## Thursday, June 01, 2017

### Fall Leaves in a Spring Classroom

The video of a trapeze artist dropping into a net filled with leaves got a lot of attention last November after it was posted on YouTube. It now has almost 80,000 views and was described in a previous post on The Blog of Phyz by the every vigilant Internet scavenger, Bree Barnett Dreyfuss. It also led to a discussion on the PTSOS Yahoo discussion group. Most teachers thought it was a great demonstration of inertia. It looked to me like the tablecloth trick if you were to rapidly pull the tablecloth down, leaving the dishes apparently hanging in the air. Paul Robinson suggested that the effect wouldn't look as compelling for objects that were not affected by air resistance as much as leaves. I thought this was a good observation and wanted to test it. I also wanted to develop a way to do the Fall Leaves video as a demonstration in class.

After some thinking I decided I could use my spacetime simulator as the net, and coins in place of the leaves. I set things up on a weekend in my classroom and dropped a free weight in the center. This is the result with an iPhone 7 in 240 fps video mode:
I hope you agree that this was a satisfying result with some unanticipated phenomena. Look closely at the coins near the edge. They get pulled toward the center by the stretching of the fabric before the fabric pulls away from them. That gives them an initial velocity toward the center, causing the spell-binding collisions in the middle. Another thing to consider is the acceleration of the fabric surrounding the impact point. For the coins to appear to be suspended, the fabric must accelerate greater than 9.8 m/s/s. But the free weight is accelerating at 9.8 m/s/s when it hits, then its starts to decrease. This is a good puzzle to ask your students, how can the fabric have more acceleration than the weight? They should be able to figure out that the fabric is starting from rest and matching the free weight's velocity in a much shorter time than it took the free weight to reach this velocity. There are some surprisingly complex dynamics going on in this collision.

I wanted to test Paul Robinson's idea about air resistance. In place of coins, I placed packing pillows on the spacetime simulator and repeated. I was not surprised by the result:
If the packing pillows worked more like the leaves, they should have appeared to be suspended longer than the coins. They don't because the fabric does not allow air to flow through it like the trapeze net. As the fabric plows through the air it shields the packing pillows from air resistance. They fall almost like in a vacuum, staying with the fabric. I suspected this would happen because of the popular Hewitt demo where you drop a book with a piece of paper on top of it. They both fall together as the book plows through the air, allowing the paper to free fall. There is something more going on here as the packing pillows appear to stay with the fabric more than the coins. I suspect it is air flowing downward with the fabric. To reproduce the Fall Leaves video I would need to use a net so air resistance could act upward on the "leaves".

Obtaining a trapeze net was a non-starter for obvious reasons. I did some image searches of nets for ideas and decided on a cargo net. These come in a range of prices so I selected the largest, cheapest one I could find, the 100" x 140" by Grizzly Gear. It was only \$12.95 from Amazon. The openings in this net were large so leaves wouldn't work. I decided to use colored 8.5" x 11" sheets of paper. Although I am sure I would have several volunteers, I decided to drop an inanimate object into the net instead of a student. My 20 lb medicine ball has many uses, this would be another good one. If you don't have one, a large bag of water or a large water balloon would be a good, inexpensive choice. It would add some other interesting elements to the slo-mo video! If you have other ideas for this demonstration, please leave them in the comments.

I needed students to support the net much like firemen holding a blanket for someone jumping from a burning building. Students also would need to place the paper on the net and drop the medicine ball, leaving me free to video it. I would need to pick a tall, trustworthy student to drop the ball accurately from the second floor from the roughly 4 meter height. If this idea gives you pause, it should work pretty well from about 2 meters like the Coins on Spandex demonstration. On the last day of class before finals, I had enough time to try this out. Here is our first attempt:
I thought there was a small chance the medicine ball would pass through the net opening, apparently the odds were much higher. We tried a second time and the ball hit a net intersection and it worked OK. Since I had 4 more classes of AP Physics, I could come up with improvements for each class. I attached some string to a small part at the center of the net, making a target for the medicine ball. The string decreased the size of the center openings and prevented it from stretching very far. We had a new problem, they stretched the net too much and the paper fell through as we were trying to place it. I had them move in some, this did the trick. It worked pretty well. I added a little more string just to be sure and had the next class hold the net up higher. This produced some satisfying results:
The only glitch is the ball rolled to the side a little and came out through the net, but only after causing the net to stretch all the way to the ground. I am going to try two more times tomorrow but without any more changes other than filming from a little further way. In each period I showed the students their video and also the coins on spandex. They seemed to like the coins the best but were glad they got to participate in the net version. I suggest you try doing both too. If you don't have a spacetime simulator, here is how to make one. You also could have the students hold the spandex like a blanket. I will probably do the net version of Fall Leaves again next year and show the coin video unless I come up with a whole new way avoid grading papers!