College-Prep Physics: Today we did another round of voting (a la Preconceptions in Mechanics) to answer the question “Does the table push up on the book?”
One snafu that happened this year that didn’t happen last year: Because we studied gravitational forces first, kids were confused by the question and thought about the gravitational attraction between the book and the table. This was something I did not anticipate. So I had to clarify the scenario (explaining that table’s gravitational force on the book pulls the book down rather than push the book up as per the question).
Last year, that confusion wasn’t an issue because we did normal forces first, which is the suggested sequence in preconceptions in mechanics. But I was dissatisfied with that sequence because there were questions about normal forces between individual objects that are stacked on top of each other. We were talking about the object at the bottom of the stack having to support the weight of the objects on top. Those complex scenarios are easily analyzed using system schema and free-body diagrams, but we hadn’t talked about gravitational forces yet.
So, despite the confusion this year, I still think gravity should be done before normal force. So for next year, I’m revising the questions. I’m going to start with the hand on the spring question, since the answer is obvious and we just wrapped up the spring lab. Hoping that question puts kids in the proper mindset, then I’ll move to the table on the book question. And instead of the foam question, I’ll replace the foam with springs. (My foam never really deformed much anyway.)
Here’s the revised slides I’ll try next year:
NGSS Science and Engineering Practice #2: Developing Models
NGSS Science and Engineering Practice #6: Constructing Explanations
College-Prep Physics: Yesterday, students designed their own experiments to determine the relationship between the stretch of a spring and the force applied to the spring. Today we shared out our results.
This year, I chose to use 2 different springs: one with a pre-load (red) and one without (green). My goal is to drive home that not all trends will go through the origin. Some groups still tried to fit a trend through the origin, though. Looking back, if I had been monitoring groups better, I would have asked those groups to go back and take more data for small stretches….hopefully continuing the linear trend down to the y-intercept.
NGSS Science and Engineering Practice #4: Analyzing and Interpreting Data
NGSS Science and Engineering Practice #5. Using Mathematics
AP Physics C: Students designed their own lab experiments to determine the relationship between the spring constant of an individual spring and the effective spring constant for: (a) identical springs in series; (b) identical springs in parallel.
NGSS Science and Engineering Practice 3: Planning and Carrying Out Investigations
NGSS Science and Engineering Practice 4.: Analyzing and Interpreting Data
College-Prep: Today we wrapped up the spring lab. Each group put their graphs on a whiteboard and we compared/contrasted graphs. We got at the notion that the slope represented the “Stiffness Factor” of the spring. To illustrate the linear nature of the spring force, we made a Counting Circle.
Considering a 0.22 N/cm spring, we stood in a circle around the room and counted off the amount of force that would be needed to get the spring to stretch every centimeter — 0.22 N, 0.44 N, 0.66 N, etc. It wasn’t easy for everyone. (In the essence of time, I use 0.25 N/cm for my other 2 classes.) Then I asked random kids what their force was (easy for them to recall) and then what their stretch was (Uh, oh. You want a calculator? How could you figure out without one? How many different ways can you solve the problem?)
I could see doing this for things like the speed of a tossed projectile every second. Or even the height of the projectile every second (TRICKY!).
I learned about Counting Circles from Sadie Estrella, a rock star math teacher from Hawaii. You can read more about her work on Counting Circles:
- TMC13 Presentation on Counting Circles
- The Blame Game (a post about why Sadie does Counting Circles).
College-Prep Physics: We’ve been discussing the ball-and-spring model for solids, so now it’s time to investigate spring behavior in more detail. What is the relationship between the force applied to a spring and the amount the spring stretches? We’re keeping it simple: using spring scales to measure force and making stretch the independent variable. Each lab group takes data for two different springs.
(Concept check: Which pulls harder — the spring on the scale or the scale on the spring? What is the scale actually measuring?)
Lab technique/concepts to focus on:
- graphing by hand
- zeroing the spring scale while it’s horizontal, not vertical
- measuring stretch (subtraction method vs. direct method)
- 5 to 10 levels of the independent variable
- Multiple trials for each level of the independent variable.
- Wide range of values for the levels of the independent variables.
- HOW TO SPACE THEM OUT? Limiting factors:
- Maximum safe stretch = limitation of apparatus, can’t overextend. So if your spring can safely stretch to 50 cm, you maximum level will be 50 cm. Space your lower levels accordingly.
- Maximum force reading = limitation of instrument, can’t go beyond 5 N. Your spring may safely stretch out to 50 cm, but perhaps doing so means the force is larger than 5 N. So your maximum level will be the stretch at 5 N. Space your lower levels accordingly.
- HOW TO SPACE THEM OUT? Limiting factors: