Experimental Measurements in the Physics Laboratory

Desirable Outcomes:
1. Verify some physical concepts and theories in a quantitative manner.
2. Learn the inherent limitations involved when the physical theories are applied to physical situations in real life.
3. Become familiar with a variety of instruments; make reliable measurements with these instruments and determine the size of the measurement uncertainty inherent in each instrument.
4. Learn the role of the experimental uncertainty in the physical measurements; find ways to minimize experimental uncertainty and appreciate the techniques of careful measurement.
5. Perform calculations with the appropriate number of significant figures.
6. Analyze data by calculations; plot and analyze graphs that illustrate functional relationships.
7. Become aware of some problems encountered in all physical measurements, which include dealing with equipment problems.
8. Maintain a complete, well-organized laboratory notebook.

Minimizing Experimental Errors

All physical measurements are subject to uncertainties that depend on the measuring instruments used and the experiment conditions. Any uncertainty in a single measurement will result in an uncertainty of the final experimental result. These uncertainties are often referred to as experimental errors!

Types of Experimental Errors

• Systematic errors
• Personal errors (or Mistakes)
• Random Errors

Systematic errors

Systematic errors usually cause the results of a measurement to be consistently too high or too low below the true value. These errors may be due to:
• Faulty instrument - due to poor calibration or zero offset;
• Theoretical over-simplification of the system - when all the variables that affect a system are not taken into account. An example is when frictional effects are neglected in the theoretical problem.
Consequently, there is always a significant discrepancy between the expected theoretical results and the experimental results obtained when these frictional effects cannot be ignored.
An experimenter's skill is crucial in identifying, preventing, and minimizing any obvious systematic errors as much as possible. Unfortunately, it is very difficult to reliably identify and estimate systematic errors.

Personal errors (or Mistakes)

Personal errors arise from the mistakes of the experimenter. Observational mistakes may be due to the personal bias or carelessness of the experimenter while reading the scale of an instrument. Arithmetic mistakes usually occur while performing the needed calculations. This class of errors can be completely eliminated if the experimenter exercises utmost caution and skepticism while performing the experiment. If the scales are read incorrectly or if the calculations are wrongly carried out, the entire result will be wrong! Therefore, the experimenter is strongly encouraged to cross-check the data and calculations. In a lab group, each partner should independently read the data and check any calculations for accuracy.

Random errors

Random errors are usually due to unknown and unpredictable variations in the experimental conditions. The sources of these random errors cannot always be identified and can never be totally eliminated in any measurement. These random errors may be:
• Observational - unbiased inconsistency of an observer in determining the measurement readings of an instrument. This often occurs in the estimation of the last digit when reading the scale of a measuring device between the smallest division.
• Environmental - physical variations that may affect the equipment or the experiment setup such as fluctuations in the line voltage, temperature changes, or mechanical vibrations.

This class of errors usually causes about half of the measurements to be too high and the other half of the measurements to be too low. Fortunately, random errors can be determined by statistical analysis and are sometimes referred to as statistical errors. Due to the random nature of these errors, their effect on the experimental results can be reduced by repeating the measurements as many times as possible so that the erroneous results become statistically insignificant.

Accuracy and Precision

The objective in most physical science experiments is the measurement of the "accepted" or "true" values of well-known physical quantities (as stated in textbooks and physics handbooks). However, there always exists some difference between the "measured" value and the "true" value.

The accuracy of a measurement is a measure of how close the measured value is to the true value. The accuracy depends on systematic errors and thus measures the correctness of the experimental measurement.

The precision of a measurement is a measure of how reliable or how reproducible the results of the measurement are when repeated. The precision depends on random errors and thus measures the uncertainty in the result.

It must be noted that sometimes a measurement appears to be highly accurate but with very poor precision. In such situations, the question arises whether or not such results should be considered as actually meaningful. Unless a measurement has a high precision, its accuracy cannot be considered as realistic. When a measurement has a high precision but poor accuracy, it is often an indication of the presence of systematic errors.