1. Measurements + Their Errors

• SI units are fundamental (base) units of physical quantities
• SI unit of mass is kilogram (Kg)
• Physical quantity measured in mol is amount of substance
• SI unit of current is Amperes (A)
• SI unit for temperature is kelvin (K) as this is the absolute scale
• SI unit of length is Metres (m)
• Quantity measured in seconds is Time
• Newtons (N) are not an SI unit, the SI units for force are kgms^-2
• SI units of energy: Kinetic energy = ½ x mass x velocity squared, Units = kg x (m/s) x (m/s) = kgm^2s^-2
• SI units of force: Force = mass x acceleration, Units = kg x ms^-2 = kgms^-2
• 60TΩ in standard form is 6 x 10^13
• 0.000003m with a suitable prefix is 3μm
• Actual value of 8MΩ is 8,000,000 Ω or 8x10^6 Ω
• 6000pF in nF is 6nF as 1 nano unit is 1000 pico units
• Multiplier associated with the prefix kilo (k) is 1000 (10^3)
• Multiplier associated with the prefix femto (f) is 10^-15
• 7GΩ in standard form is 7 x 10^9 Ω
• 1eV in J is 1.6 x 10^-19 J
• 6kWh in joules is 21.6 x 10^6 J = 21.6 MJ
• 6.6pJ in eV is 4.1 x 10^7 eV (2sf) = 41MeV
• Random error affects precision and causes differences in measurements
• Systematic error affects accuracy and occurs due to faults in equipment or experimental method
• Ways to reduce random error:

  • Take at least 3 repeats and calculate a mean
  • Use a computer or a data logger
  • Use higher resolution equipment
• Mass balance reading 1004 g with a 1kg mass is a systematic error as the reading is too high by 4g each time
• Cause of parallax error is reading a scale at a different angle each time
• Systematic error can be reduced by calibrating apparatus before using
• Electronic noise in the circuit of an ammeter is a random error
• Measuring background radiation before measuring the radioactivity of a source reduces systematic error
• Precision means consistent measurements that fluctuate slightly about a mean value
• Repeatability is achieved when the original experimenter can redo the experiment with the same equipment and method and get the same results
• Reproducibility is achieved when the experiment is redone by a different person or with different techniques and equipment and the same results are found
• Resolution is the smallest change in the quantity being measured that gives a recognisable change in reading
• Value is accurate if it is close to the true value
• Absolute uncertainty is uncertainty given as a fixed quantity e.g. 7 +/- 0.6 V
• Percentage uncertainty in 17 +/- 3 A is 17.647% = 18% (2sf)
• Fractional uncertainty of 8 +/- 0.5 m is 1/16 (0.0625)
• Percentage and fractional uncertainty can be reduced by measuring larger quantities
• Time for 1 swing of a pendulum from 10 swings of 13 +/- 0.3s is 1.3s, uncertainty is 0.03s
• Difference between a reading and a measurement: Readings are single values, measurements involve the difference between 2 readings
• Uncertainty of a thermometer with the smallest division of 5 ℃ is ± 2.5 ℃