1.1. Measurements And Their Errors

• What are SI units?

  Fundamental (base) units of physical quantities.
• What is the SI unit of mass?

  kg (kilogram)
• What physical quantity is measured in mol?

  Amount of substance.
• What is the SI unit of current?

  A (Amperes)
• Is the SI unit for temperature ℃ or K ?

  K (kelvin) as this is the absolute scale.
• What is the SI unit of length?

  m (metres)
• What quantity is measured in seconds?

  Time
• Are Newtons (N) an SI unit?


  No, newtons are not fundamental, the SI units for force are kg⋅m⋅s^-2.
• Derive the SI units of energy.

  Kinetic energy = ½ x mass x velocity squaredUnits = kg x (m/s) x (m/s)Units = kg⋅m^2⋅s^-2
• Derive the SI units of force.

  Force = mass x accelerationUnits = kg⋅m⋅s^-2Units = kg⋅m/s^-2
• Express 60 TΩ in standard form.

  6 x 10^13

  (T is tera and the multiplier is 10^12)
• Write 0.000003m with a suitable prefix.

  3 μm
• What is the actual value of 8MΩ?

  8,000,000 Ω or 8x10^6 Ω
• What is 6000pF in nF?

  6 nF as 1 nano unit is 1,000 pico units.
• What multiplier is associated with the prefix kilo (k)?

  1000 (10^3)
• What multiplier is associated with the prefix femto (f)?

  10^-15
• Express 7GΩ is standard form.

  7 x 10^9 Ω
• What is 1 eV in J?

  1 eV = 1.6 x 10^-19 J
• Express 6 kWh in joules.

  6 kW = 6,000 J/s

  1 hr = 3,600 s

  
  

  6 kWh = 6,000 x 3,600

  6 kWh = 21.6 x 10^6 J

  6 kWh = 21.6 MJ
• Convert 6.6 pJ to eV.

  6.6 pJ = 6.6 x 10^-12 J

  Divide by 1.6 x 10^-19

  6.6 pJ = 4.1 x 10^7 eV (2 sf)

  6.6 pJ = 41 MeV
• What is a random error?

  An error that affects precision and cannot be completely removed, it causes differences in measurements.
• What is a systematic error?

  An error that affects accuracy and occurs due to faults in equipment or experimental method, causing the result to be too large / small by the same amount each time.
• What are 3 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.
• A mass balance reads 1,004 g when a 1 kg mass is placed on it, is this a

  random or systematic error?

  Systematic as the reading is too high by 4 g each time.
• State a cause of parallax error.

  Reading a scale at a different angle each time, to correct this you should read scales at eye level to reduce parallax error.
• How can systematic error be reduced?

  Calibrate apparatus before using e.g. zero the balance when it is empty.
• Is electronic noise in the circuit of an ammeter random error or systematic error?

  It is a random error as it will cause fluctuations in readings that affect precision and it cannot be removed.
• Why should you measure background radiation before measuring the radioactivity of a source?


  So that only the source’s radioactivity is measured, by accounting for background radiation systematic error is reduced.
• What is precision?


  Precise measurements are consistent, they fluctuate slightly about a mean value - this doesn’t indicate the value is accurate.
• What is repeatability?


  If the original experimenter can redo the experiment with the same equipment and method then get the same results it is repeatable.
• What is reproducibility?


  If the experiment is redone by a different person or with different techniques and equipment and the same results are found, it is repeatable.
• What is meant by resolution?

  The smallest change in the quantity being measured that gives a recognisable change in reading.
• What is meant if a value is accurate?


  If the value is close to the true value.
• What is absolute uncertainty?

  Uncertainty given as a fixed quantity e.g. 7 ± 0.6 V.
• What is the percentage uncertainty in 17 ± 3 A?

  3/17 x 100 = 17.647 % = 18 % (2 sf)
• How can percentage and fractional uncertainty be reduced?

  Measure larger quantities e.g. a longer rope will have a smaller percentage uncertainty than a shorter one.
• What is the difference between a reading and a measurement?

  Readings are when one value is found, measurements are when the difference between 2 readings is found.
• What is the uncertainty of a thermometer whose smallest division is 5℃?

  The uncertainty in a reading is ± half the smallest division, so the uncertainty is ± 5/2 or ± 2.5 ℃.
• What is the uncertainty in the charge of an electron (1.6 x 10^-19 C)?


  The uncertainty in a given value is ± the last significant digit: 1.6 x 10^-19 ± 0.1 x 10^-19 C
• What is wrong with writing 7 ± 0.673 V?

  The uncertainty should be the same number of significant figures as the data ie. 7 ± 0.7 V.