Apr 14

Falling through the earth and black hole math

Falling through the worldBlack hole mathDave Francis was our guest today.  He apologized for the state of the earth that our generation is leaving for the generation of students.  He then challenged them to devise solutions.  Max, Rhys, and Maverick tackled population, thinking up solutions that Dave and I critiqued and also helped with. Ideas ranged from sending old people to war to sending old people to space. Incentives to have fewer children seemed gentler and more effective. While improved health and education appears to reduce fertility rates, it also lengthens lifespan, which increases population.

In our last class, we talked about falling through the earth and emerging in the Indian Ocean.  This time, we considered conservation of energy to help us predict how fast we might shoot out the other side.  We listed our assumptions of no friction slowing us down, no weight loss (or death) from the heat, no air pressure related problems (like the bends), and no Coriolis effect slamming us against the side of the tunnel as our speed at the surface of a spinning earth differs from the speed closer to the center of the earth.  We also assumed that changes in the gravitational force as we drop beneath much of the earth’s mass would cancel out on our exit.  “Based on conservation of energy, we concluded that if we simply stepped off the edge of the tunnel on our side of the earth, we would be similarly motionless when we reached the other end of the tunnel.

Gravity got us thinking about black holes, so we showed how the force of gravity tends toward infinity as the radius of the mass tends toward zero. We talked about how black holes might not exist, that is the radius of the mass contained might not reach zero, a singularity.  Perhaps, denser than neutron stars are quark stars, prion stars, and Planck stars, ever denser but never reaching a singularity.

Cheryls birthdayThen we tried to solve a logic puzzle Miguel found in the BBC News.  Singapore parents complained that a question on a test was so hard it was stressing their kids.  We made progress toward answering the question before a sunny day called us outside to battle with pool noodles and then race solar cars in upside-down frisbees.  Our tiny racetrack was perfect to keep a train of solar-powered cars zooming in circles.  We also raced the cars on the edge of pool noodles and elsewhere.

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