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Reporting Uncertainty

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).

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Reporting Uncertainty

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  1. 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”.

  2. 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

  3. 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

  4. 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

  5. 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.

  6. 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.

  7. 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

  8. 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%

  9. 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

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