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## These uncertain times

By Pat, 13 February 2013 Activity

‘I know because I measured it!’ you might say. But how uncertain should you be about that measurement?

### You will need

You will need these materials.

• 2 friends
• 2 stopwatches that can measure hundredths of a second
• Ball
• Metre ruler
• Pen
• Paper

### What to do

1. Give each of your friends a stopwatch.
2. Hold the ball 1 m above the ground.

Drop the ball from 1 m and have 2 friends time how long it takes to hit the ground.

3. Make sure your friends are ready. Drop the ball, and have your friends time how long it takes for the ball to hit the ground.
4. Compare the stopwatches. Write the times down on the paper.
5. Drop the ball again, and compare the times. Are the times the same?
6. Repeat a few more times, and compare the results.

### What’s happening?

You will probably observe that few (if any) of the times match exactly, although they will be similar. This is because differences in your friends’ reaction times lead to slight differences in the readings on the stopwatches.

Compare the times and write them down on the paper. Drop the ball again and compare the times. Are all the times the same?

The measurement of the height also contributes to differences in readings. The second time the ball was dropped, it may have been a few millimetres higher or lower than the first drop. It might not sound like much but it does make a difference to the times recorded on the stopwatches.

What is the correct time? The answer is, you can’t tell just from the measurements. In some cases, your friends might know they missed the start, or pushed the wrong button on the stopwatch. In such cases, if you know a mistake was made, you should ignore the measurement.

Whenever a measurement is made, it is not possible to be sure that the measurement is completely accurate. We say that there are uncertainties in the measurements. The sources of these uncertainties are called errors.

Sometimes the uncertainty will be small, at other times it can be quite large. Generally speaking, the lower the uncertainty, the more confident you can be that you have an accurate measurement. The uncertainty can sometimes be unacceptably high. In such cases you might have to change your measurement method to obtain results with a lower level of uncertainty.

### Applications

Uncertainties in measurements are important in all scientific experiments. Scientists need to know that what they measure and observe is an accurate reflection of what is actually going on.

Scientists routinely report the uncertainties in the experiments that they do. This is to demonstrate how confident they are in their results.

There are ways to reduce the uncertainty in measurements. They include improving the method used to take the measurement, using more accurate equipment, and performing repeated measurements.

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