Candidate 9 evidence...Candidate 9 evidence Results Copper Wire Reading radius (m) Reading Length of...

Candidate 9 evidence

Results

Copper Wire

Reading radius (m) Reading Length of wire (m)

1 0.00025

1 0.92

2 0.00025

2 0.86

Table 1

Mass on Hanger (kg) Load (N) Micrometer Screw Reading (mm)

Loading Unloading

0.00 0.00 0.00 0.99

0.10 0.98 0.04 1.03

0.20 1.96 0.16 1.17

0.30 2.94 0.32 1.32

0.40 3.92 0.50 1.40

0.50 4.90 0.57 1.41

0.60 5.88 0.74 1.45

Adv Higher Physics Project 2019 Candidate 9

SQA | www.understandingstandards.org.uk 1 of 34

0.70 6.86 0.93 1.53

0.80 7.84 1.30 1.62

0.90 8.82 1.51 1.69

1.00 9.80 1.72 1.72

Table 2


Loading Unloading

0.00 0.00 0.00 0.93

0.10 0.98 0.06 1.07

0.20 1.96 0.20 1.23

0.30 2.94 0.36 1.38

0.40 3.92 0.52 1.44

0.50 4.90 0.63 1.47

0.60 5.88 0.82 1.51

0.70 6.86 1.03 1.61

0.80 7.84 1.40 1.70

0.90 8.82 1.63 1.77

1.00 9.80 1.82 1.82



Average Table

Mass on Hanger (kg) Micrometer Screw Reading (mm) Load (N) Extension (m)

Loading Unloading mean

0.000 0.000 0.960 0.480 0.000 4.800 ×10-4

0.100 0.050 1.050 0.550 0.980 5.500 ×10-4

0.200 0.180 1.200 0.690 1.960 6.900 ×10-4

0.300 0.340 1.350 0.845 2.940 8.450 ×10-4

0.400 0.510 1.420 0.965 3.920 9.650 ×10-4

0.500 0.600 1.440 1.020 4.900 1.020 ×10-3

0.600 0.780 1.480 1.130 5.880 1.130 ×10-3

0.700 0.980 1.570 1.275 6.860 1.275 ×10-3

0.800 1.350 1.660 1.505 7.840 1.505 ×10-3

0.900 1.570 1.730 1.650 8.820 1.650 ×10-3

1.000 1.770 1.770 1.770 9.800 1.770 ×10-3



y = 0.0001x + 0.0004

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0 2 4 6 8 10 12

Exte

nsi

on

(m

)

Load (N)

Extension vs Load - Copper



Example Calculation

Calculation of the mean values

Sum of readings

Number of readings

0.00025+0.00025

2

0.00025m

r

r

r

Calculation for cross-sectional area:

2

2

7

7 2

(0.00025)

1.963495... 10

1.96 10

A r

A

A

A m

Calculation for mean micrometer reading:

Sum of readings

Number of readings

0.050+1.050

2

0.550mm

x

x

x

To convert into metres:

0.001

0.001 0.550

0.00055

x x

x

x m

This calculation is then repeated for all values of x.

Calculation for the load:

0.1 9.8

0.98

W mg

W

W N



This calculation is then repeated for all values of m.

Calculating the Young’s modulus:

7

10

gradient

0.89

1.96 10 0.0001

4.540816... 10

45.4 (3 . )

