Topic 4 of 6
Making useful measurements
A useful measurement depends on how you take the reading, not just which instrument you choose.
Choose a suitable range and resolution first. Then look for a specific source of error and a method that addresses it.
Read the difference between the ends
Place a rule parallel and close to the length being measured. If the object does not start at zero, read both ends and subtract. This is also useful when a rule's zero end is worn.
Look perpendicularly at the scale. If the object and markings are at slightly different heights, looking from one side makes them appear to line up differently. This is parallax error. Keep the object close to the scale as well as placing your eye correctly.
Check the zero before trusting the display
Clean and gently close the jaws of digital calipers, then check the reading. If they correctly close with no object between them but the display is not zero, there is a zero offset. Use the instrument's zero control when appropriate, or correct a stated stable offset.
Worked example
Correcting a positive zero error
Closed calipers read +0.02 mm. With an object between the jaws, they read 3.42 mm. Assume the zero offset stays the same.
Corrected reading = displayed reading - zero offset
= 3.42 - (+0.02) = 3.40 mm
The instrument adds 0.02 mm even when the true gap is zero, so subtract that extra amount. The same rule uses the sign of the offset: subtracting a negative zero offset would increase the reading.
Repeating a reading does not remove a stable zero error. Repeats help you judge and reduce random variation through averaging. A consistent offset needs a correction or a properly adjusted instrument.
Time several complete oscillations
The period of a pendulum is the time for one complete oscillation. The bob must return to the same reference point moving in the same direction. Going from one side to the other is only half an oscillation.
- Place a fixed reference mark beside the path, for example at the centre of the swing.
- Start timing as the bob passes the mark in a chosen direction. Count this as zero.
- Count one each time it next passes the mark in that same direction. Stop at 20.
- Repeat the timing under the same conditions, find the mean elapsed time, then divide by 20.
| Trial | Time for 20 oscillations / s |
|---|---|
| 1 | 40.6 |
| 2 | 40.2 |
| 3 | 40.4 |
The delay in reacting at the start and finish is a much smaller fraction of 40 s than of 2 s. Timing many oscillations reduces its fractional effect on the period. Repeating and averaging helps with variation in those delays, but cannot guarantee that all timing errors disappear.
The calculated 2.02 s does not mean a person directly timed one swing to the nearest 0.01 s. It comes from dividing a longer measured interval by an exact count of oscillations.
Use displaced water to measure an irregular solid
Choose a measuring cylinder large enough for the object and final water level, with divisions fine enough to distinguish the rise. Put it upright on a level surface. For water, read the bottom of the curved meniscus at eye level.
This works when the solid is fully submerged, does not dissolve or absorb water, and no water is lost. Remove trapped air bubbles: they displace extra water and would make the calculated solid volume too large. Avoid splashing when lowering the object.
Other common measurements
| Quantity | Instrument and useful precaution |
|---|---|
| Mass | Use a balance with a suitable range. Check its zero; tare an empty container before adding the material, or subtract the container's mass. |
| Time interval | Use a stopwatch or suitable timer. Define the starting and finishing events clearly; use repeated events when one interval is too short to time reliably by hand. |
| Temperature | Use a thermometer or temperature probe. Put the sensing part in good contact with the material as instructed and wait for a steady reading. In a liquid, avoid resting the sensor against the container. |
| Liquid volume | Use a measuring cylinder of suitable capacity and divisions. Keep it upright and read the water meniscus at eye level. |
Record what was measured
Put the quantity and unit in each table heading, such as Time for 20 oscillations / s. The entries then contain the numerical readings. Keep readings consistent with the scale or display used; do not invent extra decimal places to make a result look more precise.
Keep enough digits during a calculation to avoid unnecessary rounding, then report the result with precision justified by the measurements. Show a mean or a corrected reading separately so the original observations remain clear.
Some quantities are calculated from several measurements. For example, measuring distance and elapsed time lets you calculate average speed. The examples below apply the same measurement principles to particular quantities.
Find a method for a particular quantity
- Motion: average speed and free-fall acceleration with light gates.
- Forces and materials: mass and force, density and surface pressure.
- Turning effects: moments and the centre of gravity of a lamina.
- Energy and power: useful lifting power and electrical input energy and power.
- Temperature: temperature readings, heat capacity and latent heat.
- Waves: wavelength, period and frequency, and wave speed.
- Light: reflection angles, refraction angles and focal length; also critical angle.
- Circuits: current and charge, voltage and e.m.f., and resistance.
- Radioactivity: background correction and calibrated activity, and half-life from a decay curve.