Reporting Uncertainty

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Presentation transcript:

Reporting Uncertainty 1.2.10 State uncertainties as absolute, fractional, and percentage uncertainties. 1.2.11 Determine the uncertainties in results 1.2.13 State random uncertainty as an uncertainty range (±) and represent it graphically as an “error bar”.

Uncertainty (reading error) Measurement Tools Can be read to ½ the smallest division Digital devices are precise within +/- 1 of the last digit Example: Scale reads: 23.02g Reading error= +/- 0.01g Example: Meter reads: 14.2 mA Reading error = +/- 0.1mA

Uncertainty (Random Error) Multiple trials (measurements) are performed to determine the random error. The average, then, of the measurements is reported with D being calculated by dividing the range in measurements by two. The reported value should then be : average value +/- D

Uncertainty (Random Error) Example: The following length measurements are taken in cm: 14.88, 14.84, 15.02, 14.57, 14.76, 14.66. Determine the average value Find the range in values (max – min) Divide the range by two. Reported value: 14.79cm +/- 0.2cm

Uncertainty (Random Error) Two types are error are associated with this measurement Reading: based on the smallest division of the ruler (+/- 0.1 cm) Random: based on the range in measured values (+/- 0.2 cm) Report whichever uncertainty range is greater. This is the absolute uncertainty of the measurement.

Uncertainty (Propagating Error) When calculations are done based on your measurements, not only must the calculated result follow sig. fig. rules, but the error must be carried through. For added and/or subtracted values, the uncertainty in the calculation is the sum of the absolute uncertainties.

Uncertainty (Propagation of Error) Example: The side of a square is measured to be 12.4 cm +/- 0.1 cm. Find the error in the calculation of the perimeter of the square. 49.6 cm +/- 0.4 cm

Uncertainty (Propagation of Error) For multiplication, division, powers, and roots, the fractional or percentage uncertainties in the calculated answer will be the sum of the fractional or percentage uncertainties in the measured values. What’s fractional and percentage uncertainty? The fraction or percentage the error is of the measured value. Example: value = 4.5 kg +/- 0.1 kg Fractional uncertainty is 0.1/4.5 = 0.02 Percentage uncertainty is 0.02 x 100=2%

Uncertainty (Propagation of Error) Example: A mass is measured to be m=4.4kg +/- 0.2 kg, and its speed is 18ms-1 +/- 2ms-1. Find the Kinetic energy. KE = ½mv2 = 710 J Fractional Uncertainty = .2/4.4 + 2/18 +2/18 = 0.27 Uncertainty = 0.27 x 710 = 190 Acceptable calculation = 710J +/- 190 J