Hanging Mass on an Incline lab

Mr. Johnson shows off his hanging mass setup

In my general physics labs, we follow a familiar formula each week.:

(1) Students collect data, constructing a linear graph as they go.

(2) They take the slope of a best-fit line using far-separated points on the line that are not data points, including units on the slope.

(3) They use a relevant equation to relate the physical meaning of this slope to a measurable physical quantity.

That's it.  I keep things as simple as possible so as to work on just these three skills.  The trick is, of course, finding straightforward yet interesting experiments which lend themselves to this approach.  Oh, and these experiments must stick within the topic areas in general- (approximately Regents-) level physics.

The procedure is essentially the same each lab day.  I demonstrate a method of data collection.  I write on the board the graph that students are to make.  Students collect and graph their own data in groups of two.  Once I've approved a group's graph, then I hand them a two-page homework assignment for them to work on either the rest of the lab period, or that night if they need more time -- no one leaves early.

Ideally, I'm designing an experiment such that I know what the value of each group's slope should be, but the students do not.  This is a bastardized version of the "recurrent lab" as described by Mikhail Agrest.  Students earn credit either for predicting something using their slope, or for matching their slope to an independent measurement.

So, Greg, give us an example of such a laboratory activity.  Sure -- see the picture.  I have students set up an inclined track, on which they place a Pasco cart.  The cart is connected over a pulley to a hanging mass.    The hanging mass is adjusted until the system hangs in equilibrium.  The angle of the incline is what they are eventually going to predict; I surreptitiously come around during the period to measure each incline with my iPad clinometer app.

We graph the mass of the hanging stuff on the vertical, with the mass of the Pasco cart on the horizontal.  Some mass is added to the Pasco cart, the hanging mass is adjusted to equilibrium, and another data point goes on the graph.  Rinse and repeat for an easily obtained straight-line graph in about 30-60 minutes (including setup and cleanup).

The homework assignment based on this lab activity is available here.  In sum, students take the slope, and then are guided to identify the slope as the sine of the incline's angle.  Most groups easily match my measurement.  

This is one of my better lab exercises, because (a) it fits the formula we've been using all year with no deviation, (b) it allows for accurate prediction of a measurable but initially unknown quantity, and (c) it reinforces the content in the problem solving portion of the course.  Try it... post comments or questions.

GCJ

Revising my general physics laboratory program

Over the years, my AP physics labs have meshed into a true PROGRAM. That means not only are the individual experiments worthwhile, but that the year’s set of laboratory exercises serves to develop and reinforce a set of worthwhile skills. When the students start to roll their eyes at me as if to say, “yeah, yeah, we know what to do now, we’ve done it a dozen times,” I know that the lab program has been successful.

My AP lab program is designed to teach the lab skills necessary for the AP exam. Most prominent among these is the process of linearizing a graph, and using the best-fit line to determine an unknown quantity. That’s an important and useful skill…but one that is above the heads of my GENERAL physics students, at least at year’s beginning. For general physics, I have an entirely different set of experiments, each one solid, but without any guiding theme. In other words, my general physics labs in no way constitute a PROGRAM.

My summer mission is to begin to change this shortcoming: I want to revise my laboratory exercises so that they all mesh together. Specifically, I am going to try to use the “recurrent” lab model, as presented by Mikhail Agrest in The Physics Teacher, and as discussed earlier on this blog. My goal is for most of my experiments to ask students to use the result of their measurement to make a testable, high-stakes prediction.

[As a brief aside, note that no one is standing over me demanding that my lab exercises meet any particular “inquiry objectives” put together by “learning specialists.” No, I just have some time to invest for next year’s classes, so I’m working on general physics lab. I often see relatively new physics teachers become intimidated by the sheer volume of background work necessary to put together a strong physics course. The fact is, it takes many years before every aspect of your course will be successful. Partly this is because much trial and error is involved – I’ve wasted a couple of years here and there discovering why various physics teaching methods do NOT work for me. More to the point, no one has the time or experience to do everything perfectly right away. I’ve been teaching physics for fourteen years, and I’m only now coalescing my general physics lab program into something above the level of “adequate.” That’s fine – the labs have been adequate, and I’ve spent enormous amounts of time making other aspects of my course really good. Work on one thing at a time, and don't let anyone tell you you stink just because, say, your labs aren't perfect.]

The first topic of the year in general physics is position-time graphs. After nearly a week of lectures, demonstrations, and problems, the first lab exercise is to make a position-time graph for a “constant speed vehicle” using a stopwatch and metersticks. One goal of the experiment is to introduce my expectations for graphs in physics class, including proper labeling, as well as how to take a slope properly. Another goal is to give students kinesthetic experience with position-time graphs. They see that the slope of the position-time graph is the velocity of the vehicle, just as they’ve learned on homework.

