nth Image Angle for nth Image

n Measured nth Image Theta A

Degrees Degrees Radians m

LHS2 45.0 45.3 0.791 0.711 5.92E-07

1 20.4 20.7 0.361 0.353 5.89E-07

0 0.3 0.0 0.000 0.000 #DIV/0!

RHS1 20.7 20.4 0.356 0.349 5.81E-07

2 45.2 44.9 0.784 0.706 5.88E-07

Average Wavelength 5.88E-07

... d =


10/43

A = d.sin(Theta)

n

A = Wavelength of Light used

Slope of Graph = sin(Theta)

n

Slope = 0.354

A = d x (slope)

A = 5.90E-07 m

0 0.5 1 1.5 2 2.5

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

f(x) = 0.355x - 0.002

Sin Theta vs. Order of Image

Column F

Linear (Column F)

Order of Image (n)

SinTheta


11/43

To Investigate the Laws of Equilibrium for a Set of Coplanar Forces:

Weight of Metre Stick W = 1.20 N

Position of Centre of Gravity CoG = 0.505 m

Note: Use the Centre of Gravity as the Axis of rotation in this experiment

Positions below are read directly from the metre stick

LHS of CoG RHS of CoG

Spring Spring Masses Weights Weight Distance Moment Spring Spring Masses Weights Weight Distance Moment

Balance Balance Position From of Weight Balance Balance Position From of Weight

Reading Position Fulcrum Reading Position Fulcrum

N m kg N m m N.m N m kg N m m N.m

2.0 0.20 0.204 2.00 0.15 0.36 0.71 4.0 0.75 0.183 1.80 0.80 0.30 0.530.00 0.51 0.00 0.122 1.20 0.95 0.45 0.53

0.00 0.51 0.00 0.00 0.51 0.00

0.00 0.51 0.00 0.00 0.51 0.00

0.00 0.51 0.00 0.00 0.51 0.00

0.00 0.51 0.00 0.00 0.51 0.00

Upward Downward Clockwise Anti- Note: 1 The Net Force acting is approximately zero

Forces Forces Moments Clockwise 2 The Sum of the moments about fulcrum is zero

Moments

N N N.m N.m

6.00 6.19 1.67 1.69


12/43

To Show that Acceleration is Proportional to the Force Applied: Scaler Timer Method

Card Length 0.1 m Card Transit Initial Transit Final Acceleration Mass Weight

Length Time 1 Velocity Time 2 Velocity of Card Used Used

Distance Between Gates s = 1.2 m of Card

L u v a m W

Acceler. Due to Gravity g = 9.81 m s s kg N

0.10 0.350 0.29 0.260 0.38 0.03 0.200 1.96

u = L v = L 0.10 0.310 0.32 0.215 0.47 0.05 0.300 2.94

0.10 0.260 0.38 0.178 0.56 0.07 0.500 4.91

a =

2s

L =

t1 t2

m s-2 m s-1 m s-1 m s-2

t1

t2

v2 - u2

0.00 1.00 2.00 3.00 4.00 5.00 6.00

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08f(x) = 0.01x + 0.00

Acceleration vs. Force

Force (N)

Ac

celeration(m.s^-1)


13/43


14/43

Measurement of Velocity and Acceleration: Scaler Timer Method

Velocity:Card Length 0.1 m Card Transit Velocity

Length Time of Card

v = L

t L t v

m s

0.10 0.500 0.20

0.10 0.420 0.24

0.10 0.350 0.29

0.10 0.310 0.32

0.10 0.260 0.38

Acceleration:

Card Length 0.1 m Transit Initial Transit Final Acceleration Mass Weight

Time 1 Velocity Time 2 Velocity Used Used

Distance Between Gates s = 1.2 m of Card

Acceleration Due to Gravity: g = 9.81 u v a M W

s s kg N

u = L v = L 0.500 0.20 0.370 0.27 0.01 0.100 0.980.420 0.24 0.300 0.33 0.02 0.150 1.47

0.350 0.29 0.260 0.38 0.03 0.200 1.96

a = 0.310 0.32 0.215 0.47 0.05 0.300 2.94

2s 0.260 0.38 0.178 0.56 0.07 0.500 4.91

L =

m s-1

L =

m s-2 t1 t2

m s-1 m s-1 m s-2

t1

t2

v2 - u2


15/43

Conservation of Momentum: Linear Air Track

First Mass 0.3 kg Distance Time for Initial Initial Distance Combined Final Final

Second Mass 0.2 kg Travelled by Mass 1 Velocity Momentum Travelled by Mass Velocity MomentumDistance L = 0.1 m Mass 1 of Mass 1 Combination Time

