Race time measurement
Class practical
This is an introduction to the language of measurement, including concepts of range, reproducibility, mean value, true value, accuracy, instrument resolution and, most important, measurement uncertainty.
Apparatus and materials
For each student or student group
Stopwatch or stopclock
String
Statistics board (see technical notes)
Masses, 50 g, 5 or 6
Cones/track markers, 10 OPTIONAL
Video camera OPTIONAL
Tape measure, long (at least 10 m) OPTIONAL
Health & Safety and Technical notes
If working outside, students must be appropriately supervised.
If a trolley is used in the lab, ensure that the trolley cannot land on anyone's feet or legs.
1 A statistics board is made from a piece of wooden board about 0.5 m square. Ten slotted channels are glued to it and metal (or other suitable material) discs are cut so that they fit into the channels. The board is supported vertically.
Assign values to each channel. Students drop in a disc for the value they achieve. The distribution of results grows as results are added.
Procedure
a) One student runs a distance of 100 metres. You, and other students, all independently time the run.
b) Compare all of the measurements. What is their range (the difference between the highest and the lowest measured values)? What does this tell you about the reproducibility of the measured values of time?
c) What is the mean of all the measurements? A mean is a kind of average. Work this out by adding them all together and then dividing by the number of measurements. How closely do you think the mean value agrees with the true value of the run time? In other words, estimate theaccuracy of the mean value.
d) Did everybody use stopwatches with the same resolution? For example, were everyone’s stopwatch time indications in tenths of seconds or hundredths of seconds? (0.1 second is a tenth of a second; 0.01 seconds is a hundredth of a second).
e) Try to estimate the reaction times involved in pressing a stopwatch to both ‘start’ and ‘end’ the run. The sum of these reaction times is very likely larger than the resolution of the stopwatch.
f) How certain can you be about the actual time taken for the run? You can’t be perfectly certain! There must be some uncertainty in the measurements. The mean measurement could be 14.8 seconds. Perhaps you think that the ‘true’ time for the run is in between 14.6 seconds and 15.0 seconds. Then you can say that the uncertainty is ± 0.2 seconds.
Teaching notes
1) The most important term here is measurement uncertainty, a concept that can be introduced early in science education. Additional terminology about measurements should enhance its meaning and not distract from it. For example, you may decide to omit steps d and e from the Procedure (above).
In more advanced work, measurement uncertainty is sometimes called measurement ‘error’. Here, the word uncertainty more clearly describes a reasonable doubt about the result obtained.
2) Precision is a quality denoting the closeness of agreement between measured values obtained by repeated measurements. If values cluster closely, measurements are called ‘precise’. Reproducibility is the precision obtained when measurements are made by different operators using different instruments.
3) Statistical treatment plays very important parts in modern science. In advanced experiments students are expected to treat errors with some statistical care. In kinetic theory the steady pressure of a gas is recognized as an average of innumerable individual bombardments. Statistical methods are used to delve into details of molecular speed or sizes. In modern atomic physics statistical views are of prime importance. So you might well make a gentle start to later science studies by showing how scientists look at a number of measurements of the same thing.
The times could be collated as lists of numbers or, using a computer, as bar charts, or using a statistics board. Bar charts enable students to understand range, mean and uncertainty visually.
4) It is worth pointing out that there is such a thing as too many digits in a quoted value. A student who uses a stopwatch and gives a time of 14.77 seconds is crediting the timing process with less uncertainty than it actually has. Answers of 15 seconds or 14.8 seconds may be acceptable (depending on the timing procedure and the stopwatch).
5) ‘Mean’ is here used to indicate a particular kind of average – that found by dividing the sum of values by the sample size.
6) You could repeat the activity for a different motion, such as for a trolley pulled across a metre distance on a table, or the fall of a mass. Again, all students should measure the time for the same motion. Range, mean value, and measurement uncertainty can be compared with those for the student’s 100 metre run.
7) You may want to compare timings for real sports races. Information on sporting records can be found on the Internet. For example see Usain Bolt's record breaking 100 m run in the 2008 Olympics. Instrument resolution for different sports could be compared, and students could discuss the idea of uncertainty in the measured values.
8) How Science Works extension: This experiment covers concepts of accuracy and precision of data, as well as measurement uncertainty. The scope could be increased further, as follows:
- Arrange pairs of students every 5 m or 10 m apart along the 100 m running path. Use some kind of signal (e.g. dropping a raised arm) to start both the runner and everyone’s timers. As the runner passes each student, they stop their timer and record the time taken to reach them.
- Students then plot this data graphically (distance against time). This will make it easier for students to understand average speed and get a feel for the variation in measurements. A true value of velocity can be calculated from the gradient of the best fit line.
- If you placed cones/markers along the track, you might be able to video each student running, with a stopclock also in the camera view. This would generate a second set of results that could be compared numerically or graphically to the class set. Students could comment on whether this method improves on the previous one.
This experiment was safety-checked in January 2007