Newton's 2nd Lab

I thought that I had posted about this apparatus before, but I guess that I hadn't, so here goes:

I've tried several setups through the years for students to model Newton's 2nd law. Qualitatively (balanced vs. unbalanced, direction on "unbalance" is the same as the direction of acceleration) getting the concept should come first - I have a previous post on that here, but when it comes time for modeling acceleration's dependence on force and mass, the setup can be tricky. Some that I've tried and/or seen:

• Pulling a cart with springs, measuring acceleration with a motion detector; it involves a lot of performance (keeping the spring stretch constant) time and practice that I'd rather have them spend on the analysis, especially with my small number of class days
• Half Atwood machine: you can easily vary the hanging mass to change the force exerted on the cart, but you can't equate the hanging weight to the tension, and you can't solve for it unless you know N's 2nd already. You can change the mass of the cart, but then you're changing the tension.
• Half Atwood machine, analyzed as one system: it's procedurally easier, but mystifying for students. Looking at the whole system means that your vector directions will have to be changed because of the pulley, which seems mysterious to students that haven't done that much force analysis. Keeping the weight of the hanging mass constant while adding mass to the cart is easy, but then they really need to record the total mass of the system, which is a bit conceptually tricky so early on. Keeping the total mass of the system constant when you are changing the hanging mass is similarly black-box for them at this point. It's an elegant setup from our point of view, but doesn't ultimately make much sense to most of them at this point in their physics careers

Here's what I used this year:

Half Atwood machine, with a force sensor screwed to the cart (the string's tied to the sensor). A motion detector helps them find acceleration (from the slope of the v vs t graph):

• The system being analyzed here is just the cart. The force probe measures the tension directly, so no complex analysis or tricky conceptual arguments need to be made. About halfway through, it's good to stop them and ask them to compare the hanging weight to the tension force reading and to explain the discrepancy conceptually.
• Varying the force exerted on the cart just means varying the hanging mass, and varying the mass of the cart is simple, too - no mysteriously motivate shuffle of masses back and forth. The experimental design is completely transparent to them.
• You might want to have them split into two factions: some groups investigate how acceleration varies with force and others investigate the dependence on cart mass. They then present whiteboards and the class can determine the combined model from the two partial models. Don't underestimate the reasoning leading from the two individual models to the combined model.

Everything seemed to go quite smoothly (that last conversation's still a bit difficult - I need a better angle on that, because it happens frequently), and my students this year have become stronger conceptually and computationally than with the setups that I've tried in the past, while moving at a faster pace. This one seemed to work quite well.

Spring Wave Speed Lab

My first lab with the spring wave speed used to be a prescribed method of stretching the spring, then keeping the length the same, but not using all of the spring, using the unstretched spring amount as a stand-in for tension, etc. ... It became more about direction-following and less about understanding than I wanted, and I had to dismiss the possibilities of amplitude, etc. affecting the wave speed. At the end of it all, they still didn't have the main idea (that wave speed only depends on properties of the medium) in mind very well.

I've gone to a more open-ended WCYDWT-style lab:
"Here's a slinky: look at these cool wave pulses. What do you think might affect their speeds?"

Take down the list dutifully - this year's ideas:
First section:
- Spring tension
- Amplitude
- Carpet vs. tile floor
- Horizontal vs. vertical pulses
Second section:
- Spring stretch
- Amplitude
- Frequency (this was a fun one to test. There was a metronome involved, and it was tricky to measure the speeds of the lower frequency waves, but it was a good experience for the hearty)

They did a much better job of experimental design, whiteboarding, and presentation than in the past. I'm still having to answer too many questions/guide Socratically too much about what should be on the axes and what the order of the axes should be, but the Honors classes are much better in that regard. Time will hopefully improve this situation for both. Everybody's getting the experience of designing and analyzing, and of calculating the wave speed, too, regardless of their question.

The whiteboards:

Question Boards and Answer Boards

I've been taking pictures of student whiteboards for a while, uploading them to our online classroom on our school's website. When the problems are different, they can be a source of extra practice (complete with solutions) for students.

When the framework is WCYDWT (What can you do with this?), the problems are definitely all different, because they're generated by the students. Today, I had them shoot a launcher straight up in the air, and then they had to develop and answer a question when the launcher was at some other angle. They determined the initial velocity from the first shot, and then came up with a variety of other scenarios for the 2D shot, including simple range equation angle and distance determinations, all of the way up to firing a ball into a moving CVPM buggy.

I structured the whiteboard sharing a little differently this time, though. I had each group write up a nice solution on their big whiteboard, just like normal, but I also had them use a small whiteboard.  On the small whiteboard, they made clear what their question was and included only raw data. This is the "question" board, and the big one is the "answer" board. This makes the process of using these as practice problems more practical and more like "flying solo."

Here's an example:

Collision!

Today was the day for the collision practicum! I set up the air track, cart, and pendulum like this:

I released the cart from the top - 4.8 meters away - and they could time how long the trip took (3 trials).  I also let the pendulum swing for a while, and they could measure whatever they liked. I assigned each group a number of cycles which the pendulum must go through from the time when they release the cart until the cart reaches the bottom of the ramp. They must calculate the location at which the cart must be placed in order to make that happen. There's a piece of magnetic track from my son's train set that makes noise when the magnet attached to the bottom of the pendulum swings just above it - this signals success.

