This fascinating video tries to trace the evolution of the facial features of our homonid ancestors over the last 7 million years.
Analyzing the Motion of Soccer Ball using a Camera and Calculus
If you throw a soccer ball up into the air and take a quick series of photographs you can capture the motion of the ball over time. The height of the ball can be measured off the photographs, which can then be used for some interesting physics and mathematics analysis. This assignment focuses on the analysis. It starts with the height of the ball and the time between each photograph already measured (Figure 1 and Table 1).
Table 1: Height of a thrown soccer ball over a period of approximately 2.5 seconds. This data were taken from a previous experiment on projectile motion.
| Photo | Time (s) | Measured Height (m) |
|---|---|---|
| P0 | 0 | 1.25 |
| P1 | 0.436396062 | 6.526305882 |
| P2 | 0.849230104 | 9.825317647 |
| P3 | 1.262064145 | 11.40310588 |
| P4 | 1.674898187 | 11.30748235 |
| P5 | 2.087732229 | 9.657976471 |
| P6 | 2.50056627 | 6.191623529 |
Assignment
- Pre-Algebra: Draw a graph showing the height of the ball (y-axis) versus time (x-axis).
- Algebra/Pre-calculus: Determine the equation that describes the height of the ball over time: h(t). Plot it on a graph.
- Calculus: Determine the equation that shows how the velocity of the ball changes over time: v(t).
- Calculus: Determine the equation that shows how the acceleration of the ball changes with time: a(t)
- Physics: What does this all mean?
Ecosystem Perturbations: How DDT Lead to Parachuting Cats
The impact of a change in the ecological conditions, like the introduction of the pesticide DDT, can cascade through an ecosystem with wierd and unexpected consequences. Richard Fagerlund explains:
In the 1950s, the World Health Organization sent supplies of DDT to Borneo to fight mosquitoes that spread malaria among the people. The mosquitoes were quickly wiped out. But billions of roaches lived in the villages, and they simply stored the DDT in their bodies.
One kind of animal that fed on the roaches was a small lizard. When these lizards ate the roaches, they also ate a lot of DDT. Instead of killing them, DDT only slowed them down. This made it easier for cats to catch the lizards, one of their favorite foods.
About the same time, people also found that hordes of caterpillars had moved in to feed on the roofing materials of their homes. They realized that the lizards that previously had kept the caterpillar population under control had been eaten by the cats. And now, all over North Borneo, cats that ate the lizards died from DDT poisoning. Then rats moved in because there were no cats to control their population. With the rats came a new danger: plague. Officials sent out emergency calls for cats. Cats were sent in by airplane and dropped by parachute to help control the rats.
— Fagerlund (2013): Take a lesson from Borneo — go easy on the bug spray on SFGate.com.
The Rolling Shutter Effect
When you pluck a guitar string, the string moves up and down really fast. However, if you take a video of it with a digital camera with a rolling shutter (which most cameras have at the moment) it captures the motion of the string in a wavelike pattern that is proportional to the frequency of the motion of the string; the smaller strings move faster, create a higher pitched sound, and shows up as shorter-wavelength waves. Note: this is not the way the strings actually move, it’s an interesting, and potentially useful optical effect.
Because the optical effect really makes it look like there are a lot of internal waves rolling along the string — which there are not — I’d be quite cautious about using this in physics class. However, if a student wanted to go into the detail to understand how it works — and then explain it to the class, they can start with the math about standing waves in instrument strings and the relationship between sound pitch and wave motion, and a visual explanation of the rolling shutter effect:
What Happens When Two Black Holes Collide?
A student asked this question about black holes during a discussion, and I didn’t have a good answer. Now there’s this:
A study last year found unusually high levels of the isotope carbon-14 in ancient rings of Japanese cedar trees and a corresponding spike in beryllium-10 in Antarctic ice.
The readings were traced back to a point in AD 774 or 775, suggesting that during that period the Earth was hit by an intense burst of radiation, but researchers were initially unable to determine its cause.
Now a separate team of astronomers have suggested it could have been due to the collision of two compact stellar remnants such as black holes, neutron stars or white dwarfs.
— via The Weather Channel (2013): Black Hole Collision May Have Irradiated Earth in 8th Century.
From the original article:
While long [Gamma Ray Bursts (GRBs)] are caused by the core collapse of a very massive star, short GRBs are explained by the merger of two compact objects … [such as] a neutron star with either a black hole becoming a more massive black hole, or with another neutron star becoming either a relatively massive stable neutron star or otherwise a black hole.
— Hambaryan and Neuhäuser (2013): A Galactic short gamma-ray burst as cause for the 14C peak in AD 774/5 in
More info via The Telegraph, and the original article discussing the spike in carbon-14 in tree rings is here.
Choosing Extinction
We talked about the Voluntary Human Extinction Project (VHMET) in Environmental Science, when we were covering issues related to overpopulation and the need for genetic diversity. While I’ve never been quite sure just how serious VHMET is, I just came across this 2007 article by Robert Krulwich on NPR about a tribe of pygmies in the mountains bordering China and Burma that chose extinction because of all the genetic problems that were being caused by inbreeding.
Some Rules for Writing
Aerogramme Writers’ Studio has compiled Pixar’s 22 Rules of Storytelling as well as Neil Gaiman’s Eight Rules of Writing.
Both sets of rules focus on the search for perfection, which, like the horizon, you have to learn to deal with the fact that you’ll never reach to your ideal satisfaction.
Improvisational War
Fighting against a well armed military, the rebels in Syria have had to do a lot of improvisation. A basic knowledge of physics and chemistry has proven somewhat useful.
The Atlantic has a collection of photos of DIY (do it yourself) weapons, that includes catapults and sling-shots.
Sebastiano Tomada Piccolomini has a fascinating photo-essay in the New Republic showing the one item that members of one group of rebels considered as their most crucial weapon. These range from a radio, to a packet of cigarettes, to improvised grenades.
Finally, one of my students discovered that a cell phone and power-source from a computer can be made to look an awful lot like and improvised explosive device.
We are living in the future, but sometimes I wonder if it’s where we want to be.
