Finding the Density of an Aluminium Block

Uncertainty Included

Measurements

Mass (g) ±0.01g

Length (cm)±0.01cm

Width (cm)±0.01cm

Breadth (cm)±0.01cm

1 543.02 8.03 5.01 5.00

2 8.02 5.03 5.00

3 8.04 5.03 5.00

Mean value and Uncertainty

LENGTH

Mean value = 8.03 + 8.02 + 8.04 = 8.03 cm

3

Uncertainty = 8.04 – 8.02 = ±0.01 cm

2Percentage Uncertainty = 0.01 = 0.12%

8.03

WIDTH

Mean value = 5.01 + 5.03 + 5.03 = 5.02 cm

3

Uncertainty = 5.03 – 5.01 = ± 0.01 cm

2Percentage Uncertainty = 0.01 = 0.199% = 0.2%

5.02

Mean value and Uncertainty

Mean value and Uncertainty

BREADTH

Mean value = 5.00 + 5.00 + 5.00 = 5.00 cm

3

Uncertainty = ± 0.01 cm

Percentage Uncertainty = 0.01 = 0.20%

5.00

Mean value and Uncertainty

MASS

Value = 543.02g

Uncertainty = ± 0.01g

Percentage Uncertainty = 0.01 = 0.0018% = 0.00%

543.02

Results

DENSITY

ρ = m/V = 543.02 / (8.03 x 5.02 x 5.00)

ρ = 2.694 gcm-3

Uncertainty

TOTAL UNCERTAINTY

Total Uncertainty = 0.12% + 0.20% + 0.20% + 0.00% = 0.52%

UNCERTAINTY OF ANSWER

Uncertainty = 0.52 x 2.694 = ± 0.01 gcm-3

100

Answer

Density = 2.69 ± 0.01 gcm-3

True Density = 2.70 gcm-3