Final Mass 0.5 kg

u v

m s m s

0.10 0.20 0.50 0.15 0.10 0.35 0.29 0.14

0.10 0.25 0.40 0.12 0.10 0.42 0.24 0.12

0.10 0.32 0.31 0.09 0.10 0.55 0.18 0.09

0.10 0.43 0.23 0.07 0.10 0.75 0.13 0.07

0.10 0.51 0.20 0.06 0.10 0.92 0.11 0.05

0.10 0.70 0.14 0.04 0.10 1.25 0.08 0.04

0.10 0.80 0.13 0.04 0.10 1.63 0.06 0.03

M1 =

M2 =

Mf=

s1 t1 PFINAL s2 t2 PFINAL

m s-1 kg m s-1 m s-1 kg m s-1

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Conservation of Momentum

Column H

Column L

Momentum


16/43


17/43

Measurement of g: Freefall Method

Height Period Period Period Lowest Period Acceleration

#1 #2 #3 Period Squared Due to

Gravity

H T1 T2 T3 T g

m s s s s

1.20 0.497 0.496 0.496 0.496 0.246 9.76

1.10 0.474 0.474 0.473 0.473 0.224 9.83

1.00 0.451 0.452 0.452 0.451 0.203 9.83

0.90 0.432 0.429 0.428 0.428 0.183 9.83

0.80 0.407 0.407 0.405 0.405 0.164 9.75

0.70 0.378 0.379 0.378 0.378 0.143 9.80

0.60 0.349 0.350 0.349 0.349 0.122 9.85

0.50 0.320 0.322 0.320 0.320 0.102 9.77

0.40 0.287 0.286 0.286 0.286 0.082 9.78

0.30 0.248 0.247 0.247 0.247 0.061 9.83

0.20 0.203 0.203 0.203 0.203 0.041 9.71

Average 9.79

g = 2 x h / t^2 slope = 4.90

g = 2 x slope of graph g = 9.80

h = 0.5 x g x t2

T2

s2 m.s-2

m.s-2

m.s-2

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 f(x) = 4.90x - 0.00

Measurement of g: H vs. T2

Square of Period (T2, s2)

Height(H,m)


18/43

The Simple Pendulum

Page 18

The Simple Pendulum: Measurement of g

30 Oscillations 1 Oscillation L L g

30 x T (s) T (s) cm m

14.80 0.49 0.24 6.0 0.06 9.73

17.20 0.57 0.33 8.0 0.08 9.61

18.80 0.63 0.39 10.0 0.10 10.05

21.00 0.70 0.49 12.0 0.12 9.67

22.80 0.76 0.58 14.0 0.14 9.57

23.90 0.80 0.63 16.0 0.16 9.95

26.20 0.87 0.76 18.0 0.18 9.32

26.70 0.89 0.79 20.0 0.20 9.97

30.30 1.01 1.02 25.0 0.25 9.6832.60 1.09 1.18 30.0 0.30 10.03

Average 9.76

Slope = 4.03

g = 9.80 m/s/s

T2 (s2) m.s-2

s2/m

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

f(x) = 3.97x + 0.01

Simple Pendulum: T^2 vs. L

Length (L, m)

Sq

uareofPeriod(T^2,s^2)


19/43

The Simple Pendulum

Page 19


20/43

Verification of Boyle's Law

Pressure (P) Volume (V) 1/V P.V

1.50 14.85 0.067 22.3

1.40 15.90 0.063 22.3

1.35 16.50 0.061 22.3

1.30 17.20 0.058 22.4

1.25 17.80 0.056 22.3

1.20 18.60 0.054 22.3

1.15 19.40 0.052 22.3

1.10 20.30 0.049 22.3

1.05 21.20 0.047 22.31.01 22.10 0.045 22.3

Average 22.3

P x V = constant

where k is a constant

V

k = slope = 22.3 for this mass of gas at this specific temperature

105 Pa cm3 cm-3 105 Pa.cm3

P = k x 1

Pa.cm-3

0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6f(x) = 22.2x + 0.0

Boyle's Law

Inverse of Volume (cm-3)

Pr

essure(105Pa)


21/43

Measurement of the Speed of Sou

Page 21

Measurement of the Speed of Sound in Air D = 0.049 m0.3*D = 0.015 m

Frequency Antinode 1 Antinode 2 Wavelength 1/Wavelength Speed of Sound End Correction Revised c = f

