Errors and Uncertainties (IB)

There will always be something on the exam about this. Here’s a brief introduction

Some people get really wound up about errors. Don’t. They are easy to deal with if you just follow a few simple rules. An error isn’t a mistake, necessarily, just an uncertainty in a reading. Every measurement an experimenter makes is uncertain to some degree. The uncertainties are of two kinds: (1) random errors, or (2) systematic errors. For example, in measuring the time required for a weight to fall to the floor, a random error might occur when an experimenter attempts to push a button that starts a timer simultaneously with the release of the weight and waits a bit too long before pressing the button. Also, some external event, like a gust of wind on a falling feather might yield an anomalous result [For ‘anomalous’, read ‘weird’].  A transcription error is an example of a random error. You wrote, or transcribed the wrong number down. The voltmeter actually read 3.56V and you actually wrote down 3.65V. A systematic error can be caused, for example, by the zero on a meter being incorrectly set. All the readings thus are in error by the same amount, the ABSOLUTE UNCERTAINTY but not the same percentage.

Here’s an example. If I use a 250ml measuring cylinder calibrated in (say) 5ml steps:

The Absolute value of the reading is x ml +/- 5ml irrespective of the value of x

So, if the reading is 200+/-5ml, this represents 200+/- 2.5%

If the reading is 20+/-5ml, this represents 20+/- 25%.

So, ABSOLUTE stays the same, while PERCENTAGE (or fractional) varies dependent on the value.

Percentage and fractional errors continued:

Let’s suppose you’re measuring the current through and voltage across a small lamp, with  a view to calculating the power of the lamp [power = volts x amps , P=VI)

Here’s a particular set of readings taken with analogue meters.

err

Units are, of course, W.

Rule of thumb:

Metre ruler +/- 1 mm

Vernier calipers +/- 0.1mm

Micrometer  +/- 0.01mm

Stopwatch  +/- 1s

Otherwise,   +/- division on all other instruments. Look at the subdivisions and work it out. Now that we use digital telemetry a lot more this makes things more precise.

err2

err3

err4

In the next post, we’ll look at what to do with graphs and errors. Again, this ALWAYS comes up in the exam and you do need to get good at it.

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About John Vagabond

I have taught physics and math all over the world
This entry was posted in AS and A2 Physics and tagged , , , . Bookmark the permalink.

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