Select and use rules, vernier calipers, micrometers, and stopwatches, and reduce errors such as parallax and zero error

What this dot point is asking

SEAB wants you to choose the correct instrument for a measurement, use it properly, and recognise and remove common errors. A metre rule is fine for a length of a few centimetres or more, vernier calipers measure to $0.1\ \text{mm}$, and a micrometer measures to $0.01\ \text{mm}$. You must also know how to time short intervals with a stopwatch and how to reduce errors by repeating readings.

The answer

Choosing the right length instrument

The precision of an instrument is the smallest change it can read. Match the instrument to the size and required precision of the object.

Reading vernier calipers

The main scale gives the whole millimetres. The vernier scale gives the extra tenths: read off the vernier mark that lines up best with a main-scale mark, and that number is the number of tenths of a millimetre to add.

Reading a micrometer

The main scale on the sleeve reads to $0.5\ \text{mm}$, and the thimble is divided into $50$ divisions each worth $0.01\ \text{mm}$. The reading is the sleeve value plus the thimble divisions times $0.01\ \text{mm}$.

Zero error

A zero error happens when an instrument does not read zero when it should (jaws fully closed, nothing between them). If it reads $+0.02\ \text{mm}$ when closed, every reading is $0.02\ \text{mm}$ too high, so subtract that. A negative zero error is added.

Parallax error

Parallax error is reading a scale from the wrong angle, so the mark appears to line up with the wrong value. Avoid it by looking straight down (eye directly above the mark) so the line of sight is perpendicular to the scale.

Timing accurately

A stopwatch has a reading uncertainty, and your reaction time adds error each time you start and stop it. To time something fast and repeating, such as a pendulum, time many oscillations and divide, and repeat the whole timing for an average.

Examples in context

Example 1. Measuring a coin. To find a coin's thickness you would use vernier calipers or a micrometer, not a metre rule, because the thickness is only a few millimetres and the rule cannot resolve it. Stacking several coins and dividing also reduces the relative error.

Example 2. The pendulum clock experiment. In a practical, timing $20$ swings of a pendulum and dividing by $20$ gives a period accurate to a few hundredths of a second, even though a single human-timed swing might be out by a fifth of a second. This is the same idea as measuring the thickness of one sheet of paper by measuring $100$ sheets.

Try this

Q1. State which instrument you would use to measure the diameter of a thin copper wire, and give its precision. [2 marks]

• Cue. A micrometer screw gauge, precision $0.01\ \text{mm}$, because the wire is far too thin for a metre rule.

Q2. A micrometer reads $0.03\ \text{mm}$ when the jaws are fully closed. A measurement gives $4.55\ \text{mm}$. State the true value. [2 marks]

• Cue. Zero error is $+0.03\ \text{mm}$, so subtract: $4.55 - 0.03 = 4.52\ \text{mm}$.

Q3. Explain why a student times $25$ swings of a pendulum rather than one. [2 marks]

• Cue. Reaction-time error is the same whether timing one or many swings, so spreading it over $25$ swings makes the period per swing far more accurate.