Sunday, January 3, 2010

1-Measurement techniques

Measurement Techniques
There are four terms often used in Experimental Physics:
1 Systematic Error
2 Random error
3 Precision
4 Accuracy

Systematic Error
Systematic error is a type of error that deviates by a fixed amount from the true value of measurement which will result in all measurements taken being faulty in one direction.
Systematic errors due to:
1. Zero error of measuring instrument. A zero error is when the initial value shown by the measuring instrument is a non-zero value when it should be zero.
2. Faulty measuring instrument. For example, if your stopwatch shows 100 seconds for an actual time of 99 seconds, everything you measure with this stopwatch will be dilated, and a systematic error is induced in your measurements. In this case, the systematic error is proportional to the measurement.
3. Inherent systematic errors in the experiment itself, which means even if all the instruments were 100% perfect, there would still be an error.
For example, in an experiment to calculate acceleration due to gravity using the length and time period of a simple pendulum, the size of the pendulum bob, the air friction, the slight movement of support, etc. all affect the calculated value. These systematic errors are inherent to the experiment and need to be accounted for in an approximate manner.
Many systematic errors cannot be gotten rid of by simply taking a large number of readings and averaging them out. Therefore in such cases, calibration of the measuring instrument prior to starting the experiment is required, which will reveal if there is any systematic error or zero error in the measuring instrument.

Random Error

Random errors are errors in measurement that lead to measured values being inconsistent when repeated measures of a quantity are taken. They result in a scatter of measured values about a mean value. The errors have an equal probability of being positive or negative.
Random errors are present in all experiments. Unlike systematic errors, random errors are not predictable, which makes them difficult to detect but easier to remove since they are statistical errors and can be removed by statistical methods like averaging.
A random error can occur due to the measuring instrument and the way it is affected by changes in the surroundings. For example, a spring balance might show some variation in measurement due to fluctuations in temperature, conditions of loading and unloading, etc.
Random errors can also be due to the inability of the observer to repeat his actions precisely. For example, if the period of oscillation of a pendulum is being measured, the experimenter might be timing 50 oscillations. There are several things which cannot be reproduced exactly each time:
- the start of the first swing and the end of the fiftieth swing may not be noted exactly.
- the reaction time on the stopwatch might vary a little.

Accuracy and Precision

Accuracy is related to the closeness of a measurement, within certain limits, with the true value of the quantity under measurement.
Precision refers to the narrowness of spread of a set of measurements.


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