Measurements + Errors

• SI units and prefixses

  
• MeV to J

  x 1.6 x10^-19
• kWh to J

  1kW = 1000J/s
• kilometres per hour ----> ms-1

  x 3.6
• Random error - affects precision, meaning they cause differences in measurements, which cause a spread about the mean

  To reduce random error :

  • take repeats and calculate a mean, which alows anomalies to be identified
  • computers/data loggers/ cameras to reduce human error and enable smaller intervals
  • equipment with a higher resolution
• Systematic error - affects accuracy due to the apparatus or faults in the experimental method

  • parallax error (not reading scale at proper angle) , zero error (not callibrating the equipment properly)
  • callibration and reading the equipment properly
• Precision - precise measurements are consistent and fluctuate slightly about a mean value
• Repeatability - if the experiment can be redone with the same equipment and the same results can be obtained
• Reproducibility - if the experiment is redone by a different person and the same results can be found
• Resolution - the smallest change in the quantity being measured that gives a recognisable change in the reading
• Accuracy - a measurement close to the true value is accurate
• Uncertainty - the bounds in which the accurate value can be expected to lie
• Absolute uncertainty - based on equipment
• Percentage Uncertainty -

  abs unc / value x 100
• The uncertainty in a reading is half the smallest division, e.g. for a thermometer, the smallest division is 1 so the uncertainty is 0.5
• The unvertainty in a measurement is double the absolute uncertainty as two readings are taken
• Digital readings have the uncertainty quoted
• For repeated data, the uncertainty is half the range
• Combining uncertainty

  • Adding or subtracting data - ADD ABSOLUTE UNCERTAINTY
  • Multiplying/dividing data - ADD PERCENTAGE UNCERTAINTY
  • Raising to a power - MULTIPLY PERCENTAGE UNC BY POWER
• The uncertainty in a gradient can be found by lines of best and worst fits