F (Hz) L1 (m) L2 (m) (m) c (m/s) e (m) m/s

512.0 0.152 0.491 0.678 1.47 347.14 0.167 341.34

480.0 0.162 0.522 0.720 1.39 345.60 0.177 339.21

426.6 0.185 0.587 0.804 1.24 342.99 0.200 340.72

384.0 0.204 0.657 0.906 1.10 347.90 0.219 335.88

341.3 0.236 0.744 1.016 0.98 346.76 0.251 342.21

320.0 0.251 0.794 1.086 0.92 347.52 0.266 340.06

288.0 0.283 0.888 1.210 0.83 348.48 0.298 342.92

256.0 0.318 0.980 1.324 0.76 338.94 0.333 340.65

AVERAGE 345.67 340.37

Note:

m-1

The graph is plottedfrom the data prior to theend-correctioncalculation

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0

100

200

300

400

500

600

f(x) = 347.77x - 2.13

Frequency vs. 1/Wavelength

Inverse of Wavelength (m^-1)

Frequenc

y(Hz)


22/43

To Plot the Calibration Curve for an Alcohol Thermometer using a Mercury Thermometer as Standard

Standard Length of

Thermometer Column of

Reading AlcoholL

C cm

0.0 40.0

10.0 54.0

20.0 70.0

30.0 98.0

40.0 112.0

50.0 135.0

60.0 155.0

70.0 180.0

80.0 198.0

90.0 220.0

100.0 240.0

0 50 100 150 200 250 300

0

10

20

30

40

50

60

70

80

90

100

110f(x) = 0.49x - 16.46

Alcohol Thermometer Calibration Curve

Alcohol Column Length (cm)

Tem

perature(C)


23/43


24/43

Specific Heat Capacity of Water

Page 24

To Measure the Specific Heat Capacity of Water (Electrical Method)

1 Mass of Calorimeter Mc 0.453 kg

Mass of Calorimeter and Water Mcw 0.512 kgMass of Water Mw 0.059 kg

2 Initial Temperature of Calorimeter and Water Tiw 7.5 C

Final Temperature of Calorimeter and Water Tfw 18.3 C

Temperature Change DT 10.8 C

Joulemeter Reading (Energy Supplied) Q 4550.0 J

3 Specific Heat Capacity of Copper Cc 385.0 J/kg/C

Heat Gained By Calorimeter Mc.Cc.dT 1883.6 J

Heat Gained By Water Mw.Cw.dT 2666.4 J (BY CONSERVATION OF ENERGY)

4 Specific Heat Capacity of Water Cw 4184.6 J/kg/C

Heat Energy Supplied = Heat Gained by Calorimeter + Heat Gained by Water

Q = Mc.Cc.dT + Mw.Cw.dT


25/43

To Measure the Specific Heat Capacity of Copper (Mechanical Method)Copper filings were used here

1 Mass of Copper Calorimeter Mc 0.425 kg

Mass of Calorimeter and Cold Water Mcw 0.525 kg

Mass of Cold Water Mw 0.100 kg

2 Initial Temperature of Calorimeter and Water Tiw 8.7 C

Final Temperature of Cal., Water and Filings Tfw 12.3 C

Temperature Increase of cal + water dTw 3.6 C

Initial Temperature of Copper Filings Ticf 98.4 CTemperature Decrease of Copper Filings dTcf 86.1 C

Mass of Copper Filings Added Mcf 0.063 kg

3 Specific Heat Capacity of Water Cc 4180.0 J/kg/C

Heat Gained By Water Mw.Cw.dT 1504.8 J

4 Specific Heat Capacity of Copper Cc 386.4 J/kg/C (BY CONSERVATION O

Heat Energy Lost by Copper Filings = Heat Gained by Calorimeter + Heat Gained by Water

Mcf.Cc.dTcf = Mc.Cc.dTw + Mw.Cw.dTw


26/43

Measuring the Latent Heat of Fusion of Ice


Mass of Calorimeter and Warm Water Mcw 0.532 kg

Mass of Warm Water at Start Mw 0.079 kg

Initial Temperature of Calorimeter and Water Tiwc 79.4 C

Final Temperature of Calorimeter, Water and Ice Tfwci 12.6 C

Temperature Fall of Cal and Water DTcw 66.8 C

2 Temperature Rise of Ice DTI 12.6 C

Final Mass of Calorimeter + Water + Ice Mcwi 0.542 kg

Mass of Ice Added Mi 0.010 kg

3 Specific Heat Capacity of Copper Cc 385.0 J/kg/C

Heat Lost By Calorimeter Mc.Cc.dT 11650.3 J

Specific Heat Capacity of Water Cw 4180.0 J/kg/C

Heat Lost By Warm Water Mw.Cw.dT 22058.7 J

Mi.Cw.Dti 526.7 J (BY CONSERVATION OF ENERGY)

4 Latent Heat of Fusion of Water/Ice 3.32E+06 J/kg

Mw.Cw.dT + Mc.Cc.dT = Mi.Cw.Dti + Mi.Lf

Heat Gained By Water at 0 C to raise to T F

Lf


27/43


28/43

Heat of Vaporisation of Water

Page 28

Measuring the Latent Heat of Vaporisation of Water


Mass of Calorimeter and Cooled Water Mcw 0.532 kg

Mass of Water at Start Mw 0.079 kg

Initial Temperature of Calorimeter and Water Tiw 7.5 C

Final Temperature of Calorimeter and Water Tfw 43.3 C

Temperature Rise of Cal and Water Dtcw 35.8 C

2 Temperature Fall of Steam DTs 56.7 C

Final Mass of Calorimeter + Water + Steam Mcws 0.539 kg

Mass of Steam Added Ms 0.007 kg

3 Specific Heat Capacity of Copper Cc 390.0 J/kg/CHeat Gained By Calorimeter Mc.Cc.dT 6324.8 J

Specific Heat Capacity of Water Cw 4180.0 J/kg/C

Heat Gained By Cold Water Mw.Cw.dT 11821.9 J

Heat Lost By Steam Ms.Cw.DTs 1635.3 J (BY CONSERVATION OF ENERGY)

4 Latent Heat of Vaporisation of Water 2.39E+06 J/kg

Mc.Cc.dT + Mw.Cw.dT = Ms.Lv + Ms.Cw.DTs

Lv


29/43

Heat of Vaporisation of Water

Page 29


30/43

Joules Law

Page 30

Joule's Law: The Heating Effect of an Electric Current

Initial Temp Final Temp Current Temp Change Current Squared

I (A)

22.3 23.4 0.50 1.1 0.25

23.4 27.7 1.00 4.3 1.00

27.7 35.7 1.50 8.0 2.25

34.4 48.3 2.00 13.9 4.00

48.3 68.2 2.50 19.9 6.25

66.5 97.8 3.00 31.3 9.00

T1

(C) T2

(C) T2

T1

(C) I2 (A2)

H = I2x R x t

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

f(x) = 3.34x + 0.43

Joule's Law

TemperatureChange(*C)


31/43

Joules Law

Page 31

Square of Current (A^2)


32/43

To Measure the Resistivity of Nichrome Wire

Wire Micrometer Corrected Corrected Cross Measured Lead / Meter Corrected Wire Rc / L Resistivity

Diameter Zero Error Diameter Diameter Sectional Resistance Resistance Resistance Length (L)

mm mm mm m Area (m^2) Rm () Rc () m /m .m

1.324 0.012 1.312 1.31E-03 1.35E-06 1.06 0.86 0.20 0.25 0.80 1.08E-06

1.295 0.012 1.283 1.28E-03 1.29E-06 1.30 0.86 0.44 0.50 0.88 1.14E-06

1.312 0.012 1.300 1.30E-03 1.33E-06 1.50 0.86 0.64 0.75 0.85 1.13E-06

1.306 0.012 1.294 1.29E-03 1.32E-06 1.70 0.86 0.84 1.00 0.84 1.10E-06

1.291 0.012 1.279 1.28E-03 1.28E-06 1.83 0.86 0.97 1.25 0.78 9.97E-07

1.317 0.012 1.305 1.31E-03 1.34E-06 2.10 0.86 1.24 1.50 0.83 1.11E-06

1.320 0.012 1.308 1.31E-03 1.34E-06 2.30 0.86 1.44 1.75 0.82 1.11E-06

1.295 0.012 1.283 1.28E-03 1.29E-06 2.60 0.86 1.74 2.00 0.87 1.12E-061.293 0.012 1.281 1.28E-03 1.29E-06 2.87 0.86 2.01 2.25 0.89 1.15E-06

1.314 0.012 1.302 1.30E-03 1.33E-06 3.08 0.86 2.22 2.50 0.89 1.18E-06

AVERAGE 1.307 1.295 1.29E-03 1.32E-06 0.85 1.11E-06

p = R x A / L


33/43

Resistance vs Temperature for M

Page 33

Resistance vs. Temperature Characteristic for a Metallic Conductor

Resistance Temperature

R (Ohms) T (*C)

9.93 13.7

10.28 22.4

10.51 31.6

10.76 43.1

11.32 52.8

11.32 63.2

11.70 71.7

12.23 83.4

12.78 92.5

0 10 20 30 40 50 60 70 80

0

2

4

6

8

10

12

14

16

18

20

f(x) = 0.03x + 9.43

Resistance vs. Temperature for a Metallic Conductor

Temperature (*C)

