4.Main Content
experiments
Race time measurement
Class experiment
An exploration of issues of measurement, such as precision, range of values, uncertainty or ‘error’, repeat measurements and mean values.
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
Technical notes
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.
Safety
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.
Read our standard health & safety guidance
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 values)?
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.
d Did everybody make measurements with the same precision? For example, did everybody make measurements using tenths of seconds (0.1 second is a tenth of a second) or hundredths of seconds (0.01 seconds is a hundredth of a second)?
e 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 times can 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 error visually.
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 now by showing how scientists look at a number of measurements of the same thing.
2 It is worth pointing out that there is such a thing as too much precision in a quoted value. A student who uses a stopwatch and gives a time of 14.77 seconds is crediting the timing process with more precision than it has. Answers of 15 seconds or 14.8 seconds may be acceptable (depending on the procedure and the stopwatch).
3 ‘Mean’ is here used to indicate a particular kind of average – that found by dividing the sum of values by the sample size.
4 In more advanced work, uncertainty is conventionally called ‘error’. Here, the word uncertainty more clearly describes the concept. 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, precision and uncertainty can be compared with those for the student’s 100 metre run.
5 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, at http://www.youtube.com/watch?v=YFE1ctdRc88. Precision of measurement in different sports can be compared, and students can discuss the idea of uncertainty in the values.
6 How Science Works extension: This experiment already covers many of the areas relating to accuracy and reliability of data, as well as experimental errors. 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’ 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.