Michaela Coyle
Partner: (Hope Spurrier)

Measurements and Uncertainties
September 6, 2013

Abstract
The Measurements and Uncertainties lab showed us how to use different instruments to measure an object and how to calculate the uncertainty. It also showed that taking multiple measurements ensures accuracy because there is always uncertainty in a measurement. We obtained an aluminum block and measured the length of the block with a meter stick, the width with a Vernier Caliper, and the thickness with a Micrometer Caliper. With each instrument, five measurements were taken and the average was calculated along with the uncertainty. The average length for the block was 9 cm, the width was 3.82 ± 0.001 cm, and the thickness was 1.04 ± 0.01 cm. By multiplying all three averages together, the volume of the block was 35.76 ± 0.34 cm3. The mass of the block was calculated by using an electronic balance and was 96.7 ± 0.1 grams. The density was calculated by dividing the mass by the volume and the result was 2.70 ± 0.03 g/cm3. The precision was calculated to be 98.9% accurate, the percent error was 0.15%, and the density was 98.75% accurate.

Results
Length of the block using the meter stick:
Trial No. i Left Edge
(cm)
Right Edge
(cm)
Length L (cm)
Deviation
(cm)

Deviation²
(cm²)
(

1
17.75
26.75
9.00
0
0
2
36.55
45.55
9.00
0
0
3
56.20
65.20
9.00
0
0
4
23.60
32.60
9.00
0
0
5
30.60
39.60
9.00
0
0
To find the average length, all the measured lengths were added together and divided by 5. The average length was 9.00 cm. To find the uncertainty we used the equation below:

Since there was no deviation, there was no uncertainty.

Width of the block using the Vernier Caliper:
Trial No. i Width W (cm)
Deviation
(cm)

Deviation²
(cm²)

1
3.81
-0.012
-1.44xE-4
2
3.83
0.008
6.4xE-5
3
3.82
-0.002
-4E-6
4
3.82
-0.002
-4E-6
5
3.83
0.008
6.4E-5
The average of the widths was found by using the same technique that was used to determine the average length and the same technique was used to determine uncertainty as well (the equation above). The average was calculated to be 3.82 cm, and the uncertainty was 0.001.
This resulted in a width of 3.82 ± 0.001.

Thickness of the block using the Micrometer Caliper:
Trial No. i Thickness T
(millimeter)
Thickness T
(centimeter)
(1 mm= 0.1 cm)
Deviation
(cm)

Deviation²
(cm²)

1
10.35
1.035
-0.0052
-2.704E-5
2
10.46
1.046
0.0058
-3.364E-5
3
10.40
1.040