lE

A

E

E Pa

E GPa s f



Aluminium Wire


1 0.00023

1 0.96

2 0.00023

2 0.94

Table 1


Loading Unloading

0.00 0.00 0.00 1.03

0.10 0.98 0.18 1.10

0.20 1.96 0.35 1.17

0.30 2.94 0.49 1.33

0.40 3.92 0.60 1.46

0.50 4.90 0.76 1.52

0.60 5.88 0.88 1.57

0.70 6.86 1.09 1.64

0.80 7.84 1.24 1.74

0.90 8.82 1.46 1.83

1.00 9.80 1.85 1.85

Table 2


Loading Unloading

0.00 0.00 0.00 0.99

0.10 0.98 0.14 1.06

0.20 1.96 0.31 1.13

0.30 2.94 0.43 1.29

0.40 3.92 0.54 1.38

0.50 4.90 0.68 1.48

0.60 5.88 0.78 1.53

0.70 6.86 1.17 1.58

0.80 7.84 1.20 1.66

0.90 8.82 1.42 1.79

1.00 9.80 1.79 1.79



Average Table



0.000 0.000 1.010 0.505 0.000 5.050 × 10-4

0.100 0.160 1.080 0.620 0.980 6.200 × 10-4

0.200 0.330 1.150 0.740 1.960 7.400 × 10-4

0.300 0.460 1.310 0.885 2.940 8.850 × 10-4

0.400 0.570 1.420 0.995 3.920 9.950 × 10-4

0.500 0.720 1.500 1.110 4.900 1.110 × 10-3

0.600 0.830 1.550 1.190 5.880 1.190 × 10-3

0.700 1.130 1.610 1.370 6.860 1.370 × 10-3

0.800 1.220 1.700 1.460 7.840 1.460 × 10-3

0.900 1.440 1.810 1.625 8.820 1.625 × 10-3

1.000 1.820 1.820 1.820 9.800 1.820 × 10-3


10

gradient

0.95

0.000000166 0.0001

5.71634... 10

57.2 (3 . )

lE

A

E

E Pa

E GPa s f



y = 0.0001x + 0.0005

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0 2 4 6 8 10 12

Exte

nsi

on

(m

)

Load (N)

Etension (m) - Aluminium



Stainless Steel


1 0.00023

1 0.94

2 0.00023

2 0.98

Table 1


Loading Unloading

0.00 0.00 0.00 0.75

0.10 0.98 0.17 1.02

0.20 1.96 0.36 1.17

0.30 2.94 0.58 1.27

0.40 3.92 0.90 1.46

0.50 4.90 1.13 1.55

0.60 5.88 1.25 1.65

0.70 6.86 1.37 1.75

0.80 7.84 1.60 1.76

0.90 8.82 1.81 1.87

1.00 9.80 2.03 2.03

Table 2


Loading Unloading

0.00 0.00 0.00 0.81

0.10 0.98 0.19 1.06

0.20 1.96 0.40 1.21

0.30 2.94 0.60 1.33

0.40 3.92 0.94 1.48

0.50 4.90 1.19 1.59

0.60 5.88 1.29 1.67

0.70 6.86 1.41 1.79

0.80 7.84 1.66 1.84

0.90 8.82 1.89 1.93

1.00 9.80 2.05 2.05



Average Table



0.000 0.000 0.780 0.390 0.000 3.900 × 10-4

0.100 0.180 1.040 0.610 0.980 6.100 × 10-4

0.200 0.380 1.190 0.785 1.960 7.850 × 10-4

0.300 0.590 1.300 0.945 2.940 9.450 × 10-4

0.400 0.920 1.470 1.195 3.920 1.195 × 10-3

0.500 1.160 1.570 1.365 4.900 1.365 × 10-3

0.600 1.270 1.660 1.465 5.880 1.465 × 10-3

0.700 1.390 1.770 1.580 6.860 1.580 × 10-3

0.800 1.630 1.800 1.715 7.840 1.715 × 10-3

0.900 1.850 1.900 1.875 8.820 1.875 × 10-3

1.000 2.040 2.040 2.040 9.800 2.040 × 10-3


10

gradient

0.96

0.000000166 0.0002

2.891566... 10

28.9 (3 . )

lE

A

E

E Pa

E GPa s f



y = 0.0002x + 0.0005

0

0.0005

0.001

0.0015

0.002

0.0025

0 2 4 6 8 10 12

Exte

nsi

on

(m

)

Load (N)

Etension vs Load - Stainless Steel



Uncertainties

Scale reading uncertainties Calibration uncertainties Measuring length (metre stick): ±5×10-4m Measuring length (metre stick): ±5×10-4m Measuring radius (micrometer): ±5×10-7m Measuring radius (micrometer): ±2×10-6m Measuring extension (screw gauge): ±5×10-

7m Measuring extension (screw gauge): ±1×10-

5m

Copper Wire

Mass on Hanger (kg)

Micrometer Screw Reading (mm) Load (N) Extension (m)


0.000 ± 1% 0.000 ± 0.011

0.960 ± 0.03

0.480 ± 0.03

0.000 ± 1%

4.800 ×10-4 ± 3×10-5

0.100 ± 1% 0.050 ± 0.01*

1.050 ± 0.02

0.550 ± 0.02

0.980 ± 1%

5.500 ×10-4 ± 2×10-5

0.200 ± 1% 0.180 ± 0.02

1.200 ± 0.04

0.690 ± 0.04

1.960 ± 1%

6.900 ×10-4 ± 4×10-5

0.300 ± 1% 0.340 ± 0.02

1.350 ± 0.03

0.845 ± 0.04

2.940 ± 1%

8.450 ×10-4 ± 4×10-5

0.400 ± 1% 0.510 ± 0.01*

1.420 ± 0.02

0.965 ± 0.02

3.920 ± 1%

9.650 ×10-4 ± 2×10-5

0.500 ± 1% 0.600 ± 0.03

1.440 ± 0.03

1.020 ± 0.04

4.900 ± 1%

1.020 ×10-3 ± 4×10-5

0.600 ± 1% 0.780 ± 0.04

1.480 ± 0.03

1.130 ± 0.05

5.880 ± 1%

1.130 ×10-3 ± 5×10-5

0.700 ± 1% 0.980 ± 0.05

1.570 ± 0.04

1.275 ± 0.06

6.860 ± 1%

1.275 ×10-3 ± 6×10-5

0.800 ± 1% 1.350 ± 0.05

1.660 ± 0.04

1.505 ± 0.06

7.840 ± 1%

1.505 ×10-3 ± 6×10-5

0.900 ± 1% 1.570 ± 0.06

1.730 ± 0.04

1.650 ±0.07

8.820 ± 1%

1.650 ×10-3 ± 7×10-5

1.000 ± 1% 1.770 ±0.05 1.770 ± 0.05

1.770 ± 0.07

9.800 ± 1%

1.770 ×10-3 ± 7×10-5

Example Calculations

Uncertainty of mass on hanger and load:

The masses were measured on an accurate balance to give a value of 989.845g. This means

there was a discrepancy of 1%. This percentage uncertainty was also used for the load

values.

Uncertainty of micrometer screw reading:

Calibration uncertainty (screw gauge): ±1×10-5m

Scale reading uncertainty (screw gauge): ±5×10-7m



Random uncertainty (screw gauge):

(e.g. 2 row)

max.value - min.valueRandom uncertainty =

number of values

0.060 - 0.040Random uncertainty =

2

Random uncertainty = 0.01 mm

Since the value calculated was exactly 0.01 mm only one significant figure can be given.



This value is not combined with the scale reading uncertainty or the calibration uncertainty

since they are negligible compared to the random uncertainty. To get the uncertainty in the mean the uncertainties of the loading and unloading values are

combined:

2 2Mean uncertainty = (0.01) (0.02)

Mean uncertainty = 0.02236...

Mean uncertainty = 0.02mm

Since the value is an uncertainty it is given to one significant figure.

Uncertainty of extension:

The value for the uncertainty of the extension is the value of the uncertainty in the screw

gauge converted to metres.

5

Extension uncertainty = 0.01 0.001

Extension uncertainty =1 10 m

The uncertainties would then be plotted on the graph however these values are too small to

be graphed.

Overall Uncertainty:

To find the overall uncertainty the LINEST function on Excel is used.

(e.g. Copper wire)

Gradient: 0.000132839

Uncertainty in gradient: 4.91797 × 10-6

Y-intercept: 0.000429091

Uncertainty in y-intercept: 2.85132 × 10-5

These values are calculated by the LINEST function on Excel. From these, the percentage

uncertainty in the gradient is then calculated:

6

4

uncertainty in gradientPercentage uncertainty in gradient = 100

gradient

4.91797 10Percentage uncertainty in gradient = 100

1.32839 10

Percentage uncertainty = 3.702...%

This percentage uncertainty is then used to find the uncertainty in the calculated Young’s

modulus.



Young's Modulus Percentage uncertaintyUncertainty in Young's Modulus =

100

45.4 3.702...Uncertainty in Young's Modulus =

100

Uncertainty in Young's Modulus = 1.6808...

Uncertainty in Young's Modulus

= 1.7



Aluminium Wire

Mass on Hanger (kg)



0.000 ± 1% 0.000 ± 0.011

1.010 ± 0.02

0.505 ± 0.02

0.000 ± 1%

5.050 × 10-4 ± 2×10-5

0.100 ± 1% 0.160 ± 0.02

1.080 ± 0.02

0.620 ± 0.03

0.980 ± 1%

6.200 × 10-4 ± 3×10-5

0.200 ± 1% 0.330 ± 0.02

1.150 ± 0.02

0.740 ± 0.03

1.960 ± 1%

7.400 × 10-4 ± 3×10-5

0.300 ± 1% 0.460 ± 0.03

1.310 ± 0.02

0.885 ± 0.04

2.940 ± 1%

8.850 × 10-4 ± 4×10-5

0.400 ± 1% 0.570 ± 0.03

1.420 ± 0.04

0.995 ± 0.05

3.920 ± 1%

9.950 × 10-4 ± 5×10-5

0.500 ± 1% 0.720 ± 0.04

1.500 ± 0.02

1.110 ± 0.04

4.900 ± 1%

1.110 × 10-3 ± 4×10-5

0.600 ± 1% 0.830 ± 0.05

1.550 ± 0.02

1.190 ± 0.05

5.880 ± 1%

1.190 × 10-3 ± 5×10-5

0.700 ± 1% 1.130 ± 0.04

1.610 ± 0.03

1.370 ± 0.05

6.860 ± 1%

1.370 × 10-3 ± 5×10-5

0.800 ± 1% 1.220 ± 0.02

1.700 ± 0.04

1.460 ± 0.04

7.840 ± 1%

1.460 × 10-3 ± 4×10-5

0.900 ± 1% 1.440 ± 0.02

1.810 ± 0.02

1.625 ± 0.03

8.820 ± 1%

1.625 × 10-3 ± 3×10-5

1.000 ± 1% 1.820 ± 0.03

1.820 ± 0.03

1.820 ± 0.04

9.800 ± 1%

1.820 × 10-3 ± 4×10-5

LINEST Calculation

Gradient: 0.000129128






Stainless Steel Wire

Mass on Hanger (kg)



0.000 ± 1% 0.000 ± 0.011

0.780 ± 0.03

0.390 ± 0.03

0.000 ± 1%

3.900 × 10-4 ± 3×10-5

0.100 ± 1% 0.180 ± 0.01*

1.040 ± 0.02

0.610 ± 0.02

0.980 ± 1%

6.100 × 10-4 ± 2×10-5

0.200 ± 1% 0.380 ± 0.02

1.190 ± 0.02

0.785 ± 0.03

1.960 ± 1%

7.850 × 1 ± 2×10-

50-4

0.300 ± 1% 0.590 ± 0.01*

1.300 ± 0.03

0.945 ± 0.03

2.940 ± 1%

9.450 × 10-4 ± 3×10-5

0.400 ± 1% 0.920 ± 0.02

1.470 ± 0.01*

1.195 ± 0.02

3.920 ± 1%

1.195 × 10-3 ± 2×10-5

0.500 ± 1% 1.160 ± 0.03

1.570 ± 0.02

1.365 ± 0.04

4.900 ± 1%

1.365 × 10-3 ± 4×10-5

0.600 ± 1% 1.270 ± 0.02

1.660 ± 0.01*

1.465 ± 0.02

5.880 ± 1%

1.465 × 10-3 ± 2×10-5

0.700 ± 1% 1.390 ± 0.02

1.770 ± 0.02

1.580 ± 0.03

6.860 ± 1%

1.580 × 10-3 ± 3×10-5

0.800 ± 1% 1.630 ± 0.03

1.800 ± 0.05

1.715 ± 0.06

7.840 ± 1%

1.715 × 10-3 ± 6×10-5

0.900 ± 1% 1.850 ± 0.04

1.900 ± 0.03

1.875 ± 0.05

8.820 ± 1%

1.875 × 10-3 ± 5×10-5

1.000 ± 1% 2.040 ± 0.01*

2.040 ± 0.01*

2.040 ± 0.01*

9.800 ± 1%

2.040 × 10-3 ± 1×10-5*

LINEST Calculation

Gradient: 0.00016364




* Calculated value was given as exactly 0.01 or 1 × 10-5 therefore 2 significant figures could

not be used.

Conclusion

The value obtained for the Young’s modulus of copper wire was (45.4 ± 1.7) GPa.

The value obtained for the Young’s modulus of aluminium wire was (57.2 ± 1.4) GPa.

The value obtained for the Young’s modulus of stainless steel wire was (28.9 ± 1.0)* GPa.

* Calculated value was given as exactly 1.0 therefore 2 significant figures could not be used.

Discussion

The values obtained for all three wires are less than the given values from Engineering

Toolbox. A possible reason for this is because the values given online are just for the



material itself not for the wire form. Theoretically the Young’s modulus should not be

affected by this however the manufacturing of the wire could alter the internal stress and

strain, thereby reducing the overall Young’s modulus.

