College-Prep Physics: Today I tried an idea from Andrew Morrison (blog, Twitter), which appeared in the November issue of The Physics Teacher: Single Sentence Labs. Andrew writes, “a truly authentic scientific experiment does not come with any instructions.”
So as an introduction to our unit on acceleration, students were given this single-sentence lab: Does a spring rolling down an inclined lab table speed up? Justify your claim with evidence and reasoning.
It was fantastic. Lots of discussion within and between groups about possible experimental designs and analysis.
Some students went the traditional stopwatch and meter stick route:
Others asked for motion detectors:
One group did video analysis:
On Friday, we’ll share our experiments and results.
NOTE: Last year, I did something similar, but used batteries instead of springs. Since the springs are hollow, they have a larger rotational inertia and accelerate more slowly than batteries. It takes about 5 seconds for the springs to travel the length of the 6 foot lab tables at a slight incline (about 3 volumes of Conceptual Physics texts high). I assume PVC pipe cut to pencil length would work well, too.
NGSS Science and Engineering Practices:
#3. Planning and carrying out investigations
#4. Analyzing and interpreting data
#5. Using mathematics and computational thinking
#7. Engaging in argument from evidence
College-Prep Physics: This actually happened a few days ago, but it’s too awesome not to share.
In an attempt to differentiate acceleration practice, I gave students a few choices. They could work on practice problems, work on graph interpretations, or do an acceleration challenge. Only one group of students from all 3 of my sections decided to go with the challenge. The goal of the challenge is to determine how far up the ramp to release a free-rolling cart so that it collides with a constant speed buggy at the bottom of the ramp. Students were not allowed to attempt any collisions, but could take data in order to determine the speed of the buggy and the acceleration of the cart down the ramp.
There are several ways to determine the cart’s acceleration:
- Collect position-time data by hand and calculate acceleration using kinematics.
- Film it and use Logger Pro or Tracker video analysis
- Use a motion detector and get the slope of the velocity-time graph
This time, the group decided to try the Ubersense app to take video and use the frame-by-frame feature to extract position-time data rather than using a stopwatch. They marked off 1 meter distances and videoed the cart rolling down the ramp. No need for the whole trip to be visible within the entire video frame — we can follow along with the cart and use the frame-by-frame playback to extract position-time data from the video:
Then they input the data into Desmos and tried to find a parabola of best fit to model the cart’s position as a function of time.
Next, they found the speed of the constant velocity buggy. Then I told them how far away from the crash point (X) the buggy would start. They then calculated the time it would take the buggy to travel to the X. Then they used that time and the Desmos graph to determine the distance the cart would travel down the ramp in the same time (e.g., the starting position of the cart).
As you can see at the beginning of the post, they nailed it!
College-Prep Physics: When an object moves with constant velocity, we know that the area under a velocity-time graph is the displacement. But what about for an object that’s speeding up or slowing down? So we used Logger Pro and a motion detector to get position and velocity data for a cart rolling down a ramp. From the position graph, you see that the cart started at x = 0.2 meter and reached the bottom of the ramp at x = 1.0 meter — which makes the displacement 0.8 meter. Then we used the area tool to find the area under the velocity graph and…. 0.79 meter! Now we’ve got a handy tool for solving for displacement and distance in acceleration problems.
College-Prep Physics: Given the position-time graph (left), what do the corresponding velocity and acceleration graphs look like?
We’ve been dealing with accelerated motion this week, so this problem is a throwback to the constant velocity motion from a couple of weeks ago. Several groups made the common mistakes shown here.
College-Prep Physics: Ramp n’ Roll is a fun Java applet that lets you adjust the heights of the ramps, starting position of the ball, and initial position of the ball. Then it animates the motion along with the graphs of position, velocity, and acceleration. I’ve used it as formative assessment — give the class a ramp set-up and ask them to predict the velocity-time graph.
You can access Ramp n’ Roll here: http://www.laboutloud.com/rampnroll/
Many thanks to NSTA’s Lab Out Loud for hosting the applet!
College-Prep Physics: Today we started looking at motion diagrams, position-time graphs, velocity-time graphs, and acceleration-time graphs using a cart, ramp, and motion detector. We started going through the scenarios in this packet:
College-Prep Physics: Today I flew down to Orlando for AAPT’s Winter Meeting. While I’m away, students are working on a pen-and-paper lab to find the relationship between the height of a paragraph of text and its width. It’s their first inverse relationship. This should make our future exploration of Newton’s Second Law easier.
You can download the paragraph passages here: http://www.eeps.com/pdfs/paragraphsWithRulers.pdf
And there’s also a more detailed student handout (with different paragraphs though) which has both inverse (height vs. width) and quadratic (height vs. font size) relationships to investigate:
College-Prep Physics: Today we explored graphical relationships for proportional, quadratic, inverse, and inverse square functions using Desmos. Here’s the sheet: MATH RELATIONSHIPS 2014
The goal is for students to be able to determine the type of relationship by looking at data.
Proportional: If X changes by factor of N, Y will change by factor of N.
Quadratic: If X changes by factor of N, Y will change by factor of N2.
Inverse: If X changes by factor of N, Y will change by factor of 1/N.
Inverse Square: If X changes by factor of N, Y will change by factor of 1/N2.
College-Prep Physics: We had shortened periods today because of the early dismissal due to the storm. But we had a block today of two 30 minute periods.
First period (pictured above): Students were challenged to show with data that a battery rolling down a ramp was speeding up. Then we shared experimental methods and results. 3 different approaches came up, but none involved time as the independent variable. So…
Second period: Students were asked to design an experiment to determine the relationship between distance and time for the rolling battery.