Measurement and Uncertainty Smackdown
So, here is the plan. I will very briefly describe these three methods and then use them to determine the uncertainty for the volume of the ball above. I will also (for comparison) find the uncertainty in the coefficient of friction for a block sliding down a plane – just because it is different.
I performed an experiment to see what the differences were between semi-automatic pistols and revolvers. The advantage of shooting under water is that you can see the boundary of the gas flow fields almost perfectly.
[W]hen you look up something in a map book, the thing you’re looking for always seems to be right on the edge, forcing you to flip back and forth between two pages. Answer: because most of the map is on the edge.
Suggestion for anyone who replicates this: Try it with food coloring (something that will give contrast)
Young Naturalist Award — Aiden: The Secret of the Fibonacci Sequence in Trees
My investigation asked the question of whether there is a secret formula in tree design and whether the purpose of the spiral pattern is to collect sunlight better. After doing research, I put together test tools, experiments and design models to investigate how trees collect sunlight. At the end of my research project, I put the pieces of this natural puzzle together, and I discovered the answer. But the best part was that I discovered a new way to increase the efficiency of solar panels at collecting sunlight!
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The tree design takes up less room than flat-panel arrays and works in spots that don’t have a full southern view. It collects more sunlight in winter. Shade and bad weather like snow don’t hurt it because the panels are not flat. It even looks nicer because it looks like a tree. A design like this may work better in urban areas where space and direct sunlight can be hard to find.
Update: I missed that he was measuring the open-circuit voltage output, not current, for his arrays.
They’re so very polarizing…
Polarized rainbow, what does this mean???
Rainbows are created when sunlight reflects inside water droplets, bouncing back to you. When the light enters the droplet and also when it leaves, it bends a little bit as well (like how a spoon looks bent in a glass of water). Different colors bend by different amounts, so the sunlight colors get spread out, forming an arc in the sky.
The light forming the rainbow gets polarized when it reflects off the back of the raindrop. The amount of polarization is pretty strong, as the video shows. When I hold the glasses horizontally the light gets through, but as soon as I rotate the glasses, the rainbow disappears entirely! Almost all the polarized light is blocked, and the rainbow vanishes.
But wait, there’s more!
This is the same effect that makes it easier to see through heavy rain or fog with polarized sunglasses.
Wild Close-Ups of Rare Mammals From Huge Camera-Trap Study
A massive camera trap survey of tropical mammals around the world has returned a magical series of glimpses into animal life.
The survey was conducted by Conservation International and partners and partners in South America, Africa and Asia. They installed 420 camera traps in key protected areas, amassing some 52,000 photographs between 2008 and 2010.
Why Do Mirrors Reverse Left and Right?
Answer: Mirrors don’t reverse left and right and they don’t reverse up and down. Wouldn’t that be kind of funny if I just stopped here? But you know I can’t.
I like Feynman’s explanation as well.
Back when I was playing with a strong magnet dropping through a coil of wire I wondered how much energy I could extract from the dropped magnet and if I could do anything with it. The coil I was using was at least 15 cm in diameter, which means that I wasn’t capturing all of the flux lines from the magnet — the field of a dipole drops off as 1/r^3, so a smaller diameter would be much better and the slowing of the magnet could be noticeable, as we’ve seen before with someone dropping a magnet down a copper tube.
Since I’m a physicist, I wanted to quantify this. I didn’t have a copper tube handy, but I do have a roll of aluminum foil which is on a roll with an inner diameter of about 3.8 cm (1.5 in), which is a reasonably tight fit for my strong magnet. I set up my slow-motion camera and my ipod in stopwatch mode to double-check the timing (yes, it was shooting at a rate of 210 frames per second)
I exported the video to individual frames to make it easier to analyze, and counted frames. The free drop takes about 0.25 seconds, give or take (it’s hard to tell exactly which frame represents release) and I estimate the distance as being about 32 cm (a foot-long roll = 30 cm, with the start just above and stop just below). The drop through the aluminum foil roll takes about 0.38 seconds. The freefall drop is easy to analyze: v = gt, and to double-check for g, just rearrange the familiar kinematics equation and solve. The drop time implies a speed of about 2.45 m/s at the exit. For g we get 10.2 m/s^2, so my little experiment seems good to 10% or better.
For the drop through the tube, we don’t know exactly what’s going on. There’s a damping force that varies with speed and eventually we would expect the magnet to reach terminal velocity. To get an estimate, though, let’s first assume it’s a uniformly lower acceleration. That would give us a value of 4.4 m/s^2 for the acceleration and an exit speed of 1.67 m/s. If we assume it hits terminal speed immediately then the speed would be 0.84 m/s. The truth is somewhere in the middle. There are probably several ways I could test this further, but the ones I can think of either require dropping the magnet from a distance above the tube, and it’s a tight fit, so it probably means lots of trials before I got lucky and got the magnet to drop in, or using a longer tube. I know aluminum foil comes in different lengths, but I only have the one. Since I want an idea of the energy extracted, let’s use the worst case value of 1.67 m/s.
I found the mass of the magnet using a small electronic scale and a plastic cup to keep the magnet away from the metal pan (where it might also be attracted to the interior or the case and mess up the measurement) and subtracted the mass of the cup. 60 grams.
Which means the magnet lost about 0.1 Joules of kinetic energy in the foil, in less than 0.38 seconds, or an average power of just over a quarter of a Watt, in that worst-case scenario. The best-case is 50% higher. And this is using aluminum — copper will give is a better result. Recall that Faraday’s law is
\(V = -frac{dphi}{dt}\)
Copper’s resistivity is about 2/3 of aluminum’s, so a given potential will drive about 50% more current and boost the resistive force owing to the larger field from the additional current. In other words, we can expect copper to be more efficient at converting the mechanical energy to electrical. It will more closely approximate the terminal-speed-quickly scenario, and it should have a smaller terminal speed.
What I want to do in the near future is wind a coil on one of these cardboard tubes and see if I can light up a little light bulb.