The use of the auxiliary wire eliminates any changes in length of the wire due to

temperature changes during the experiments.

The cross-sectional area of the wires may not be consistent. Three readings of the radius

were taken at different points on the wire and an average was calculated to account for this.

It was found that on all three wires the readings for the radius were the same, this means

that if the wires did have inconsistent cross-sectional areas it was a small discrepancy since

it was not picked up in three measurements.

Due to the use of apparatus from previous students the ceiling fixture was worn, and this

could encourage slipping. To account for this, plyers were used to tighten the metal fixtures

into place.

If the experiment was to truly show the Young’s modulus of these wires, then the wires

should be able to return to their original length after the removal of the masses. However,

we can see from the results of all three experiments that this did not occur. This implies

that the wires were permanently misshapen by the weight of the masses.

In the previous examples of this experiment greater total masses were used. Masses this

great were originally used but this resulted in the wires slipping from the ceiling fixture.

This meant that smaller masses had to be used in the final experiment.



Results

Copper wire


1 0.00023

1 0.94

2 0.00023

2 0.98



Table 1

Mass on Hanger (kg) Load (N) Metre Stick Reading (mm)

Loading Unloading

0.00 0.00 0.00 1.50

0.10 0.98 0.50 1.50

0.20 1.96 0.50 1.50

0.30 2.94 1.00 2.00

0.40 3.92 1.00 2.00

0.50 4.90 1.00 2.00

0.60 5.88 1.50 2.00

0.70 6.86 1.50 2.00

0.80 7.84 2.00 2.00

0.90 8.82 2.00 2.50

1.00 9.80 2.50 2.50

Table 2

Mass on Hanger (kg) Load (N) Metre Stick Reading (mm)

Loading Unloading

0.00 0.00 0.00 1.50

0.10 0.98 0.50 1.50

0.20 1.96 1.00 2.00

0.30 2.94 1.00 2.00

0.40 3.92 1.00 2.00

0.50 4.90 1.50 2.00

0.60 5.88 1.50 2.00

0.70 6.86 1.50 2.50

0.80 7.84 2.00 2.50

0.90 8.82 2.50 2.50

1.00 9.80 2.50 2.50



Average Table

Mass on Hanger

(kg) Metre Stick Reading (mm) Load (N) Extension (m)

Loading Unloading Mean

0.000 0.000 1.500 0.750 0.000 7.500 × 10-4

0.100 0.500 1.500 1.000 0.980 1.000 × 10-3

0.200 0.750 1.750 1.250 1.960 1.250 × 10-3

0.300 1.000 2.000 1.500 2.940 1.500 × 10-3

0.400 1.000 2.000 1.500 3.920 1.500 × 10-3

0.500 1.250 2.000 1.625 4.900 1.625 × 10-3

0.600 1.500 2.000 1.750 5.880 1.750 × 10-3

0.700 1.500 2.250 1.875 6.860 1.875 × 10-3

0.800 2.000 2.250 2.125 7.840 2.125 × 10-3

0.900 2.250 2.500 2.375 8.820 2.375 × 10-3

1.000 2.500 2.500 2.500 9.800 2.500 × 10-3


7 4

10

gradient

0.78

1.8095... 10 2 10

2.16666... 10

21.6 (3 . )

lE

A

E

E Pa

E GPa s f



y = 0.0002x + 0.0008

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 2 4 6 8 10 12

Exte

nsi

on

(m

)

Load (N)

Extension vs Load - Copper



Aluminium wire


1 0.00023

1 0.81

2 0.00023

2 0.87

Table 1

Mass on Hanger (kg)

Load (N) Metre Stick Reading (mm)

Loading Unloading

0.00 0.00 0.00 2.00

0.10 0.98 0.50 2.50

0.20 1.96 0.50 2.50

0.30 2.94 1.00 2.50

0.40 3.92 1.00 2.50

0.50 4.90 1.50 3.00

0.60 5.88 2.00 3.00

0.70 6.86 2.50 3.00

0.80 7.84 3.00 3.00

0.90 8.82 3.00 3.50

1.00 9.80 3.50 3.50

Table 2

Mass on Hanger (kg)


Loading Unloading

0.00 0.00 0.00 2.00

0.10 0.98 0.50 2.00

0.20 1.96 1.00 2.50

0.30 2.94 1.00 2.50

0.40 3.92 1.50 3.00

0.50 4.90 2.00 3.00

0.60 5.88 2.50 3.00

0.70 6.86 3.00 3.00

0.80 7.84 3.00 3.50

0.90 8.82 3.50 3.50

1.00 9.80 3.50 3.50



Mass on Hanger (kg)

