Archive for October 2011
Back to the slinky drop. The last of the Veritasium videos shows a slinky with a ball attached to the end being dropped (as opposed to the slinky stretched only by it’s own mass). This particular video is here.
The ball-on-slinky video appears to show the ball moving downward almost immediately, as opposed to the slinky-alone situation, where the lower coils do not move until the slinky has collapsed upon itself. In the comments to the Dot Physics blog where Rhett Allain has posted a computational model of the slinky drop, it is suggested that the mass of the ball shifts the center of mass lower in the slinky-ball system, thus making the lower end of the system move sooner. This puzzled me, because the ball seemed to move right away.
Since my students were busy learning how to use Tracker to do video analysis on the slinky-alone situation, I dove into looking at what was going on with the ball-on-slinky situation. The video that Derek had sent me was 300 fps, and I looked at every third frame (every 0.01 s), since I was unsuccessful in getting the autotracker feature to work on the top of the slinky. The slinky is dropped very quickly after the high speed video starts, so I started my analysis on the very first frame. The vertical position of the top edge of the tennis ball with respect to time is shown below (autotracker worked great on this… yay!)
As you can see, the ball is moving by 0.02 s after the start of the video. This is the seventh frame of the video. Interestingly, the ball falls with a constant velocity, indicating zero net force. Hmm. So I looked at the top of the slinky to see when it was released. This was hard. Rod Cross’s fingers obscure the top of the slinky, so I tried to track his pinky (the finger closest to the camera) and see when it moved. The result of manual frame-by-frame point selection is below:
Now I think that shift at 0.01 s is due to the limits of my ability to click in the same place on the video when selecting points. At any rate, nothing much happens until after 0.06 s. But let’s see, even if the top of the slinky is initially obscured by fingers, maybe we can get some kind of information from tracking the top edge of the slinky as soon as we can see it. Here’s the data.
Now I can’t really see the top of the slinky until about 0.09 s. But I feel good about my ability to track the top of the slinky after that. Note that the slinky is still speeding up until 0.012 s. And the position at 0.09 s is pretty close to where I would suspect Rod’s fingers are gripping the top coil, given the shape of his hands in the video. So it appears that the slinky is definitely not released until somewhere after 0.06s.
Note that by this time (0.06s), the ball at the bottom of the slinky is already moving at a constant velocity! When the top of the slinky is finally released, the entire system is moving downward at a constant velocity. Rod must have shifted his hands at the very last moment (or the last 0.05 s) before releasing the top coil. Or maybe the ball was in the middle of a bounce when it was released (I wish the video had started about 0.1 s earlier!). By the way, 0.42 s is about where the slinky is fully compressed. Note the beginning of non-zero downward acceleration of the ball at that point.
The constant downward velocity of ball before the slinky is released, and its continuing constant velocity of approximately the same magnitude after release, make me think that this velocity is not due to the release at all. If Rod Cross had been able to hold everything stock still before release, I think we would see the ball stay at rest for awhile. What do you think? Have I missed something?
About a week ago, Derek Muller ( of Veritasium Science Videos) posted a series of three videos on what happens when you drop a hanging slinky. The videos use some high speed video footage to observe how the lower end of the slinky hovers (quite unintuitively) in place as the top of the slinky falls. The videos first came to my attention Thursday morning when Frank Noschese tweeted that his students were all over the video, wanting to do their own slinky drop. Later that morning, Rhett Allain posted a Vpython computational model of a falling slinky… cool!
Now Thursday was a tough day for me. My students in my second year physics class had done a poor job on a problem set and a “meh” job on a test, and it was clear I needed to give them a “pep talk” about level of effort and seriousness of purpose. To complicate matters, I was in the throes of a bad cold, leading to several nights of insomnia. I was grouchy and did a poor job of “inspiring” my students in class when I spoke with them about their poor performances. They were sitting there, looking like puppies with their tails between their legs, so I said, “Ok, enough of that… you know what to do in the future. Let’s do something fun now,” and we watched the slinky drop videos. And we dropped a super long slinky ourselves from the top of the science building. And we started discussing the physics, which led some to propose using Tracker to analyze the motion. I realized that if we wanted to do a good job of analyzing the video, we needed the raw high speed video of the drop and something in the video to set our scale. A quick tweet to Derek resulted in all the information we needed by Friday morning.
So Friday rolls around, and I have my other section of advanced physics. They are ahead of the class I had Thursday and that other class was going to be mostly missing for Saturday’s meeting due to SAT’s. So I decided to let everyone loose on Tracker with the high speed video. Most of the class was spent just learning the software, but a few students were able to confirm Rhett’s computational model (see the comments on Rhett’s blog).
Now I’m two days behind my syllabus, but I think my students are far ahead of where they were on Wednesday. The discussions we’ve been having about forces on various parts of the slinky are detailed and nuanced in ways that my students’ problem sets weren’t. We’ve just finished talking about Young’s modulus and the speed of sound in solids, so this is an excellent “weak spring” example for them to ponder. And, in a huge win, I convinced at least one student to post a comment on a blog. I tried to get them to email Rhett and Derek, but they are too shy for that. Soon, maybe.
In addition to energizing my second year physics class, the slinky work gave me something to do with my Friday afternoon first-year class, which had been decimated by early sports dismissals. While the six students in attendance did not do video analysis or read Rhett’s blog, they did get to drop a really, really long slinky from the third floor in our main building (in the stairwell, right near the main entrance, where we captured the attention of a bunch of freshmen and some visitors… win!). And they were able to discuss what must be true about the forces on the top and bottom loops of the slinky (after I told them that the video analysis shows the ends have constant velocities). The Balanced Force Particle Model pays off in the real world.