Errors and Uncertainties

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Presentation transcript:

Errors and Uncertainties LT: I can make the difference between random and systematic errors

Types of Experimental Errors: Random Errors: A result of variations in the performance of the instrument and/or the operator Do NOT consistently occur throughout a lab Some examples: Vibrations or air currents when measuring mass Inconsistent temperature (i.e. of the air) throughout a lab Irregularities in object being measured (i.e. the wire is not the same thickness at all points along its length) Human parallax error

Types of Experimental Errors: So what can be done about random errors? Don’t rush through your measurements! Be careful! Take as many trials as possible—the more trials you do, the less likely one odd result will impact your overall lab results

Types of Experimental Errors: Systematic Errors: Errors that are inherent to the system or the measuring instrument Results in a set of data to be centered around a value that is different than the accepted value Some Examples: Non-calibrated (or poorly calibrated) measuring tools A “zero offset” on a measuring tool, requiring a “zero correction” Instrument parallax error

Types of Experimental Errors: What can be done to reduce these? Unfortunately, nothing…HOWEVER: We can account for the systematic errors sometimes: i.e. if there’s a zero offset, make sure all your data has been adjusted to account for that. Recognizing systematic errors will impact the size of your absolute uncertainty (more details soon )

Are These “Errors”? Misreading the scale on a triple-beam balance Incorrectly transferring data from your rough data table to the final, typed, version in your report Miscalculating results because you did not convert to the correct fundamental units Miscalculations because you use the wrong equation

Are These “Errors”? NONE of these are experimental errors They are MISTAKES What’s the difference? You need to check your work to make sure these mistakes don’t occur…ask questions if you need to (of your lab partner, me, etc.) Do NOT put mistakes in your error discussion in the conclusion

Accuracy vs. Precision Accuracy: Precision: How close a measured value is to the actual (true) value. Precision: Precision is how close the measured values are to each other.

Accuracy vs. Precision

Measuring in Physics When I record a measurement in physics, I write down all of the numbers I’m sure of – PLUS one estimated place. Example: I’m certain of: 4.9 cm (not quite to 5 yet) I estimate: It reached 3/10ths of the space between markings My measurement is recorded as: 4.93 cm

Absolute Uncertainty The smallest uncertainty in a measurement is ± half the smallest division Example: I’m certain of: 2.3 cm I estimate: 2/10ths of the space between markings ½ the smallest division: 0.05 cm My measurement is recorded as: 2.32 ± 0.05 cm

The maximum value – the average Absolute Uncertainty Consider a ruler: The uncertainty is +/- ½ a division It has an uncertainty of ±0.5mm Now consider the time taken for a ball to drop: Drop no. Drop 1 Drop 2 Drop 3 Uncertainty Time taken to fall/s 0.46 0.43 0.50 The maximum value – the average 0.46 (+/- 0.04)

How Accurate or Precise Am I? How precise is my measurement? 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦= 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑉𝑎𝑙𝑢𝑒 ×100% How accurate is my measurement? 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟= 𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒−𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 ×100%