Metre Stick Reading (mm) Load (N) Extension (m)


0.000 0.00 2.00 1.000 0.000 1.000 × 10-3

0.100 0.50 2.25 1.375 0.980 1.375 × 10-3

0.200 0.75 2.50 1.625 1.960 1.625 × 10-3

0.300 1.00 2.50 1.75 2.940 1.75 × 10-3

0.400 1.25 2.75 2.000 3.920 2.000 × 10-3

0.500 1.75 3.00 2.375 4.900 2.375 × 10-3

0.600 2.25 3.00 2.625 5.880 2.625 × 10-3

0.700 2.75 3.00 2.875 6.860 2.875 × 10-3

0.800 3.00 3.25 3.125 7.840 3.125 × 10-3

0.900 3.25 3.50 3.375 8.820 3.375 × 10-3

1.000 3.50 3.50 3.500 9.800 3.500 × 10-3


7 4

10

gradient

0.84

1.6619... 10 3 10

1.68481... 10

16.8 (3 . )

lE

A

E

E Pa

E GPa s f



y = 0.0003x + 0.0011

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0 2 4 6 8 10 12

Exte

nsi

on

(m

)

Load (N)

Extension vs Load - Aluminium



Stainless Steel


1 0.00023

1 0.71

2 0.00023

2 0.75

Table 1

Mass on Hanger (kg)


Loading Unloading

0.00 0.00 0.00 3.50

0.10 0.98 1.00 4.00

0.20 1.96 1.50 4.00

0.30 2.94 2.50 4.00

0.40 3.92 3.00 4.00

0.50 4.90 3.50 4.50

0.60 5.88 4.00 4.50

0.70 6.86 4.00 4.50

0.80 7.84 4.50 5.00

0.90 8.82 5.00 5.00

1.00 9.80 5.00 5.00

Table 2

Mass on Hanger (kg)


Loading Unloading

0.00 0.00 0.00 3.50

0.10 0.98 1.00 3.50

0.20 1.96 1.00 4.00

0.30 2.94 1.50 4.00

0.40 3.92 2.50 4.50

0.50 4.90 3.00 4.50

0.60 5.88 3.50 4.50

0.70 6.86 4.00 4.50

0.80 7.84 4.50 5.00

0.90 8.82 5.00 5.50

1.00 9.80 5.50 5.50



Average Table

Mass on Hanger

(kg) Metre Stick Reading (mm) Load (N) Extension (m)


0.000 0.000 3.500 1.750 0.000 1.750 × 10-3

0.100 1.000 3.750 2.375 0.980 2.375 × 10-3

0.200 1.250 4.000 2.625 1.960 2.625 × 10-3

0.300 2.000 4.000 3.000 2.940 3.000 × 10-3

0.400 2.750 4.250 3.500 3.920 3.500 × 10-3

0.500 3.250 4.500 3.875 4.900 3.875 × 10-3

0.600 3.750 4.500 4.125 5.880 4.125 × 10-3

0.700 4.000 4.500 4.250 6.860 4.250 × 10-3

0.800 4.500 5.000 4.750 7.840 4.750 × 10-3

0.900 5.00 5.250 5.125 8.820 5.125 × 10-3

1.000 5.250 5.250 5.250 9.800 5.250 × 10-3


7 4

10

gradient

0.73

1.6619... 10 4 10

... 11.099 0

11.0 (3 )

397

.

lE

A

E

E Pa

E GPa s f



y = 0.0004x + 0.002

0

0.001

0.002

0.003

0.004

0.005

0.006

0 2 4 6 8 10 12

Exte

nsi

on

(m

)

Load (N)

Extension vs Load - Aluminium



Uncertainties

Scale reading uncertainties Calibration uncertainties Measuring length (metre stick): ±5×10-4m Measuring length (metre stick): ±5×10-4m

Copper Wire

Mass on Hanger (kg)



0.000 ± 1% 0.000 ± 0.0005

1.500 ± 0.0005

0.750 ± 0.0007

0.000 ± 1%

7.500 × 10-4 ± 7 × 10-7

0.100 ± 1% 0.500 ± 0.0005

1.500 ± 0.0005

1.000 ± 0.0007

0.980 ± 1%

1.000 × 10-3 ± 7 × 10-7

0.200 ± 1% 0.750 ± 0.25

1.750 ± 0.25

1.250 ± 0.4 1.960 ± 1%

1.250 × 10-3 ± 4 × 10-4

0.300 ± 1% 1.000 ± 0.0005

2.000 ± 0.0005

1.500 ± 0.0007

2.940 ± 1%

1.500 × 10-3 ± 7 × 10-7

0.400 ± 1% 1.000 ± 0.0005

2.000 ± 0.0005

1.500 ± 0.0007

3.920 ± 1%

1.500 × 10-3 ± 7 × 10-7

0.500 ± 1% 1.250 ± 0.25

2.000 ± 0.0005

1.625 ± 0.25

4.900 ± 1%

1.625 × 10-3 ± 2.5 × 10-4

0.600 ± 1% 1.500 ± 0.0005

2.000 ± 0.0005

1.750 ± 0.0007

5.880 ± 1%

1.750 × 10-3 ± 7 × 10-7

0.700 ± 1% 1.500 ± 0.0005

2.250 ± 0.25

1.875 ± 0.25

6.860 ± 1%

1.875 × 10-3 ± 2.5 × 10-4

0.800 ± 1% 2.000 ± 0.0005

2.250 ± 0.25

2.125 ± 0.25

7.840 ± 1%

2.125 × 10-3 ± 2.5 × 10-4

0.900 ± 1% 2.250 ± 0.25

2.500 ± 0.0005

2.375 ± 0.25

8.820 ± 1%

2.375 × 10-3 ± 2.5 × 10-4

1.000 ± 1% 2.500 ± 0.0005

2.500 ± 0.0005

2.500 ± 0.0007

9.800 ± 1%

2.500 × 10-3 ± 7 × 10-7

LINEST Calculation

Gradient: 0.000165816






Aluminium Wire

Mass on Hanger (kg)



0.000 ± 1% 0.00 ± 0.0005

2.00 ± 0.0005

1.000 ± 0.0007

0.000 ± 1%

1.000 × 10-3 ± 7 × 10-7

0.100 ± 1% 0.50 ± 0.0005

2.25 ± 0.25

1.375 ± 0.25

0.980 ± 1%

1.375 × 10-3 ± 2.5 × 10-4

0.200 ± 1% 0.75 ± 0.25

2.50 ± 0.0005

1.625 ± 0.25

1.960 ± 1%

1.625 × 10-3 ± 2.5 × 10-4

0.300 ± 1% 1.00 ± 0.0005

2.50 ± 0.0005

1.75 ± 0.0007

2.940 ± 1%

1.750 × 10-3 ± 7 × 10-7

0.400 ± 1% 1.25 ± 0.25

2.75 ± 0.25 2.000 ± 0.4

3.920 ± 1%

2.000 × 10-3 ± 4 × 10-4

0.500 ± 1% 1.75 ± 0.25

3.00 ± 0.0005

2.375 ± 0.25

4.900 ± 1%

2.375 × 10-3 ± 2.5 × 10-4

0.600 ± 1% 2.25 ± 0.25

3.00 ± 0.0005

2.625 ± 0.25

5.880 ± 1%

2.625 × 10-3 ± 2.5 × 10-4

0.700 ± 1% 2.75 ± 0.25

3.00 ± 0.0005

2.875 ± 0.25

6.860 ± 1%

2.875 × 10-3 ± 2.5 × 10-4

0.800 ± 1% 3.00 ± 0.0005

3.25 ± 0.25

3.125 ± 0.25

7.840 ± 1%

3.125 × 10-3 ± 2.5 × 10-4

0.900 ± 1% 3.25 ± 0.25

3.50 ± 0.0005

3.375 ± 0.25

8.820 ± 1%

3.375 × 10-3 ± 2.5 × 10-4

1.000 ± 1% 3.50 ± 0.0005

3.50 ± 0.0005

3.500 ± 0.0007

9.800 ± 1%

3.500 × 10-3 ± 7 × 10-7

LINEST Calculation

Gradient: 0.000258581






Stainless Steel Wire

Mass on Hanger (kg)



