8.There are many ways to measure range of motion: goniometers, inclinometers, tape measures and even using apps on phones. In your opinion, do you think one tool is more accurate than another

the relative error is similar in all of them, which is why they all have the same precision.

Explanation:

For this question we must be careful since there are several important concepts to take into account:

* the absolute error that is directly related to the precision or error in the mean given by the instrument

* the relative error to take into account the precision of the instrument and the magnitude of the measurement

The precisions of the different measuring instruments are

metric conta           ± 0.1 cm

micrometric screw ±0.001 cm

vernier                    ± 0.005 cm or 0.001 cm

goniometers           ± 1º

I tilt meters              ± 1º

Mobile applications varies a lot, but on the order of  ±0.01cm

We can see that the tape measure, the micrometric screw and the vernier are the only ones that give us a direct measurement, in the others some calculation must be made to obtain the distance reading, for which the error must also be propagated for the calculation.

We must also take into account that the vernier and micrometric screw are for short measurements only a few centimeters, the meters allow a medium to about 20 m, for measurements of more distance the other instruments are needed

If we only take into account the absolute error, the device with a smaller error is the most accurate, but this is not very correct.

The precision must be related to the magnitude of the measurement carried out, that is why the error or relative uncertainty was defined.

Let's take an example with the tape measure.

If we measure a distance of 1 cm the relative error is ±0.1, for a distance of 10 cm the relative error is ±0.01 which is very good

if we use a vernier to measure 2 cm the error is ±0.0025

if we use an inclinometer or a goniometer to measure a distance of 100 m in error it is of the order of ±0.09 m

With a cell phone it depends on the form of measurement, but all programs involve the measurement of time of a pulse of light, and assume a constant speed of light regardless of the refractive index of the medium that changes this speed. In principle this could be a very precise method, but you must know the calculation procedure and the approximations used.

As we can see, to give a correct answer we must use the relative error in this case the instruments that use the optical measurement method should be the most accurate, but the software for the calculation can involve large approximations.

Of the other instruments, the relative error is similar in all of them, which is why they all have the same precision.

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