Measuring acceleration due to gravity in the lab

I am measuring the acceleration due to gravity in the lab with an electromagnet apparatus.

My textbook says to take the average time for a number of falls (keeping the height constant of course).

But I recall many moons ago being told to take the shortest value, not the average.

The explanation being that the electromagnet can retain some magnetism for a short time after being switched off. So the ball can take longer than it should but not shorter.

Any thoughts on this?

Should I go with the shortest value or the average?

• These are the things that I never understood in error treatments. And I am even a chemist :( Another I hate is measuring a rod with the same ruler. But I think you can be wise in this case . However there won't be space for much error analysis..... – Alchimista Sep 21 at 10:49
• @Alchimista What do you mean by '' measuring a rod with the same ruler '' ? – Kantura Sep 21 at 10:51
• Lab exercise in which I was asked to do error analysis doing exactly that :( which by the way isn't in principle different from your current task. Except that you likely got different time readings. – Alchimista Sep 21 at 10:53
• @Alchimista Was it the same person doing the measurement over and over ? Or were there different people involved ? – Kantura Sep 21 at 10:57
• It does not change much assuming decent operators. Especially not in the rod case. But note that I was commenting, not answering. I do have a fundamental trouble on these topic. Namely I can see the sense of averaging samples but I fail at the same for the same sample repeatedly measured, at least for measurements with no noise. I personally would be wise in your case. But let's wait for an answer. – Alchimista Sep 21 at 11:03

1 Answer

Generally there are two types of errors in an experiment, random errors and systematic errors. In this case there is a random error due to your limited ability to record the time of fall precisely. There may or may not be a systematic error due to the fact the electromagnet does not release the ball the instant you press the switch.

Random errors show up in your measurements because they are random. That is, when you measure the same thing many times you get results that are scattered. We generally assume the errors follow a normal distribution, so then we can calculate a standard deviation $$\sigma$$, and the final standard error from doing $$N$$ measurements is $$\sigma/N$$.

Systematic errors are much harder to find because they can't (or at least can't easily) be spotted from a statistical analysis of your results. If your electromagnet took e.g. 0.1 seconds to release the ball after you pressed the switch you wouldn't easily be able to spot this. So as a general rule we do the best we can i.e. calculate the random error. That's why you are being told to take the average value of the time (and the standard deviation?). If there is a systematic error due to the magnet you would have to find that by other means. For example you could do the experiment for a range of different heights.

• The answer is written as if the OP doesn't understand the difference between systematic and random errors, and the issue is they they need that explained. My reading of the question is that the OP understands that, but is wondering whether there is a random element in the process of releasing the ball. (I would think there was not, since it seems like it would be a deterministic process involving an LR time constant with some hysteresis thrown in.) – Ben Crowell Sep 21 at 12:48
• @BenCrowell To give an answer about whether the errors in OP's measurement are systematic or random, we'd need to know an awful lot more about the apparatus than they've shared. – The Photon Sep 21 at 14:28