Hints on ISAs

Most recently added stuff above the line

Assessing reliability

This has to do with how small your uncertainties are, and how closely the points hug the eventual best-fit line. Don't get bogged down on ways of improving the experiment, which will be asked separately.

Very often there is an 'accepted' or 'expected' result. If this accepted value lies within the uncertainty range of your experiment then this might reasonably lead you to declare the result as reliable.

You could perfectly well calculate the percentage deviation of your result from the accepted result

           = (difference between the results / one of the results) x 100%

Note that this is NOT the experimental error - that role is taken by assessing uncertainties in the usual way!

  • When two quantities are added (or subtracted), you add their individual absolute uncertainties to get the absolute uncertainty of the sum (or difference)

  • When two quantities are multiplied (or divided), you add their individual fractional uncertainties to get the fractional uncertainty of the product (or quotient)

So you may need to be nifty at changing between fractional and absolute if you have a multi-stage calculation.
Be clear about different types of variables:
  • The independent variable: the one you deliberately change during an experiment
  • The dependent variable: the one you measure as a result of the change you've made in the independent variable
  • Controlled variables: all those that you might have decided on as the independent variable but haven't. You make sure that these do NOT change in order to ensure a 'fair test'.

Technically, something  only counts as a variable if it can be measured and have a number+unit attached to it. So the material of which something is made doesn't count as a variable, even though you may wish to keep it unchanged in the interests of fairness.

There are two main sources of uncertainty:

  • Random errors. You cannot eliminate these, and the only way of reducing their importance is by repeat readings - the more the better.

  • Systematic errors. These can be eliminated, once they have been identified. Examples include

    • reaction time when operating a stopwatch

    • zero errors (e.g. when the needle is pointing to 0.1 A even with no current, so that 0.1 A has to be subtracted from all readings)

    • parallax errors

Make sure you can classify any particular source of uncertainty as one of these. Don't use the words 'Human error' - choose a more particular phraseology (e.g. 'reaction time error' or 'parallax error'). Note that, in principle, many systematic errors will be the same every time. Variation in readings is nearly always because of random errors.
Always think about fiducial aids. If it proves difficult to take a measurement, feel free to make marks, draw grids, etc to make it easier. Feel free to ask for ancillary apparatus such as setsquares, mounted pins, etc.

Consider the possibility of better techniques, even if it isn't going to be possible to implement them. Would a data-logger help (with, for example, rapidly changing readings, simultaneous readings, readings over a long period of time)? Might it be a good idea to take video footage and then analyse frame by frame (you'd have to remember to include a ruler in the picture, to set the scale.
Your textbook has a section at the back on ISAs. Do read it. Also read Tables and Graphs and Uncertainty.

Be clear about code words.

  • 'per' means 'divided by'. So '6 percent' means '6 divided by 100' (i.e. 0.06).

  • 'rate' means 'per second', which you could find either by dividing something by the time it took, or by taking the gradient of a something-time graph.
It's really important to do as you are told. E.g. don't do something from the graph if you are told to do it from the table - and vice versa. Don't give a fractional uncertainty or an absolute uncertainty if you are asked for a percentage uncertainty, and vice versa (of course you can use any of the three at will during your calculations!)
The exam could ask you to deal with fractional uncertainty or with percentage uncertainty. To calculate a percentage uncertainty you multiply the fractional uncertainty by 100, and then put the % sign after it (which effectively divides it by 100). You can still use the same symbolism (dx/x), provided you remember to keep the % sign while you're in percentages.

So you could say, for example, at the end of a calculation of velocity

dv/v = dx/x + dt/t = 0.02 + 0.03 = 0.05

or

dv/v = dx/x + dt/t = 2% + 3% = 5%.

Then, if v had come out as 12 m/s, you would calculate dv with

dv = 0.05 ´ v =  0.05 ´ 12 m/s = 0.6 m/s

or

dv = 5% ´ v =  5% ´ 12 m/s = 5/100 ´ 12 m/s = 0.6 m/s

My advice is to steer clear of percentages unless you are told to use them. I'd advise always using an adjective to qualify 'uncertainty':

        fractional uncertainty in v = 0.05 (NB no units)

        percentage uncertainty in v = 5% (NB % sign essential)

        absolute uncertainty in v = 0.6 m/s (NB units present)

Quite a lot of marks are given for uncertainties. Make sure you've read the relevant web pages on this site, and make sure you have thoroughly understood all the remarks made on this topic on the sample write-up I sent to you. Among important points are to work out the fractional uncertainty in each quantity in order to see which quantities are contributing most to the overall fractional uncertainty (and which quantities, therefore, need concentrating on in the quest for improved certainty).
Upon reflection, I am of the opinion that you should never use "scales of three" on graph axes, even when you are doing a time scale in seconds. Just record the times in seconds and then put them on a conventional scale of 1, 2 or 5, even though a takes a little longer, and you can't use the autopilot method of going for the heavier lines. Better safe than sorry.
Beware that AQA are careless about quantity algebra, so they are perfectly capable of asking you to manipulate an equation that has a mixture of symbols and values-without-units, asking you arbitrarily to introduce an appropriate unit at the end of the calculation. For example, they might say, "Calculate the distance travelled in 3s, using the equation x = 5 t. Give an appropriate unit for x." So you just have to do as you are told, difficult thought it can sometimes be. Try to keep a clear head.

Bear in mind that some collections of terms have to be dimensionless. Powers, for example. If you see, in an electrical question, V = V0e– (t/RC), then you know that, because t is in seconds, RC must be in seconds as well, in order that the units cancel out when you divide one by the other. Similarly, if the activity at a distance x from a b-emitter is A0e– px, then the fact that x is in metres, means that p has to be in metres-1 so that the product is dimensionless.
It's probably worth looking at the Wikipedia entry for dataloggers, in order to see some of the benefits. There's a paragraph in your textbook on them, too. Try to make a list of their benefits: acquiring data at closely spaced intervals, acquiring data from various sensors simultaneously and at precisely known times, acquiring data on a round-the-clock basis, and in inhospitable environments, etc, etc.