Conservation of energy

Twas the night before the conservation of energy laboratory and all through the lab the banana leaves were arranged.

A sign was left in the hopes that the cleaning crew would read and leave the leaves alone.

The next morning the leaves were gone. I knew the trade winds had destroyed most of the leaves, I had taken the last of the usable ones. And the area was wet, muddy, full of ants. With a long day ahead including the arrival of the new president, this was no day to be sweaty, muddy, and wet. I stared out on to the lawn for a while trying to figure out what to do.

Nothing was out there that looked all that promising. And then I realized...

Ravenala madagascariensis. I had never looked to see if the petiole had a groove that a marble could roll in. I went to cut them and discovered that they are full of rain water between the petioles. A lot of rainwater. 

Turns out that the petiole has a closed groove, but the rachis in the blade has an open groove. The blade length is less than a large banana leaf, so overall heights maxed out at 65 to 75 centimeters.

The petiole was trimmed. In some sense these leaves work better - they have a stiffer petiole/rachis than a banana, sag less, and hold up better. This term I managed to remember the stopwatches, the masking tape, the scissors, the scotch tape, the tape measure, and marbles. 

I opened by noting that while we had shown that a falling ball falls with increasing velocity as height increases, we could not measure the velocity with which the ball hits the floor. The leaves would change the direction so we could measure the speed using a speed trap. I then ran a demonstration including the use of three meter sticks to determine height above the table - this has produced data which is much more consistent with the theory and all but eliminates height errors.

Halia and K'con set up to make measurements using three meter sticks, the third will be a cross member. Heights of 5, 10, 20, 40, and 80 were suggested, but no ramp reached 80 cm in vertical height. 

K'con prepares to release a marble while Sharla, Ashlen, and Halia look on.

The marble in motion on the table. The speed trap was 157 centimeters long. The full 157 was used at all heights. This has also been shown to improve the data and simplifies the procedure.

Ashalina, Jonathan, Jarret, and Athina Viola work on calculations. 

I had run the calculations at 5 cm and a couple calculations at ten centimeters. At each height five times were taken, the median was used to calculate the speed. This too has a beneficial impact on the accuracy and consistency of the data. This laboratory used to use single times at every 10 centimeters and a speed trap that was lengthened as speeds increase. This approach led to data that did not clearly show a square root relationship. The results were unpredictable. Shifting to the median time for five trials at fewer heights, with heights doubling up the ramp, has had a strong positive impact on the consistency of the data. Getting a lab to work consistently is a multi-year effort. The details make all the different. The board above also notes that the southern speed trap is 138 centimeters. Data beyond 10 cm was from student measurements.

With all of the groups done and the data confirming a square root relationship, I went ahead and showed them the underlying theory, minus the component of rotational kinetic energy. Note that for g I reached back to the data from the prior week. I did not use the published value as the class median value of 10.055 meters per second squared is sufficiently close.

Desmos

Data from the two morning teams. This lab lends itself well to slightly larger groups, although two group can work on a single ramp.

Ozimy prepares to release the marble, Shane times, Rizal records data. In the back Kaylem and Jack make a measurement at the top of the open petiole using the three meter stick approach - an approach developed by students in the course during a prior term.

Melina, Billie, Serjean, and Ivan compare results. This class is tech equipped. Smartphones are not a distraction, they are a tool. Basic equipment. Technologically advanced analyses.

Ivan makes notes. 

Fiji assists.

Jenna and Milain enter data into Desmos.

Thevonna and Harvey at the 138 cm speed trap rig.