An Accurate Hooke's Law Laboratory - Comments

Greg Bernhardt submitted a new blog post

An Accurate Hooke's Law Laboratory


Continue reading the Original Blog Post.

That is a thoroughly enjoyable article. Thank you @Dr. Courtney.

I never did well in laboratory lessons in school, and I thought they were boring. Perhaps if I had a teacher who so clearly explained what we were doing and why, as you did in the article, that outcome may have been different.

anorlunda said:

That is a thoroughly enjoyable article. Thank you @Dr. Courtney.

I never did well in laboratory lessons in school, and I thought they were boring. Perhaps if I had a teacher who so clearly explained what we were doing and why, as you did in the article, that outcome may have been different.

I have to confess, for my first 5 years as a teacher, I used canned laboratory exercises that had been written by others that had many of the flaws you mention. Student engagement was low due to the lack of excitement and interest, so the care they exercised and the learning they accomplished also tended to be low. I also viewed the point of the lab as reinforcing material from the lecture.

Eventually, I shifted in my view so that the main focus of labs became understanding and applying the scientific method itself. This naturally caused me to desire greater accuracy, since an experiment with 1% errors tests any hypothesis more rigorously than the experiments with 5-10% errors that I had been doing. I think the biggest part in motivating accuracy is showing it can be achieved with due care at a few important points along the way. But one also needs to avoid labs and equipment where the learning curve is just too steep for most students to have accurate results. Consequently, one needs to be content not having a lab that corresponds with every chapter in the book.

These days, I write my own labs and before being overly confident in student ability to achieve results, I pilot the experiments myself and also check out the lab equipment carefully. It is extremely demotivating for students to be expected to have accurate results using faulty equipment in the compressed time frame of most lab experiments.

I guess I was fortunate enough that most of the science labs were enjoyable to participate in. I do remember that sometimes we did not get the desired result. That was frustrating.

I like how you designed the experiment for the students to learn about the concept as well as the scientific method.

scottdave said:

I guess I was fortunate enough that most of the science labs were enjoyable to participate in. I do remember that sometimes we did not get the desired result. That was frustrating.

I like how you designed the experiment for the students to learn about the concept as well as the scientific method.

You may not believe it, but part of my Hooke's law experiment that I gave to my students were DESIGNED to not work "as expected". I gave them springs that had been abused and no longer exhibit the linear behavior, but I never told them that. Looking at the F versus x graph will show that this wonky spring did not show the same behavior as the Hooke's law spring.

You'd be surprised how many students IGNORED this, and blindly fit a straight line to something that clearly could not be accurately represented by a straight line.

Part of doing an experiment is the ability to handle things when something unexpected happens. You cannot be oblivious to what the data are telling you and simply forced it into ways that you expect them to be, or if there was something weird going on that may be attributed to error in the measurement or setup. I repeatedly have told to my students that they can get away with getting unexpected result and still get very good grade for the lab report, IF they are able to account for the strange result and were cognizant to the fact that something unexpected was obtained.

Zz.

Zz, too bad I'm so old. It sounds like it would be fun to be one of your students.

anorlunda said:

Zz, too bad I'm so old. It sounds like it would be fun to be one of your students.

May I quote you on that and give it to my current students?



Zz.

ZapperZ said:

May I quote you on that and give it to my current students?



Zz.

Certainly, but your students might not appreciate it. We get old too soon and smart too late, probably applies.

ZapperZ said:

You may not believe it, but part of my Hooke's law experiment that I gave to my students were DESIGNED to not work "as expected". I gave them springs that had been abused and no longer exhibit the linear behavior, but I never told them that. Looking at the F versus x graph will show that this wonky spring did not show the same behavior as the Hooke's law spring.

You'd be surprised how many students IGNORED this, and blindly fit a straight line to something that clearly could not be accurately represented by a straight line.

Part of doing an experiment is the ability to handle things when something unexpected happens. You cannot be oblivious to what the data are telling you and simply forced it into ways that you expect them to be, or if there was something weird going on that may be attributed to error in the measurement or setup. I repeatedly have told to my students that they can get away with getting unexpected result and still get very good grade for the lab report, IF they are able to account for the strange result and were cognizant to the fact that something unexpected was obtained.

Zz.

Good point. A well designed lab course should include a number of cases where the hypothesis is not supported. But I prefer to put most of these later in the semester for several reasons:
1. Students tend to ascribe the lack of experimental support for a hypothesis to human or experimental error. I design most earlier labs to develop skills and build confidence in measurement accuracy to empower them to consider the possibility that the hypothesis might simply be wrong.
2. In cases like Hooke's law, the rule is more important than the exceptions for downstream courses. I would only present an experimental exception after the rule has been verified. There is probably time for cases that include both the rule and exceptions to Hooke's law in a 3 hour college lab once students are reasonably skilled and efficient. But this is unlikely in most 1 hour high school physics and physical science classes.
3. If a hypothesis will not be supported, I like students to have built enough analysis skills to suggest a different hypothesis. At some point in a lab course, students will be familiar with the most common functional forms: linear, quadratic, power law, square root, etc. and will have tested various data sets against multiple possibilities. If one hypothesis is not supported (such as a linear relationship), it is nice if students can explore other possibilities and suggest an alternative hypothesis from their data.

Dr. Courtney said:

Good point. A well designed lab course should include a number of cases where the hypothesis is not supported. But I prefer to put most of these later in the semester for several reasons:
1. Students tend to ascribe the lack of experimental support for a hypothesis to human or experimental error. I design most earlier labs to develop skills and build confidence in measurement accuracy to empower them to consider the possibility that the hypothesis might simply be wrong.
2. In cases like Hooke's law, the rule is more important than the exceptions for downstream courses. I would only present an experimental exception after the rule has been verified. There is probably time for cases that include both the rule and exceptions to Hooke's law in a 3 hour college lab once students are reasonably skilled and efficient. But this is unlikely in most 1 hour high school physics and physical science classes.
3. If a hypothesis will not be supported, I like students to have built enough analysis skills to suggest a different hypothesis. At some point in a lab course, students will be familiar with the most common functional forms: linear, quadratic, power law, square root, etc. and will have tested various data sets against multiple possibilities. If one hypothesis is not supported (such as a linear relationship), it is nice if students can explore other possibilities and suggest an alternative hypothesis from their data.

I think you missed my scenario. I included a non-Hooke's law spring. I didn't say that that was the only spring that the students were given. They were given 2 springs to find the spring constant. One was straight-up Hooke's law behavior. The other was not.

Whatever the situation, we have sit back and figure out what we are trying to accomplish here. Our Syllabus for this class includes training the students with the skills and ability to perform experiments and analyze data, including systematic and analytical evaluation of experimental results. So seeing them respond to something that was completely unexpected is part of it. I made it a point to discuss this situation when I return their lab reports.

Here's the thing. If they were walking down the street, and I show them a random graph that looks like the non-Hooke's law graph, none of then would say that the straight line is a good representation of the data. Yet, many of them seem to throw out this sensibility when they walk into a physics class! I want them to learn (often, the hard way) that they need to bring that sensibility into the physics classroom, and that just because we are learning physics, it doesn't mean that all their worldly experiences no longer apply.

I find that they learn more when they make the mistake without my warning them first, rather than if I talk till I'm blue about it before hand.

Zz.

ZapperZ said:

I think you missed my scenario. I included a non-Hooke's law spring. I didn't say that that was the only spring that the students were given. They were given 2 springs to find the spring constant. One was straight-up Hooke's law behavior. The other was not.

I caught your scenario. The next lab (immediately after Hooke's law) in my lab course is usually the simple harmonic oscillator, where the hypothesis is basically the formula for the SHO period, using the previously measured spring constant. Using Tracker as the timer and timing 10 periods usually yields an accuracy comparable to that of k in the original experiment for linear springs. Of course, this hypothesis will not be supported for a non-linear spring.

Since my labs are designed for 1 hour experiments, there is insufficient time to do multiple springs. But with a long enough class period, one could keep the fun going by having students perform the SHO experiment with the same set of springs as used in the Hooke's law experiment.

But the whole propensity to allow students to "eyeball" whether data is linear feeds their disposition to conclude data is linear when it really is not. Even high school students can learn how R-Squared and the uncertainty in the slope can be used to determine that one spring is a lot less linear than the other. If one has an estimate on the uncertainty in k, students can see how the SHO formula for period becomes a garbage in - garbage out exercise for the non-linear spring. A careful experiment with a linear spring can yield a 1% or better uncertainty in k, which can yield a 1% or so support for the SHO period formula. The uncertainty in k for a nonlinear spring is going to be much larger.

That's why I like the way we run our class here. We basically used the concept of "Studio Physics", where we really do not have an assigned session for "labs". Rather, the lab is considered as part of the lesson, where I often stop discussing the material and let the students check out something that is relevant to the topic. This works especially well when we do Lenz's law, where everyone has a bar magnet, a galvanometer, and a solenoid. I actually let them discover the property themselves as we go through various combinations of the magnet going in and out of the solenoid.

And since writing ability is included as part of our Syllabus, the students had to find the most accurate way to describe what they learned and to try to come up with a "rule" of what would happen under any circumstances.

But coming back to the non-Hooke's law experiment, during our class session, I had some of the best in-class discussion among the students based on this part of the experiment. It sets up perfectly for the rest of the semester what is expected out of the students, and they get a very early wake-up call that this is not going to be your normal, boring "labs". Even if they don't learn anything else, that realization by itself is worth doing this experiment.

Zz.

ZapperZ said:

scottdave said:

I guess I was fortunate enough that most of the science labs were enjoyable to participate in. I do remember that sometimes we did not get the desired result. That was frustrating.

I like how you designed the experiment for the students to learn about the concept as well as the scientific method.

You may not believe it, but part of my Hooke's law experiment that I gave to my students were DESIGNED to not work "as expected". I gave them springs that had been abused and no longer exhibit the linear behavior, but I never told them that. Looking at the F versus x graph will show that this wonky spring did not show the same behavior as the Hooke's law spring.

You'd be surprised how many students IGNORED this, and blindly fit a straight line to something that clearly could not be accurately represented by a straight line.

Part of doing an experiment is the ability to handle things when something unexpected happens. You cannot be oblivious to what the data are telling you and simply forced it into ways that you expect them to be, or if there was something weird going on that may be attributed to error in the measurement or setup. I repeatedly have told to my students that they can get away with getting unexpected result and still get very good grade for the lab report, IF they are able to account for the strange result and were cognizant to the fact that something unexpected was obtained.

Zz.

Wow ZapperZ, that's a nice experiment to do...

Pick any functional form, and any data, and there exists a best fit. This is the basis of politically motivated “science”.

PAllen said:

Pick any functional form, and any data, and there exists a best fit. This is the basis of politically motivated “science”.

Sure, but in teaching science we can do better. We can have an honest look at how well a hypothetical functional form "fits" the data - R2, residuals, p-values, and so on. Not that every intro lab needs it, but most intro courses would do well to have several labs where students are required to compare their residuals to their instrumental accuracy. Most intro courses would also do well to have a few labs where students fit alternate functional forms to their data. If a power law, square root, quadratic, or exponential fits the data better than a straight line, what does this say about the hypothesis that predicted a linear fit? These data analysis steps help students see beyond their possible confirmation bias if only the hypothetical model is tried. It also gives students experience and analysis tools to help them see through "junk science."