0.000 ± 1% 0.000 ± 0.0005

3.500 ± 0.0005

1.750 ± 0.0007

0.000 ± 1%

1.750 × 10-3 ± 7 ×10-7

0.100 ± 1% 1.000 ± 0.0005

3.750 ± 0.25

2.375 ± 0.25

0.980 ± 1%

2.375 × 10-3 ± 2.5 ×10-4

0.200 ± 1% 1.250 ± 0.25

4.000 ± 0.0005

2.625 ± 0.25

1.960 ± 1%

2.625 × 10-3 ± 2.5 ×10-4

0.300 ± 1% 2.000 ± 0.5

4.000 ± 0.0005 3.000 ± 0. 5

2.940 ± 1%

3.000 × 10-3 ± 5 ×10-4

0.400 ± 1% 2.750 ± 0.25

4.250 ± 0.25 3.500 ± 0.4

3.920 ± 1%

3.500 × 10-3 ± 4 ×10-4

0.500 ± 1% 3.250 ± 0.25

4.500 ± 0.0005

3.875 ± 0.25

4.900 ± 1%

3.875 × 10-3 ± 2.5 ×10-4

0.600 ± 1% 3.750 ± 0.25

4.500 ± 0.0005

4.125 ± 0.25

5.880 ± 1%

4.125 × 10-3 ± 2.5 ×10-4

0.700 ± 1% 4.000 ± 0.0005

4.500 ± 0.0005

4.250 ± 0.0007

6.860 ± 1%

4.250 × 10-3 ± 7 ×10-7

0.800 ± 1% 4.500 ± 0.0005

5.000 ± 0.0005

4.750 ± 0.0007

7.840 ± 1%

4.750 × 10-3 ± 7 ×10-7

0.900 ± 1% 5.00 ± 0.0005

5.250 ± 0.25

5.125 ± 0.25

8.820 ± 1%

5.125 × 10-3 ± 2.5 ×10-4

1.000 ± 1% 5.250 ± 0.25

5.250 ± 0.25 5.250 ± 0.4

9.800 ± 1%

5.250 × 10-3 ± 4 ×10-4

LINEST Calculation

Gradient: 0.000352505




Conclusion

The value obtained for the Young’s modulus of copper wire was (21.6 ± 1.4) GPa.

The value obtained for the Young’s modulus of aluminium wire was (16.8 ± 1.1) GPa.

The value obtained for the Young’s modulus of stainless steel wire was (11.0 ± 0.7) GPa.



Discussion

The values calculated from this experiment are, again, much lower than the values given by

Engineering Toolbox. This could also be due to the metals being in the form of wires.

This experiment also does not have any sort of auxiliary wire to account for changes in

temperature. The experiments were conducted in different labs, so the temperature may

have varied between them.

Due to the way the wires were held in place in this experiment, slipping could occur. To

minimise this the wires were wrapped around a wooden block before clamping, however if

slipping did occur this could skew results and could explain why the experimental results are

so different to the given values.

Again, the results show that the length does not return to its original length when the

masses are removed this means the true Young’s modulus could not have been measured.

The measurements in this experiment were made on a metre stick which is less accurate

than the screw gauge used in experiment 1 which means the results from this experiment

are therefore less reliable. A more accurate measurement tool could have been used e.g. a

travelling microscope, this would have reduced the scale reading uncertainty in the

extension.

Project Conclusion and Evaluation

Conclusion

This project found the experimental values for Young’s Modulus in selected metal wires

through two experiments. These experiments were the use of Searle’s Apparatus and the

bench pulley method. The values found are:

Metal Wire Given

Value

(GPa)

Calculated Value (3 s.f)

(GPa)

Searle’s Apparatus

Calculated Value (3 s.f)

(GPa)

Bench Pulley

Copper 117 45.4 ± 1.7 21.6 ± 1.4

Aluminium 69 57.2 ± 1.4 16.8± 1.1

Stainless Steel 180 28.9 ± 1.0 11.0 ± 0.7

Discussion

The values found are not concordant with the given values (Engineering Toolbox, N.D.). This is due to several factors including experimental procedure and human error.

None of the overall uncertainties given are great enough to allow for the line of best fit to pass through the origin. Therefore, there was a systematic error in all the experiments, this could be due to scale reading uncertainties or calibration errors during the manufacture of the apparatus.



The results from the first experiment are closer to the given values than those from experiment 2. However smaller overall uncertainties from experiment 2 show that the bench pulley method is more precise but not more accurate than Searle’s Apparatus.

The results for aluminium wire from the first experiment are the closest to the given value. The same material tested using the other method gives a value 40.4GPa less. This is the biggest discrepancy between the two experiments, even though the first value is closes to the given value.



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