My tests before school were all very successful, so I was hopeful before class about their success.

I had each group write up a whiteboard that just needed data plugged in, and we began the data-taking with about 30 minutes left in class.

In the first class, almost all of the runs looked extremely close, but we couldn't get the sensor to trip - downer. :(  In the second class, I adjusted the sensor setup, and two out of four were successful. One of the others had a good method, but was just a touch off in execution and/or measurement.

Success!

Whiteboards:

A Practicum I Can Believe In

I've had some difficulty coming up with a good end-of-term practicum for the physics class for a while. This year, we put motion up front (CVPM and CAPM, all graphical analysis) and then went into oscillations (this used to be our first topic).  In oscillations, I've traditionally looked at period/frequency and amplitude, oscillation graphs, using proportional reasoning to solve problems, and qualitative restoring/driving/damping forces.  Proportional reasoning is something that this crew needs to work on in practice, so much of the year is topics that yield to it fairly well.

There have been several benefits to changing the order, though:
- the oscillation graph analysis seems to come just after they cover it in Pre-Calculus, so that saves me a lot of headache
- I can add motion analysis (where's the acceleration the highest?, find the max v from the position graph, etc.) that I couldn't do before
- the reasoning goes down better after they've done a lot of it in CVPM and CAPM, even though it should've been better to start with the easier reasoning here. It probably has something to do with their familiarity with speed vs. their unfamiliarity with period

Another benefit is that I can put together a robust practicum that uses both CAPM and OPM:

• On the day, I will set up a ramp of unknown length.  There will be a pendulum at the end, oscillating perpendicular to the track.
• I will let them observe the pendulum in motion.
• I will demonstrate for them, three times, the cart starting at rest at the top and traveling freely to the bottom.  I will tell them the length of the track.
• I will assign each group a number of oscillations - the pendulum must complete this number of oscillations between the time the cart is released and the time that the cart gets to the end, and the pendulum must collide with the cart as it reaches the end
• They need to have a procedure ready to determine how far up the track the cart needs to be released in order for these things to happen.

I let them work for a couple of days in groups, with a pendulum and a 1.2 m cart track. They need to develop and test their method so that it can work in any situation that I give them. 

I give them a packet with several pages: one for outlining a plan of attack (which they need to revise, if that plan changes), and several pages for completing each sub-task. Identifying that they need to determine how long the cart will have to travel, and that they need to measure the period of the pendulum and use the given number of cycles to find that time, is one example of a sub-task here. 

Students tend to be bad at laying out an abstract 'path' through a problem, especially if there's unknown information there. It's a tricky issue to tackle, but requiring these kinds of tasks of the students is certainly part of the equation. It's basically the same thing that I'm trying to address with the chains of reasoning exercises.

I laid out that structure on the first day, and students jumped into the problem at different spots, and most figured out a couple of sub-tasks at least.  There was a lot of average velocity vs. final velocity confusion, as is typical for these students.  On the second day, I had them start by writing out a list of the sub-tasks that they had identified - this is the "flow" of problem-solving that I'm trying to help them with. Most were good at this point, even though most groups hadn't figured out how to accomplish all of the sub-tasks yet. Here are the summary boards: interestingly, the first section was able to parse the task very well, but the second section had a great deal of difficulty understanding what the task was, which numbers were measurements and which were calculations, which variables explicitly affect their calculations (and should be measured, like the amount of time for the cart to go down the track) and which implicitly affected it (like the angle of the ramp, which affects the acceleration, but which doesn't appear in their calculations).

For the practicum itself, I'm using my 5 meter (!) air track :)

Nonuniform Circular Motion

I was trying to create a non-uniform circular motion experiment this summer, but I was barking up the wrong tree.  I thought about swinging a ball in a circle at constant speed and have students derive the tension as a function of time or angle - measuring it with a force sensor - but you have to mess with the pivot point of the string (in a really interesting way) to make the ball move like that. Also - that's not non-uniform CM anyway! I then tried (at Physics Teacher Camp) to put a horizontal pole through the force sensor's mounting point and let a weight swing on a string - nonuniform CM was good, but the non-zero mass of the sensor ended up being a huge issue, and the tension was hardly ever parallel to the sensor's axis.

This week, I figured it out: the sensor is the ball. I attached a string to a rotary motion sensor (so that I could determine the angle and angular v as a function of time) and hung the force probe from it.

Puling it back and letting it swing, I got a good data set, even though I couldn't effectively zero the rotary motion sensor for some unknown reason.

Students then looked at the forces acting on the probe at some arbitrary angle and derived the tension as a function of angle and angular velocity.

To get the model to work without the rotary motion sensor being zeroed, I added an offset to the formula when I created a calculated column in Logger Pro. Once I did that, we could compare the graphs of actual tension (red) and predicted tension (pink):

There's an interesting time offset that I haven't explained yet: ideas?