Students worked very diligently, as you can see in the pictures above (7th hour) and below (6th hour), solving force problems. Today was the first day that I felt like they had confidence in solving the problems, a huge success! They have a big University of Minnesota exam next Thursday and Friday, so today is a great day to start seeing success.
Today we were investigating how friction works as a class. We had talked about static and kinetic friction way back when we introduced forces in the first place, now it was time to find the similarities and differences between them. We started with magnitude comparison in my first class. I have cardboard ‘sled’ that I add mass to, then pull with a rope attached to a force detector. The force detector really reads the tension in the rope, but we talked about (complete with FBD’s) that when the sled is at rest or moving at a constant velocity, the tension must be equal to friction. Thus the detector gives us the value of friction, for those cases.
I started the demo, pulled gently until the sled moved, then pulled it at a constant velocity. The graph looked very much like the top one on the picture above. I asked when the sled started moving, someone said ‘before the peak…the peak is the accelerating part.’ Challenge accepted. I wanted to show, as textbooks do, that the peak of the graph is when the object starts moving. So we grabbed a motion detector. We hooked it up, redid the trial, found the time when the object started moving based on the velocity graph, and found that….the object started moving significantly before the peak, as shown above. Hmm. Let’s try that again. Same thing. Wow. We broke physics. Although, in most cases, at least the force at the time of movement was still greater than the force while it moved at a constant velocity…but not convincingly so.
As often happens in class, I didn’t have a good explanation at the time (I am a processor…I come up with great comebacks to what people say to me, 5 minutes after the leave). But it turns out that I continue to increase the pull even when it starts moving. Seems obvious now, as the time between moving and the max force is 0.15 seconds, similar to human reaction time.
I tried another trial where I increased the pull quickly, that certainly didn’t help. But then I tried increasing very slowly (this was after school was out when I had a couple minutes to play).
It was important to be able to feel the breaking point happen, as I was increasing my pull so little that the sled moving allowed the pull to decrease at that instant. Nice to know that physics still works. It’ll be fun to discuss this with the class tomorrow!
Today we worked on a problem with two accelerating bodies (modified Atwood), no friction. The students drew great free body diagrams!
I also got a text sample in the mail; we are thinking about adopting AP Physics C and this would be a strong candidate for the text.
I’m no artist, but the sunshine combined with awesome math (and our new diagram, force addition diagrams) made for what I thought was a pretty cool pic.
Another idea from Kelly, students were given the ramp angles and that the shallow ramp cart will be released from the 1 meter mark, then had to find where the 2nd cart should be released from such that they hit the end stops at the same time. A note, turns out the ratio of the angles is very close to the ratio of the sines of the angles, so you either can’t let them test till they have physics that supports their answer, or find a way to maximize the difference between the two ratios so it is obvious that the ratio of just the angles doesn’t work.
Today we whiteboarded elevator problems, and the students blew me away. They’ve got it! We had 10 minutes at the end, usually unheard of, so we grabbed the force plate and Labquest and headed over to the elevator. Half the class rode with me while and crowded around to see the detector as we watched the force readings in real time, while the other half waited on the floor above. Then we switched, and the other half rode down. We still had time for a group photo op at the end. Check out the pretty awesome data below. A question to leave you with; was this going up or down?
Kelly O’shea tried to convince me and a couple other physics folks at our Thursday night physics teacher meeting that using tip-to-tail vector addition was the way to go for problem solving with forces. I resisted. How could that possibly be better than components? Then I saw how well it works for ramps in particular, as shown above. The first is a simple diagram of the situation where I added some lines so we could find where theta should go in the force addition diagram. The second diagram is a free body diagram in which I added the second, lower normal force at some point to show how the FBD is turned into the force addition diagram, and the third diagram is the force addition diagram complete with the huge Fnet arrow. We talked about this conceptually, such as how Fnet and acceleration have to be in the same direction, and how finding Fnet would allow us to find the acceleration through the newly discovered Newton’s 2nd Law. I must admit, this method makes ramp problems much easier. I’ll probably still show them axis tilting, as some kids will probably like it and I want to make sure they know ‘conventional’ methods still, at least until I am confident enough that they can do everything needed using the ‘unconventional’ methods in future classes. Plus this method actually gets more at the core as to why tilting the axis works. But I digress.
I introduced the new diagram using the typical pull-a-box-along-the-ground-with-a-rope-at-an-angle type example (which is actually shown in the link to the Thursday meeting above). I couldn’t believe it; the class ate it up. Audible oohs and aaahs! They really like this diagram, at least right now. We’ll see how it goes for problem solving the next couple of days.