IB Physics: Measurement and Uncertainties – Part 2 Uncertainty and error in Measurement Describe and give examples of random and systematicerrors Random errors: These are errors that are random! Basically, the errorhere is unpredictable. Examples of random error: ❖ Instrumental error – ➢ Instruments usually have “inherent” error, usually thesmallest unit division of the scale. ❖ Problems with the observer/experimentalist. ➢ We’re not perfect ; But luckily Bruno Mars says that “you’reamazing, just the way you are”. What a joke. LOL. ❖ Change in surroundings ➢ Again, factors such as humidity, air pressure, wind speed,those seemingly trivial things can have an impact on yourresults Systematic errors: These are errors that occur at each reading. E.g.When you set a piece of equipment (voltmeter), you expect the readingon the voltmeter to be initially zero right? However, in practice, this isn’tentirely true. We call this a systematic error. Examples of systematic errors: ❖ Improperly calibrated instrument ➢ The solution here would be to calibrate the instrument! ❖ An instrument with zero error.
➢ Basically, if you have a balance – to weigh something, itmakes sense to start at 0. But sometimes, the instrumentmay ﬂuctuate slightly from 0. ➢ We can mitigate this problem by subtracting the zero errorvalue from each reading. Distinguish between precision and accuracy Precision and Accuracy are two similar BUT di erent concepts. Anexperiment can be “precise” but “inaccurate”, just as it can be“accurate” but “imprecise”. ❖ A precise experiment is one that has small random error. Thismeans that each reading is very close to each other in terms ofvalue ❖ An accurate experiment is one that has small systematic error.This means that each reading is very similar to the referenceliterature value. Example: If you had an experiment measuring g =9.8 ms -2 (which if you did not know, is the value of the free-fall acceleration on earth). If you obtained a values 7.8,7.9,7.8,7.8,7.9, we can say that are results areprecise but quite inaccurate. Why? ❖ Precision: This is a measure of basically, the consistency of theresults.If we were to calculate the Standard Deviation (the spreadof the results), we would obtain a small value. ❖ Accuracy: This is not very accurate. If we were to propagateuncertainties, we would see that there is quite a signiﬁcantdiscrepancy between the reference value (9.8) and the average ofthe obtained values.
➢ Now, what causes the discrepancy here? ■ It’s likely to be a combination of systematic andrandom errors. Explain how the e ects of random errors may be reduced. We can reduce the e ects of random errors by taking multiple readings. ● This can reduce the e ect of anomalous results As systematic errors occur at each reading, taking multiple readings willnot reduce the e ects of systematic errors. ● Instead, reducing systematic will really depend on the context ofthe experiment. ● E.g. Systematic errors caused by insu cient mixing may bereduced by purchasing more sophisticated equipment (E.g. anelectronic swirler). Calculate quantities and results of calculations to theappropriate number of signiﬁcant ﬁgures. When we calculate the number of signiﬁcant ﬁgures in a calculation, wehave to make sure that the number of signiﬁcant digits of the answerdoes not exceed the least precise value in the calculation. For example: ● Find the speed of a bus that travels at 10.234 meters in 1.33seconds? Well, we would ﬁrst use the Speed = Distance / Time formula. If you plugin the answers in your calculator, you would get a speed of: Speed = 7.694736842 ms -1 However, you’re not going to write that as your answer!
We will use the value of the fewest signiﬁcant values in the question,which will be 1.33 seconds (3sf). Therefore, our answer should be in 3sf! Speed = 7.69 ms -1