What am I going to do differently this year? After each group has calculated the slope of their position-time graph, I will ask them to predict the position of the vehicle after it has been moving for, say, 10 s. Each group will give a location with uncertainty – i.e. 300 +/- 10 cm. Finally, *I* will measure the position of the cart after 10 s. Points will be earned for matching my measurement; more points, including some extra credit, can be earned for groups who match my measurement with the smallest uncertainty.

The second experiment uses “tape timers” to make a position-time graph for a cart on an incline. By taking the slope at several points, a velocity-time graph can be made, and used to find the acceleration of the cart. Except that this year, I will use a sonic motion detector to determine the acceleration of each group’s cart. Matching the acceleration that I measure will be a major part of the lab score.

You see? While every experiment won’t match this format, I’ll adjust as many as I can. You got good ideas? I’d love to hear them. Post a comment.

GCJ

“Recurrent” labs: image distance for a convex lens

I’ve been reading The Physics Teacher journal for over a decade. Every issue contains at least one interesting idea that’s somewhat new to me. I encourage you not to be put off by the frequent buzzword-heavy piece by someone trying to show “scientifically” that his pet new teaching method works… mine each issue for the experiments, demonstrations, and new ways of thinking about old topics.

This month’s issue (May 2009) contains what, to me, is the most revolutionary article I’ve ever read in TPT. Mikhail Agrest, of the College of Charleston, writes about his approach to introductory physics labs, which he calls the “Recurrent” method. Agrest presents a fully developed method that includes pieces of things that I have done, but never completely in the way he suggests. I’m going to try a Recurrent lab tomorrow.

According to Agrest, a Recurrent lab consists of three separate stages. First, an essentially traditional lab is conducted in which a parameter (like the focal length of a lens) is measured. Next, students are asked to use that parameter to predict the results of a slightly different experiment – for example, use the measured focal length to predict the location of an image given an object distance. Finally, students must perform that very experiment in front of the teacher to verify their prediction. Students’ grades are based in part on the accuracy of the prediction.

I’ve done similar experiments in the past, in which students predict an unknown quantity for a grade. The major inspiration provided by Agrest is to let the students develop their experimental method first, before challenging them to make a high-stakes prediction. My own contribution is to make the final prediction into a sort of competitive game: the lower the uncertainty in the prediction, the more credit the lab group can earn.

Stage I: We conduct a standard laboratory exercise with a convex lens. Students project the image of a candle onto a screen, and measure image and object distances. I ask each partnership to set up a graph of 1/do vs. 1/di before they start collecting data – each data point is to be graphed immediately. This way the students better see the relationship between the physical measurements they make and the graph… if they just make a table and graph it later, the lab becomes an exercise in arithmetic manipulation. A substantial part of their grade will be earned for the quality of the graph’s presentation.

Stage II: Once a lab group and I agree that they have investigated a reasonable range of object and image distances, I give them a new object distance: 5 meters. They are asked to use their graph to predict an image distance, including an uncertainty. They will do some calculation, and discover that they’re really looking for the x-intercept of their graph. (Tomorrow, I’ll explain that they’ve found the focal length of their lens.)

I give guidance as to the format of the image distance prediction (i.e. “30 +/- 2 cm), but I let them estimate the uncertainty in any way they please. The rules for stage III will guide their determination of uncertainty.

Stage III: I will compare their measured focal length to the value stated on the box. Eight of twenty points for the lab will come from the accuracy of their measurement. I set up a system of rewards for these eight points:

0 points are earned if the box’s focal length does not fall within the stated uncertainty.
4 points are earned if the measurement matches the box’s focal length, no matter how large or crazy the uncertainty.
7 points are earned if the measurement matches the box’s focal length, and the uncertainty is 10% or less of the measured value.

Then, for all groups whose measurement matches the box’s focal length, bonus points are awarded: everyone gets one point for each group with a larger uncertainty.

I suggest the students imagine that I have hired them to predict the image distance… it is most important that they be RIGHT. After that, the more precise the prediction, the better. My own thought is that this kind of game teaches the deep meaning of experimental uncertainty better than any mathematical exercise. Much credit to Mr. Agrest for the inspiration to refine the experimental approach described here.

(And yes, folks, I'm aware that the picture at the top of the post is emphatically NOT a convex lens. Please feel free to explain how I know that in your comment.)

GCJ