Resistance

(Ohms)


34/43


Page 34


35/43


Page 35

90 100


36/43


Page 36


37/43

Resistance vs. Temperature Characteristic for a Thermistor

Resistance Temperature

R (Ohms) T (*C)

176.0 11.0

152.0 14.5

83.0 29.0

49.0 41.0

36.0 49.0

24.0 58.0

16.0 68.0

13.0 76.0

9.0 90.0

0 10 20 30 40 50 60 70 80 90 100

0

20

40

60

80

100

120

140

160

180

200

f(x) = 254.3472534815 exp( -0.0390537077 x )

Resistance vs. Temperature Curve for a Thermistor

Temperature (*C)

Resistance(Ohms)


38/43

To Investigate the Variation of Fundamental Frequency vs Length for a Stretched String

The Resonance Point is found for a series of tuning forks by varying the Length of the wire

Fundamental Length

Frequencyf L 1 / L f x L

Hz m m.Hz

173.0 0.80 1.25 138.40

193.0 0.70 1.43 135.10

230.0 0.60 1.67 138.00

273.0 0.50 2.00 136.50

335.0 0.40 2.50 134.00455.0 0.30 3.33 136.50

675.0 0.20 5.00 135.00

Slope = 135.6 Hz.m

Product of f x L should be a constant

m-1

0.0 1.0 2.0 3.0 4.0 5.0 6.0

0

100

200

300

400

500

600

700

800

f(x) = 134.4x + 3.6

Fundamental Freq vs Length for Stretched String

1/Length

F

requency(Hz)


39/43

Stretched String vs Tension

Page 39

To Investigate the Variation of Fundamental Frequency vs Tension for a Stretched String

The Resonance Point is found for a series of tuning forks by varying the Tension of the string

Fundamental Tension Sq. Root

Frequency Tension

F T

Hz N

264.0 15.0 3.87

304.0 20.0 4.47

342.0 25.0 5.00

371.0 30.0 5.48

402.0 35.0 5.92

431.0 40.0 6.32

456.0 45.0 6.71

Slope = 68.03

T0.5

0 1 2 3 4 5 6 7 8

0

50

100

150

200

250

300

350

400

450

500

f(x) = 67.79x + 1.34

Fundamental Freq vs. Tension

SQ. Root of Tension

Frequenc

y(Hz)


40/43

Current vs Voltage Curve for a Metallic Conductor:

Voltage Current Resistance

Volts Amps Ohms

V I R

2.00 0.25 8.03

4.00 0.50 7.94

6.00 0.75 7.97

8.00 0.99 8.06

10.00 1.26 7.96

Average 7.99

Resistance = 1 / slope

Slope = 0.13 A/V

R = 7.69 Ohms

1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40f(x) = 0.13x - 0.00

Metallic Conductor

Voltage (V)

Curren

t(Amps)


41/43

Current vs Voltage Curve for a Filament Bulb:


Volts Amps Ohms

V I R

0.00 0.00 #DIV/0!

1.00 0.20 5.00

2.00 0.30 6.67

3.00 0.35 8.57

4.00 0.38 10.53

5.00 0.39 12.82

6.00 0.40 15.19

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Filament Bulb

Voltage (V)

Current

(Amps)


42/43

Current vs Voltage Curve for a Copper Sulfate Solution with Copper Electrodes:


Volts Amps Ohms

V I R

0.00 0.00 #DIV/0!

2.00 0.64 3.12

4.00 1.24 3.23

6.00 1.97 3.05

8.00 2.53 3.16

10.00 3.26 3.0712.00 3.81 3.15

The electrodes take part in the chemical

reaction (anode is consumed here)

This process is called Active Electrolysis

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5f(x) = 0.32x - 0.00

Copper Sulfate Solution

Voltage (V)

Current(Amps)


43/43

Current vs Voltage Curve for a Semiconductor Diode:

Forward Bias Reverse Bias

Voltage Current Voltage Current

Volts milliamps Volts microamps

V mA V uA

0.00 0.00 0.00 0.00

0.10 0.70 -0.40 -0.50

0.20 1.30 -0.80 -0.60

0.30 2.30 -1.20 -1.20

0.40 4.10 -1.60 -1.38

0.50 10.00 -2.00 -1.90

0.60 22.00 -2.40 -2.23

0.70 47.00 -2.80 -2.51

0.80 100.00 -3.20 -2.87

-4 -3 -2 -1 0 1 2

-20

0

20

40

60

80

100

Semiconductor Diode

Voltage (V)

Current(milliAmps)

Physics Experiment Calculations

Documents