Accuracy and precision

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Accuracy and precision
Topic Physics 2a Motion
Friday 3rd February

• Prior learning
• Know ways accuracy and precision can be improved
  In an experiment.
• Key words
• Accuracy, precision, absolute error, uncertainty

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Starter task Recap standard measurements /
Scientific notation
Heinemann Questions 1.1 1-5 page 41
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Topic Physics 2a
By the end of this lesson we should be able to

• Define terms accuracy, precision, uncertainty and
  absolute error
• Use uncertainty of common lab equipment to
  calculate measurement with uncertainty
• Estinate the uncertainty of a result using an
  experiment

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Task 1 notes

• Accuracy relates to an instruments use.
• An instrument is accurate if it truly reflects
  the quantity being measured e.g. if you wanted to
  measure the width of this page you would use a
  ruler with millimetre markings.
• Precision relates to how an instrument
  differentiates between slightly different
  quantities e.g. bathroom scales, kitchen scales
  and laboratory scales all measure mass and are
  accurate for the mass they measure.
• Laboratory scales are more precise as they can
  measure to 0.01 g whereas bathroom scales can
  measure to 0.5 kg

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Task 1 notes

• Uncertainty
• All measurements you make have some amount of
  uncertainty.
• The uncertainty of an instrument is usually one
  half of the finest scale e.g. a ruler which
  measures in millimetres has an uncertainty of 0.5
  mm. An electronic timer usually to ?0.005 s
• The uncertainty of an instrument measure its
  precision. If you measure the width of an A4
  piece of paper you will get a reading of 21.1 cm.
  The uncertainty is 0.5 mm so the reading is 21.1
  ? 0.05 cm

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Uncertainty in common laboratory equipment

• Metre rule ? 0.05 cm
• 50 mL measuring cylinder ? 0.2 mL
  
• 50 mL measuring cylinder ? 0.2 mL
  
• 10 mL measuring cylinder ? 0.1 mL
• -100C 1100C thermometer ? 0.50C (does depend
  on precision of thermometer)

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Task 2 Activity

• Use a timer, ruler, thermometer and measuring
  cylinder to take some measurements including the
  uncertainty in each measurement.

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Estimating the uncertainty in a result

• An experiment or a measurement exercise is not
  complete until the uncertainties have been
  analysed. The report should include an estimate
  of the total uncertainty. This gives the reader
  of the report some idea of your confidence in the
  result.
• The following processes are used for estimating
  uncertainty.
• When adding or subtracting data, add the absolute
  uncertainties.
• e.g. ?T (change in temperature) 40 ? 0.5 0C
  - 35 ? 0.5 0C 5 ? 1 0C
• When multiplying or dividing data, add the
  percentage uncertainties.

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Absolute and uncertainty
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• You would calculate as follows
• Specific heat of metal to a whole number so
  answer so far is cmetal 198 J kg-1 K-1
• Uncertainty () 0.120 0.6 23 0.476
  1.351 25.547
• Hence, you would obtain the following result
  cmetal 198 Jkg-1J-1 ?
  25.547
• now 25.547 of 198 50.6
• so cmetal 198 ? 51 Jkg-1J-1
•  
• Once you have done all of this you can consider
  the relative success of your measurement
  exercise.
• Your result is 147 J kg1 K1 ? cmetal
  ? 249 J kg1 K1

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• If I then give you the actual specific heat of
  the metal and it falls within your values, you
  can conclude that your experiment is consistent
  with known values (accurate). Or in other words,
  there are probably no major errors.

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Summary task

• Read pg 43/44
• Work through example 1.2A
• Then questions from text pg.45
• Check answers in the back of book
• Ask for help!!

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Topic Physics 2a
By the end of this lesson we should be able to

• Define terms accuracy, precision, uncertainty and
  absolute error
• Use uncertainty of common lab equipment to
  calculate measurement with uncertainty
• Estimate the uncertainty of a result using an
  experiment