First Principles 4.0 - Inside Stars (MP3 file, 26.7MB, 28:24)

Black holes are the most likely source of the mysterious ultra high-energy cosmic rays that bombard the planet… Observations at the world’s largest cosmic ray detector suggest the particles are emitted by huge black holes in the middle of nearby galaxies. 

Cosmic rays are a pain in the ass for spectroscopy, astrophotography and other CCD-based astronomy. Especially spectroscopy is plagued by cosmic rays. There are 3 kinds of cosmic rays that I’m aware of, electrons, protons and Helium nuclei (or alpha particles). The cosmic rays discussed in this article are high-energy and create a shower of interactions when they slam into the earth’s atmosphere.Pretty cool that we are starting to see results out of the Pierre Auger Observatory.

A while back I wrote a post about energy.

Here’s another example of energy that I think is interesting. When you take an automobile which is initially at rest and get it going 55 miles per hour, it gains kinetic energy. KE = (1/2)mv^2. So a car that weighs 2000 lbs. (900 kg) going 55 mpg (25 m/s) would have KE=(1/2)(900)(625)=280 kJ (kilo-joules) of energy. That energy comes at the expense of gasoline — chemical energy — exactly 281 kJ’s worth. Excluding all the messiness of friction and air resistance and such, we used exactly the same amount of chemical energy as we gained in kinetic energy. So it doesn’t matter if you use gasoline, hydrogren, electricity or biodiesel, it takes 281 kJ of energy to get your car going 55 mph.

Now you see a stop sign and you hit the brakes. You take all of that kinetic energy and put it into heat, given off by your brakes. The energy went from the gas into your car’s kinetic energy and then the friction from your brakes heated up the air. What some hybrids do, which is really cool, is instead of putting that energy into heating up the air, they put it back into the car. In some cases they literally spin up a big, heavy gyroscope. So they put the kinetic energy of the car into kinetic energy of a big spinning thing. Then when you hit the accelerator, it puts that energy back into the drive shaft and you accelerate back up to 55 mph without starting from zero energy. Cars that do this get “free” energy compared to cars that don’t. When we accelerate and brake, back and forth, all day long in our cars, we are throwing away ridiculous amounts of energy.

If you were flying in space instead, once you got going 55 mph you could turn off that gas and you’d keep going 55 mph forever (or until some force started messing with you). The reason you can’t do this on earth is because all sort of things steal the energy. The heat from your engine, friction in the moving parts, air resistance — they all steal energy that you have to keep putting back with your engine.

So one of the challenges facing us with our on-going “energy crisis” is figuring out how not to turn energy into a form that is not usable to us. The classical example is heat, like the brakes on our car. Anything that gives off heat is wasting energy. Your laptop wastes tons of energy in heat. If they could make CPU’s that didn’t heat up, your battery would last for days.

There is no shortage of energy on earth. The Sun rains down something like 1 kilowatt per square meter. There is tons of kinetic energy in the wind and ocean. We like to burn things like coal and oil –they are ridiculously finite compared to the Sun, the wind and the ocean. Renewable energy isn’t just a good idea, it’s the only long term option.

What is harder, going up 5 flights of stairs or going down 5 flights of stairs? Going up, of course. That is a qualitative statement, meaning it addresses the qualities of the situation and describes going up as “harder” than going down. How much harder? This is a question that expects a quantitative answer — what quantity, i.e. a number in some units, describes how much harder going up stairs is than down stairs? The question of units is itself interesting, too. Amongst things like meters (m), seconds (s), and pounds per square in (psi), what is the correct unit to describe how much harder it is going up stairs than down stairs.

In physics the word “work” has a very specific definition: it means the force times the distance that the force moves something. Common units for work (energy) are Joules (J), BTUs, ergs, electron-volts (eV), foot-pounds and calories (among others). Most of us are used to thinking of energy in things like watts (W) and that is close — watts (a unit of power) is energy per second.

To go up the stairs, the force you are opposing is gravity and the distance you are going is 5 flights. The acceleration of gravity (g) on the surface of the Earth is 9.81 m/s^2 and a flight of stairs is about 3 meters. Let’s say you weigh 150 lbs which is 68 kilograms (kg), so the work you need to do is W=Fd=gmd=(9.81 m/s^2)*(68 kg)*(15m)=10,012 J. If we say it took you 30 seconds to go that distance you “put out” more than 300 watts to go up the stairs! The bad news is, this equals only about 2 food Calories. A food Calorie is 4180 Joules so if you want to burn 100 Calories you need to go up 209 flights of stairs! This a a little misleading, though. We exert a lot of energy in other ways when we climb stairs — not all of it goes to overcoming gravity. So you’d have to climb at most 209 flights of stairs and probably many less to burn 100 Calories.

Technically speaking, going down the stairs takes negative energy. Thus, if you step off the roof of a building, you will have some nice kinetic energy going by the time you hit bottom. So in theory it is infinitely harder to go up stairs than down stairs, because going up you expend energy and going down you are given energy. But in practice we know that going down stairs is a little bit harder than just standing there. So it takes about 10,000 Joules of energy more to go up 5 flights of stairs than down, or about 2,000 Joules per flight of stairs.

For comparison, there are 2,942,720 Joules of energy in a Big Mac with cheese, 130,880,000 Joules in a gallon of gas and the Sun puts out 400,000,000,000,000,000,000,000,000 Joules per second!