# Is it appropriate to award points for this answer? (experimental physics)

The experiment in question asks the student to take several measurements for the period with different pendulum lengths.* Then it asks the student to pick a length, with justification, before proceeding to more complicated experiments.

The student should pick the longest length. This is because the longest length has the lowest percentage error.

The answer that a student wrote is:

I pick the shortest length. This is because I only have 15 minutes left to do the rest of the experiment, so I cannot wait a long time between measurements.**

The student's answer is not wrong, in fact it is a very good reason, but it's completely different from the answer in the grading scheme. Is it appropriate to award points? If it is appropriate, is partial or full credit correct?

Related: Is it ethical to award points for hilariously bad answers? This answer is funny in its own way, but it's not hilariously bad.

Edit: since people repeatedly want to see the full question.

1. Adjust the length of the pendulum, then measure the period.
2. Estimate the percentage uncertainty in your value of the period.
3. Repeat the above for at least two more lengths. Tabulate the results.
4. Comment on the trend in your results.
5. In the upcoming, choose ONE of the above lengths that you used.
6. (i) Record your choice of length. (ii) Explain your choice of length.
7. Vary [a parameter x which I have simplified out of the experiment]. Record the new period. Comment on the effect the parameter has on the period.
8. Vary [a third parameter y which I have simplified out of the question]. Record the new period. Vary y again. Record the new period.
9. It is suggested that the period is equal to k/y, where k is a constant. Use your values from (8) to determine k.
10. Justify the number of significant figures in your value of k.
11. State whether your results support the assertion that the period is equal to k/y.
12. [And more stuff that I really don't see how they are relevant to the question].

*The length of a pendulum is related to its period by T = 2pi sqrt(L/g), where L is the length of the pendulum and T is the period. In other words, a longer pendulum takes longer to oscillate.

**The description of the experiment I gave is simplified. In the actual experiment, it takes up to one minute between measurements while using the longer length. With shorter length, it takes ~10 seconds.

• The grading scheme is wrong, not the student. Don't ask students to magically grok the mind of the questioner. Commented Jun 22 at 9:57
• Can anybody enlighten me what should be off-topic on this question? It’s about teaching in an academic setting (or at least it might occur within an academic setting). Commented Jun 22 at 10:17
• @Allure: But that still assumes that your ultimate goal is the lowest relative error. Neither did you specify this in the task nor is this how one should choose experimental subjects. Commented Jun 22 at 15:06
• " It should be implicit..." Exam questions need to be explicit and "should" makes assumptions. Commented Jun 22 at 16:08
• Asking the student to "...pick a length, with justification...,' with no other guidance, seems like an example of the classic, "Guess what I'm thinking?" bad practice by educators. See publications.aap.org/pediatrics/article/149/6/e2022057450/… Commented Jun 22 at 22:23

If the question just says “pick a length, with justification,” it would be unfair to deduct points. The student’s strategy might not be what you had in mind, but it’s a very valid strategy. Even the famous scientific collaborations make decisions based on the realities of limited budgets and timelines.

If the question says something like “pick the length that will give the best expected results, with justification,” I would give full credit only for a complete justification, which should mention both the advantages of the student’s selected strategy (can’t get good results if you don’t finish) and the disadvantages (higher expected fractional error).

Neither of these formulations is very clear, however. I would suggest phrasing the question much more precisely for future instances of this class.

• give the best expected results – I would consider even this too vague without further context. What is best depends on the scientific question. If the goal is to determine the local gravity (g) and the rule for the pendulum frequency is treated as given, it would indeed be a good choice. However, if the goal is to check the rule for the pendulum frequency, one should test as many combinations of lengths and weights as reasonably possible. Commented Jun 22 at 15:12
• It could be interpreted that the students justification was to maximise the number of trials in finite time, which might result in lower overall error even if error per trial is higher. Commented Jun 22 at 16:06
• @user1937198: Nice point. And it becomes even more poignant if the pendulums have sufficiently low friction. Then you can reduce the inaccuracy of measuring oscillation times by measuring subsequent oscillations: E.g., if it takes roughly one minute for the shorter pendulum needs to take 100 swings and for the longer pendulum to take 10 swings, your expected relative error is exactly the same, as the dominating source of inaccuracy is you starting and stopping the timer. Commented Jun 22 at 16:30
• @user1937198 Maximizing the number of trials does not automatically result in a lower error. If the uncertainty of measuring the period T is constant (reasonable), then it actually most efficient to take the longest pendulum, to obtain the smallest relative error for T and hence absolute error for g. Commented Jun 23 at 14:14

Different viewpoint here. If the instructions clearly indicate that the student was supposed to do the experiment with multiple lengths, then that clearly creates the context in which the justification must incorporate the data from the experiment to form some explanation of why one length would be better than another. If they only did the experiment for one length, they simply didn't follow the instructions, they don't have data available to compare lengths, and no justification would be valid. Zero points.

If they had done multiple lengths, but not all of them, then I would consider partial points if they had gotten the justification correct because they would have at least some data to incorporate into their justification. But even if the student in the question did do some, but not all, lengths, the student's justification still wouldn't work because it doesn't incorporate any of that experimental work.

Now, for a multi-part question or assignment where future points depend on earlier parts, if a student does something like provide the wrong number, I used to grade the rest as if that number was correct. The idea is that I didn't want to penalize them multiple times for one mistake; I want them to get points for the things they clearly can do correctly.

Some people have mentioned how the question isn't clear or is an example of "Guess what I'm thinking." I'd like to point out that we don't have the assignment in full or any of the other corresponding learning materials that would lend context. Presumably, the rest of the course material has given them the information they need to determine the answer. If it truly is an unclear question, then there would be multiple students having issues with it, and it should be addressed if that's the case. But I see nothing to indicate that from the original question.

It depends what the intention of the measurements really are.

If the intention spelled out in the assignment was to obtain an estimate for g=L(2π/T)² from measuring T and the accuracy δΤ of individual measurements is independent of T (a sensible assumption), then the typical error from each measurement is δg=δΤ(g/T) and after N measurements it is δg=δΤ(g/T)/√N.

Thus, to achieve a certain accuracy δg, one needs to make N=(δΤ/δg)²(g/T)² measurements. Each takes a time proportional to T, so that the total time required is proportional to 1/T.

Hence, taking the pendulum with the longest period is the correct choice if one wants to complete the task in minimum total time. The students answer is wrong (if the intention was to measure g with a specific accuracy).

• "Each [measurement] takes a time proportional to T" How do you know that? According to the question, the experimental set-up is such that there is a considerable delay between (!) the measurements, with the longer pendulum causing a longer delay. It is not clear whether the delay is proportional to the period T. Commented Jun 23 at 15:06
• None of that is clear from the question asked. The student shouldn't have to guess what the professor "intended". Commented Jun 23 at 16:45
• @Buffy Did you read my answer? No, this is not clear from the question asked here at SE, but it may be completely clear from the question asked of the student (which we are not told). Moreover, my answer stated If the intention was to obtain an estimate for g, implying that this was the stated in the question asked of the student. Commented Jun 23 at 16:57
• Sorry, but "intention" and "clear statement" are quite different. Nothing in the original question here mentioned any criteria for a choice. Your "implying" is a leap into the void. Commented Jun 23 at 17:00
• Okay, I can make that clearer in my answer Commented Jun 23 at 17:00