UNCERTAINTIES What are they? How do you quote them? How do you find them?
UNCERTAINTY is NOT an ERROR. It is inherent in any measurement.
RULE 1. Decide on the most uncertain measurement. ESTIMATE the uncertainty in this measurement.
Rule 2. Quote the uncertainty to ONE significant figure. When in doubt, round UP, not DOWN.
Human uncertainty Example 1 Professor Messer is trying to measure the length of a piece of wood: Discuss what he is doing wrong. How many mistakes can you find? Six?
Human uncertainty 1. Measuring from 100 end 2. 95.4 is the wrong number 3. ‘mm’ is wrong unit (cm) 4. Hand-held object, wobbling 5. Gap between object & the rule 6. End of object not at the end of the rule 7. Eye is not at the end of the object (parallax) 8. He is on wrong side of the rule to see scale. Answers: How many did you find?
Human uncertainty Example 2 Reading a scale: Discuss the best position to put your eye. your eye
Human uncertainty 2 is best. 1 and 3 give the wrong readings. This is called a parallax error. your eye It is due to the gap here, between the pointer and the scale. Should the gap be wide or narrow?
Anomalous results When you are doing your practical work, you may get an odd or inconsistent or ‘anomalous’ reading. This may be due to a simple mistake in reading a scale. The best way to identify an anomalous result is to draw a graph. For example...
Anomalous results Look at this graph: Which result do you think may be anomalous? A result like this should be taken again, to check it. x x x x x x
Let’s say you’re finding the Young’s Modulus of copper wire. You use a ruler to find the extension of the wire and a vernier caliper to find its diameter. The ruler is clearly your LEAST CONFIDENT measurement. You decide you can measure the ruler scale to the nearest millimetre. A reading of 8.6 cm has an uncertainty of +/- 0.1 cm. Don’t quote it as +/- 0.10 cm. This means you can read the ruler to 0.01 cm……………… 0.1 of a mm!!
The +/- 0.1 cm is called the ABSOLUTE UNCERTAINTY. Many students quote it as a PERCENTAGE UNCERTAINTY: Percentage uncertainty = 0.1/8.6 x 100 = 1.16% = 1% Always ROUND UP your % uncertainty to the nearest whole number. Note your % uncertainty will change with every reading: a reading of 4.5 +/- 0.1 cm will have a % uncertainty of 2%.
Young’s modulus = Stress/Strain = Force x length Area x extension +/- 1% +/- 6% +/- 2% Overall uncertainty: +/- 11%
If your measurement involves a SQUARE term, such as r 2, the % uncertainty in r must be DOUBLED, not SQUARED! A 1% uncertainty in r (or diameter) leads to a 2% uncertainty in cross-sectional area A.