REPORTING MEASUREMENT RESULTS [1]

This term you will perform 3 experiments. During an experiment you are to record all raw data in an appropriate laboratory notebook. This record of your actual measurements must be handed in with all final laboratory reports. There are two new section to be included in your report. They are:

a) Introduction. Motivate the experiment and give a concise summary of the physics involved, including any mathematical detail relevant to later discussion in the report.

b) Method. Describe the experimental method. Include a careful drawing of relevant parts of the experimental apparatus if one was not given in the laboratory manual.

These two sections should be written in your own words and in single paragraph.

An account of an experiment, as presented in a formal report, may contain many sections with headings such as introduction, materials and methods, results, analysis and conclusion. With respect to the analysis of data, best estimates of particular quantities obtained through experiment and by other means should be communicated clearly, concisely, and in a manner that is useful to others. In particular, it is necessary to provide an account of the uncertainty components and how they were evaluated. Steps in the calculation of uncertainties should be sufficiently transparent that the calculation of (for example) a standard uncertainty can be verified by others. When calculating and reporting the best estimate of a quantity and uncertainty, we should do the following.

Fully define the measurand. For example, if the electrical resistance of a metal wire is to be determined, the temperature at which the resistance is measured is an essential piece of information.

State the best estimate of the measurand found by bringing together best estimates of the particular quantities that contribute to the calculation of the measurand. The unit of measurement of the measurand must be clearly stated.

Describe the standard uncertainties that have been carried out. Show howthese evaluations have been merged in the calculation of a combined standard uncertainty.

Retain as many figures as possible in intermediate calculations, so that rounding errors do not accumulate. Once the expanded uncertainty has been determined, the best estimate of the measurand can be rounded to a ‘sensible’ number of significant figures. The analyses in this chapter were carried out with the aid of Excel. Excel retains 15 digits internally, and therefore it is assumed that rounding errors are negligible.

Quote the uncertainty to two significant figures.

Your reports will vary in length from 3 to 10 pages. A concise summary of relevant material is far more desirable than an exhaustive and wordy treatise.

Determination of the density of steel

  1. Introduction

In this section describe the purpose, theoryfor the experiment (experimental formula) and rationale for theexperiment(This describes why the experiment is being done, which may include references to previous research or a discussion of why the results are important in a broader context) and method of the experiment in your words.

  1. Purpose. The purpose of this experiment is to find the best estimate, average of the density ρ, of a steel ball bearing at ambient temperature. The experiment requires determination of the standard uncertainty in the best estimate or average of ρ and the combined uncertainty. The value for density is compared with published values for the density of steel.
  1. Theory. A fundamental property of any material is its density. If the mass of the object is m and the volume is it occupies V, then the average density of the material ρ, is defined as
  1. Method.

In this section, describe apparatus used to test the scientific model.

A steel ball bearing was weighed using an electronic balance with uncertainty of 1mg. Eight repeat measurements of the mass of the ball was made of the diameter of the ball bearing using a micrometer. The smallest scale marks on the micrometer were separated by 0.01mm. All measurements were made at (23+-1C).

  1. Results. Data analysis.

The results are a presentation of both observed and derived quantities.

Table 1 contains the values obtained for the mass of the ball bearing and values for diameter of the same bearing measured at different positions around the ball obtained through repeated measurements.

Table 1. Values of the mass and diameter of the ball bearing.

# / Mass of steel ball bearing xmi (g) / Diameter of steel ball bearing xdi (mm)
1 / 8.348 / 12.68
2 / 8.349 / 12.68
3 / 8.351 / 12.68
4 / 8.350 / 12.70
5 / 8.349 / 12.69
6 / 8.350 / 12.69
7 / 8.351
8 / 8.349
  • Calculate uncertainty of measured quantities
  • Calculate combined uncertainty of derived quantities.

(or you canderive results from fitting (least squares…) of observed data.

  • Bring equation to the form y=ax+b
  • Fitting graph. )
  1. Discussion

The discussion section is an opportunity to describe both the significance and limitation of your result. It should answer the question “What does your result mean?”It should outline the major sources of random and systematic error in an experiment. Your emphasis should be on those which are most significant, and on which you can easily place a numerical value. Wherever possible, you should try to suggest evidence as to why these may have affected your results, and include recommendations for how their effects may be minimized. These can be accompanied by suggested improvements to the experiment.

  1. Conclusion

This section is a concise summary of your experiment, main results, and their implications.The best estimate of the density of ball bearing at 23’C is ρ=7.810 x 10-3g/mm3 . The combined standard uncertainty in the best estimate of the density is ∆ρ=7.810 x 10-3g/mm3. We may compare the value obtained here for the density of the ball bearing with published values for the density of stainless steel. While the largest component to stainless steel alloy is iron, several other elements may also be present, such as nickel and chromium. The range of densities of stainless steel is normally in the range 7.73x10-3 g/mm3 to 7.96x10-3 g/mm3 as published by the company 67GMC [1]. Our results agree with the published result.

  1. Les Kirkup and Bob Frenkel. An Introduction to Uncertainty in Measurement, Cambridge, Cambridge University Press, 2006, pp. 203-210
  2. PC141: Mechanics for Life Sciences and PC1422: Thermodynamics and Waves) from the lab manuals, chapter 6,7…at
  3. You can access to a presentation about how to write lab report by Emmy Misser, manager of the Writing Center at