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

Question

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 intended answer as given by the grading scheme is:

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].

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*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.

Answer 1

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.

Answer 2

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.

Answer 3

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).