Uncertainties in A Level Physics

The A level reform brings uncertainty (pardon the pun!) of how the practical work will be examined and what level of error analysis will be required. I set up Guzled to make life easier for physics teachers. So I set to trying to iron this out.

The exact requirements of errors and uncertainties can be quite ambiguous. We have been through all specifications with a fine tooth comb and here is what we have found.

Calculating Uncertainties in Repeated Readings

Example: A student measures the velocity of a ball as it passes a light gate and records the following results:

• The average velocity is (1.24 + 1.92 + 1.34) / 3 = 1.50m/s.
• The uncertainty in the velocity is half the range of the readings: 1.92 - 1.24) / 2 = 0.340m/s.
• It is good practice to then add any error in the measurement. In this case, it is 0.005m/s.
• The final uncertainty is 0.340 + 0.005 = 0.345m/s.

The uncertainty may also be found as the difference between the average reading and the biggest or smallest value obtained, whichever is the greater. Since it is expected that students produce an estimate of the uncertainty, either of these two methods are acceptable.

Error Bars

There seems to be no requirement to use error bars in AS. However, it expected that error bars should be plotted in A2. The uncertainties calculated in the data relate to the size of error bars on each point.

The error bars produce, in effect, an error box around the point. The value could exist anywhere within the error box.

Maximum and Minimum Lines

Maximum and minimum lines of best fit can be used to find the uncertainty in the gradient. The maximum line of best fit is the line that passes through all the error boxes at the steepest possible angle. The minimum line of best fit is the line that passes through all the error boxes at the least steep possible angle.

If the graph does not have error bars, then judgement of maximum and minimum lines of best fit should be judged by eye.

You can download a help sheet for your students on error analysis here.