Problem — Direct or indirect measurement

Problem

Determine which of these is a direct measurement and which is an indirect measurement: (a) the length of a table read with a tape measure; (b) the average speed of a cyclist computed as $\Delta s/\Delta t$; (c) the temperature of a room read on a digital thermometer; (d) the density of a pebble obtained from mass and volume.

Solution

It’s worth fixing the underlying distinction. A direct measurement is one obtained by reading the value of the quantity directly on an instrument calibrated for that quantity, with no intermediate calculation. An indirect measurement, by contrast, is one in which the quantity sought is not read on any instrument, but is calculated from other quantities (these being directly measured) via a mathematical relation.

Let’s apply the criterion to the four cases:

• (a) Length of the table with the tape measure — direct. The value in centimetres or metres is read straight off the tape’s scale.
• (b) Average speed $v = \Delta s/\Delta t$ — indirect. There is no instrument that “reads the average speed”: the displacement $\Delta s$ and the time interval $\Delta t$ are measured, then the ratio is calculated.
• (c) Temperature with the digital thermometer — direct. The number appears on the instrument’s display, which is calibrated in degrees.
• (d) Density of the pebble — indirect. The mass $m$ (with the balance) and the volume $V$ (for example with a graduated cylinder) are measured separately, then $\rho = m/V$ is calculated.

$\ev{\text{(a) direct} \quad \text{(b) indirect} \quad \text{(c) direct} \quad \text{(d) indirect}}$

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Topics: Metodo sperimentale · Grandezze fisiche e misura