11 Question 4: How do we determine how certain we are when taking data? Measurement = Best Estimate +/- UncertaintyOrExamples:Uncertainty has one significant figure* The signigicant figure in the uncertainty will be the most precise digit in the the Best Estimate
12 Representing uncertainty: Absolute or Raw uncertaintyPercentage Uncertaintytime = 1.98 0.01 stime = 1.98 9%
13 Determining uncertainty with common measuring devises. Measurement = Best Estimate +/- Least CountRuler – half the smallest division (0.05), but on either side, so therefore 0.1Voltmeter, we can discern one half the least count. I can confidently say that it is neither 3.8 or 3.9, but it is in between, so 3.85
14 Determining Uncertainty with common measuring tools: Stopwatch does the roundingDemo – time how long it takes for the pendulum to do three whole swingsYOU are less accurate than the stopwatch, so a better method for getting an uncertainty is max-min/2
15 Uncertainty isn’t only due to the tool… * Limitations for the data collector* YOU decide the uncertainty, but if it is anything other than the uncertainty of the tool, you must justify your choiceEx. The ability to stop a timer the instant a ball rolls past a given point adds an uncertainty greater than that of the least count. It’s hard to see just when the ball passes the point you want. You make a judgment that this additional uncertainty is perhaps 0.02s. Hense the uncertainty in a single measurement of the time might be +/-0.03s.
17 Fig 2 What is the reading that should be recorded here? Answer: ......... mm
18 What is the reading that should be recorded here? Answer: ......... mm
19 Give a value for the following: State which tool you used and why.State why you chose the uncertainty that you did.Length of the lab tableThickness of a 1 zloty coinThe height of your calculator
20 Question 5: What is the difference between precision and accuracy?
21 Precision vs. AccuracyAccuracy: an indication of how close a measurement is to the accepted value.Precision: the degree of exactness to which the measurement of a quantity can be reproduced (how close are repeated measurements to each other? If someone else were to make the same measurement how close would they be? Often defined by the tool)
22 Precision vs. Accuracy Label each of the ducks with the either: High Accuracy, High precisionHigh Accuracy, Low precisionLow Accuracy, High precisionLow Accuracy, Low precision
28 Question 7: How do we know what the uncertainty of a calculation is? Ex: You have just measured the radius of a ball to be (6.1 +/- 0.02)mm, but now you want to find the volume.
29 Repeated measurements - Averaging If repeated trials of the same measurement are made, the greatest deviation from the average of the trials can be taken as the uncertainty. For example,Time Trials2.011.821.972.161.94
30 Adding and Subtracting An uncertainty range can be found by examining the minimum and maximum values for the calculated value.Ex: Ti = 16 2 oC = 14 to 18 oCTf = 34 2 oC = 32 to 36 oCbest value for T = ___________minimum value for T = ____________maximum value for T=___________ T = Tf – Ti = ____________
31 Adding and Subtracting Shortcut:Whenever two quantities with uncertainties are added or subtracted, the uncertainty of the answer is equal to the SUM of the individual ABSOLUTE uncertainties.eg. T = Tf – Ti= (34 2 oC) – (16 2 oC)= (34 – 16 ) (2 + 2) oC= 18 4 oC
32 Multiplying and Dividing An uncertainty range can be found by examining the minimum and maximum values for the calculated value.ex. m = 84.2 0.1 g = 84.1 to 84.3 gV = 25 2 mL = 23 to 27 mLBest value for D = m V =Minimum value for D =Maximum value for D = D =
33 Multiplying and Dividing Shortcut:Whenever two quantities with uncertainties are multiplied or divided, the uncertainty of the answer is equal to the SUM of the individual PERCENT uncertainties.Ex. m = 84.2 0.1 g = 84.1 g 0.12%V = 25 2 mL = 25 mL 8%D = (84.1 g 0.12%) (25 mL 8%)= (84.1 25 g / mL ) ( %)= g / mL 8.12%= g / mL= 3.4 0.3 g / mL
34 You try:The lengths of the sides of a rectangular plate are measured. The width is (50+/-1)mm and the length is (25 +/- 1)mm. What is area (with uncertainty) of the plate.Find the area of the top of your lab table. Report your answer with uncertainties. Show all measurements and calculations.
35 Power FunctionsPower functions are just like multiplication!
36 Other FunctionsIf the calculation involves mathematical operations other than + , - , or (eg. root functions, trigonomeric functions, logarithmic functions, … ), then the short cuts do not apply and we must find the minimum and maximum values and use the greatest deviation from the best value as the uncertainty.ex. = 33C 2C = 31C to 35Cbest value for sin = sin(33) =minimum value for sin = sin(31) =maximum value for sin = sin(35) =Take the maximum: sin =
37 Volume of a sphereEx: You have just measured the radius of a ball to be (6.1 +/- 0.02)mm, but now you want to find the volume.
38 You try:The power dissipated in a resistor of resistance R carrying a current I is equal to I^2R. The value of I has an uncertainty of +/- 2% and the value of R has an uncertainty of +/-10%. The value of the uncertainty in the calculated power dissipation is: