IB Physics: Measurement and Uncertainties – Part 2

IB Physics: Measurement and Uncertainties – Part 2 Uncertainty and error in Measurement Describe and give examples of random and systematic errors Random errors: These are errors that are random! Basically, the error here is unpredictable. Examples of random error: ❖ Instrumental error – ➢ Instruments usually have “inherent” error, usually the smallest unit division of the scale. ❖ Problems with the observer/experimentalist. ➢ We’re not perfect ; But luckily Bruno Mars says that “you’re amazing, 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 your results Systematic errors: These are errors that occur at each reading. E.g. When you set a piece of equipment (voltmeter), you expect the reading on the voltmeter to be initially zero right? However, in practice, this isn’t entirely 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, it makes sense to start at 0. But sometimes, the instrument may fluctuate slightly from 0. ➢ We can mitigate this problem by subtracting the zero error value from each reading. Distinguish between precision and accuracy Precision and Accuracy are two similar BUT different concepts. An experiment can be “precise” but “inaccurate”, just as it can be “accurate” but “imprecise”. ❖ A precise experiment is one that has small random error. This means that each reading is very close to each other in terms of value ❖ An accurate experiment is one that has small systematic error. This means that each reading is very similar to the reference literature 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 are precise but quite inaccurate. Why? ❖ Precision: This is a measure of basically, the consistency of the results.If we were to calculate the Standard Deviation (the spread of the results), we would obtain a small value. ❖ Accuracy: This is not very accurate. If we were to propagate uncertainties, we would see that there is quite a significant discrepancy between the reference value (9.8) and the average of the obtained values. ➢ Now, what causes the discrepancy here? ■ It’s likely to be a combination of systematic and random errors. Explain how the effects of random errors may be reduced. We can reduce the effects of random errors by taking multiple readings. ● This can reduce the effect of anomalous results As systematic errors occur at each reading, taking multiple readings will not reduce the effects of systematic errors. ● Instead, reducing systematic will really depend on the context of the experiment. ● E.g. Systematic errors caused by insufficient mixing may be reduced by purchasing more sophisticated equipment (E.g. an electronic swirler). Calculate quantities and results of calculations to the appropriate number of significant figures. When we calculate the number of significant figures in a calculation, we have to make sure that the number of significant digits of the answer does not exceed the least precise value in the calculation. For example: ● Find the speed of a bus that travels at 10.234 meters in 1.33 seconds? Well, we would first use the Speed = Distance / Time formula. If you plug in 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