Good Example Of Statics, Measurement And Error Report

Introduction

The aims of the lab is adoption of knowledge about density via performing experiments with spherical sample and practice calculations. In the laboratory assignment, the density of the spherical sample is calculated on the basis of measurements of sphere sample diameter and weight. The replicates of measurements are performed to ensure precision and calculate errors.

The measurements of the sample dimension (diameter) are performed and recorded in Table 1.

The measurements of the sample diameter
The measurements of sample weight are presented in Table 2.

Measurements of the sample weight

Data analysis
The average value of diameter is calculated: D=D1+D2+D3++Dn10.
For example, D=2.504 + 2.50 + 2.460 + 2.482 + 2.490 + 2.492 + 2.454 + 2.492 + 2.500 + 2.49810 =2.49 mm.
The same way, the average value of mass is calculated: m = 10.03 g.
For errors assessment, we calculate σ=(Mi-Maverage)2N-1, and variance σ2.
where Mi – the measurement (diameter or weight), Maverage – the average value, N – the number of measurements. The calculations are presented in Tables 3 and 4.

The error calculation of the sample diameter

For errors assessment, we calculate standard deviation σ=0.02659=0.01 and variance σ2 = 0.002. Therefore, the percentage of diameter deviation is %σ=0.012.49=0.4%

The error calculation of the sample mass

Following the same procedure, we calculate the standard deviation and error for mass.
σ=0.06 and variance σ2 = 0.003. Therefore, the percentage of diameter deviation is % σ=0.0510.03=0.5%.

The density of the sample:

ρ=mV.

The volume is calculated as:

V = π∙d3/6,
V = π∙2.493/6 = 8.06 mm3
The density is calculated: ρ=10.038.06=1.24 kg/m3.

Discussion

The results are presented in Table 5.

The summary of the results

The obtained density value states that the object will sink in the water because its density is greater than the water density (1 g/cm3).
Density is determined experimentally by measuring mass of a sample of a known volume. Thus, the density is referred to a mass of a volume unit and it shows how compact matter is. The CI unit of density is kg/m3, so it is obvious that density shows the weight of 1 m3 of matter.
The experimental measurements are close to each other, and the error values are small. Therefore, there are no systematic errors. The errors that cause variations are random experimental errors, and they are inevitable. The sources of errors are motion of air in the laboratory (weight measurement) and instrumental error at diameter measurement. There were no intrinsic errors during the measurements.
If the systematic error occurred, it would have made the result incorrect, and it could have increased or decreased the result. The diameter measurement has the highest error due to limitation in instrument accuracy. Although this error has the highest value, the weight measurement has proportional value and thus both measurements errors contribute in the total error.

The experiment was successful since the experimental value is close to the theoretical.

Conclusions
During the lab, the successful experiment on density calculation was performed. The measurements of spherical sample (weight, diameter) were performed with high precision. The errors were less than 1%. The calculated density is close to the theoretical value.