Measuring length: read square-on from a clear mark
Definition
Parallax
The shift in a reading that appears when a scale is viewed from an angle instead of square-on, so the mark seems to line up with the wrong division.
- Length is measured in metres (m\text{m}m) in SI units, and in centimetres or millimetres in the laboratory.
- A metre rule is divided into millimetres, so its smallest scale division is 1 mm1\ \text{mm}1 mm and a reading is quoted to the nearest millimetre, as 12.4 cm12.4\ \text{cm}12.4 cm rather than 12 cm12\ \text{cm}12 cm.
- Lay the rule alongside the object and in contact with it, so there is no gap.
- Line up one end of the object with a clear scale mark, using the zero mark only if the end of the rule is undamaged, otherwise starting from a mark such as 1.0 cm1.0\ \text{cm}1.0 cm and subtracting it at the end.
- A worn or damaged end adds the same error to every reading, a systematic error that repeating cannot remove.
- Read the far end with your eye directly above the mark, along a line perpendicular to the scale, so you avoid parallax.
- Record the value with its unit.
Measuring volume: read the bottom of the meniscus
Definition
Meniscus
The curved surface of a liquid in a narrow container, which dips lowest at the centre; the scale is read at the lowest point.
- Volume is the space an object or a sample of fluid occupies, measured in m3\text{m}^3m3 in SI units and in cm3\text{cm}^3cm3 in the laboratory, where 1 cm3=1 ml1\ \text{cm}^3 = 1\ \text{ml}1 cm3=1 ml.
- For a regularly shaped solid you need only a ruler: measure each dimension and multiply, V=l×w×hV = l \times w \times hV=l×w×h.
- For a liquid, use a measuring cylinder standing on a horizontal bench, lower your eye until it is level with the liquid surface, and read the scale at the bottom of the meniscus.
- Choose a cylinder only a little larger than the sample, because a narrower cylinder has smaller divisions and so reads more precisely.
- For an irregular solid that sinks, use displacement: record the water volume V1V_1V1, lower the solid in gently on a thread until it is fully submerged, record the new volume V2V_2V2, and take V=V2−V1V = V_2 - V_1V=V2−V1.
Measuring time: match the timer to the interval
- A time interval is the duration between two events, measured in seconds (s\text{s}s).
- Use an analogue clock or watch for long intervals, such as a puddle evaporating over an afternoon, read to the nearest second or minute.
- Use a digital stopwatch for everyday laboratory timings, displaying to 0.01 s0.01\ \text{s}0.01 s and started and stopped by hand.
- Use a digital timer triggered by light gates for intervals too short for a person, started and stopped electronically as an object cuts the beam.
- A hand-operated stopwatch displays hundredths of a second, but the person pressing it cannot react that quickly: reaction time is roughly 0.2 s0.2\ \text{s}0.2 s at the start and again at the stop.
- That reaction-time error is random, so repeat the timing and take a mean.
- It also matters far more for a short interval: 0.2 s0.2\ \text{s}0.2 s out of 2 s2\ \text{s}2 s is a tenth of the reading, but out of 200 s200\ \text{s}200 s it is negligible.
Common Mistake
- Reading the top of the meniscus, or holding the cylinder up to your eye instead of standing it on the bench.
- Treating a stopwatch reading to 0.01 s0.01\ \text{s}0.01 s as accurate to 0.01 s0.01\ \text{s}0.01 s: precision is not accuracy, and hand timing is limited by reaction time, not the display.
- Converting volume with the wrong power: 1 cm3=1×10−6 m31\ \text{cm}^3 = 1 \times 10^{-6}\ \text{m}^31 cm3=1×10−6 m3, not 1×10−2 m31 \times 10^{-2}\ \text{m}^31×10−2 m3, because all three dimensions scale.
- Assuming repeats fix everything: they cut random error only, so a worn rule end or an un-zeroed instrument must be corrected instead.
Exam technique
- A "describe how you would measure..." answer is point-marked, so give short separable steps: name the instrument, say how it is positioned, say how the reading is taken, and give the reading with its unit.
- Quote every reading to the precision of the instrument, as 25.0 cm325.0\ \text{cm}^325.0 cm3 rather than 25 cm325\ \text{cm}^325 cm3.
- Head each results-table column quantity / unit, for example time / s\text{s}s.
Self review
- What is parallax, and how do you position your eye to avoid it when reading a scale?
- How do you find the volume of an irregular solid that sinks in water?
- Convert 1 cm31\ \text{cm}^31 cm3 into m3\text{m}^3m3.
- Why is a stopwatch reading shown to 0.01 s0.01\ \text{s}0.01 s not accurate to 0.01 s0.01\ \text{s}0.01 s?
- Which type of error does repeating and averaging reduce, and which does it leave unchanged?
