Here is a super cool veritasium video about the Magnus Effect.
And, a confusing video about the physics of turning a bike.
The photoelectric effect is the basis for solar panels. It’s really famous because it’s also some of the first evidence we had that light was a particle (this of course became extremely confusing when the double slit experiment gave us evidence that light was a wave, but that’s for another time.)
First, remember that materials are made of atoms, which are made of protons and neutrons and orbited by electrons:
Different materials hold their electrons more or less tightly. Metals happen to hold their electrons pretty loosely, like kids in a neighborhood where all the kids just run around wherever they want:
These kids wander around wherever they feel like it, but they generally stay inside the metal (in this case copper). However, they can get knocked out of the metal by light (photons).
This is kind of like a game of red rover (I hated this game so much when I was a kid.) Let’s imagine that the kids line up at the edge of their town, and they play red rover with the neighboring kids, who just happen to be photons (light). The kids are there just hanging out in the metal, and the photon comes and tries to knock them out.
If the photon is weak enough, nothing happens.
In fact, if the photons are too weak, it doesn’t matter how many of them hit the metal, no electrons are knocked off.
In photon-terms, a weak photon is one without a lot of energy. The energy of a photon is its frequency, which is also its color. For example, red is a lower frequency than blue. And, infra-red is lower frequency than red. Ultra-violet is higher frequency that violet. Radio waves are lower frequency than infra-red, and x-rays are higher frequency than ultra-violet. (All of these are just frequencies of light that we can’t see.)
So, if the light hitting the electrons gets more energy, let’s say its violet now (like violent!)
Now, the more photons that hit the metal, the more electrons will be kicked off.
Different metals hold their electrons more or less tightly, so different metals require different energies of photons before electrons will get kicked off. This is called the “work function” of the metal, and it’s often denoted with the Greek letter phi:
Sometimes the incoming photon has more energy than it needs to kick off an electron. If that’s the case, then the leftover energy becomes kinetic energy of the electron. (i.e. the stronger the kid from the neighboring town is, the faster you’ll be going when he tosses you out of the line of electrons.) Here’s the fancy equation for that, if you’re interested:
But, we said earlier that the energy of a photon depends on its frequency. It turns out we can calculate the energy of the photon by taking its frequency (in Hertz) and multiplying it by planck’s constant (6.6 x 10-34). This gives us the energy in Joules. So, another way to write the above equation is this:
For example, the work function of copper is 4.7 electron volts, which is 7.53e-19 Joules. This works out to a frequency of 1.14e15 Hz, which is a wavelength of 260 nanometers of light. This is higher than the visible spectrum, it’s just into the ultraviolet range, so you need ultraviolet light to knock electrons off of copper (or gamma rays 🙂
The really cool thing is that this is evidence that light is a particle. Because, if you hook up some wires to the piece of copper, and you hook those wires up to a detector that makes a sound every time there’s some current (ie. every time an electron gets kicked off- current is just moving electrons) it would make a sound like rain on a tin roof.
Thoughts? Questions? Comments? Concerns?
(Or, how to tell how fast you’re going based on how much mud is hitting you in the face.)
I was riding my bike in the rain yesterday, along a dirt road, listening to Let it Go from Frozen, when I realized that if I leaned forward I started getting a lot of mud in my face from water kicked up off my tire. That water gets flung off the tire at whatever the rotational speed of the wheel is. The faster I go, the higher the water goes. Maybe I could use that to tell how fast I was going. (I have a bike speedometer, but I still haven’t installed it. That was Christmas two years ago so it might never happen.)
Then I was like, but, I’d have to estimate the size of a water droplet, and if there was dirt in it that would increase the mass, so I’d also have to make some assumptions about percent dirt content.
But, no! The height of the droplet can be calculated with conservation of energy, which means the mass drops out. As long as I’m ignoring air resistance, which is probably ok, I can pretty simply calculate my speed based on how far I have to lean forward before I start getting mud in my face.
Here’s how it works:
As I ride forward, water droplets cling to the surface of the tire. At some point, they are flung off. When they are flung off, they travel in a straight line out from the surface of the tire. They travel tangentially, and their speed is equal to the linear speed of the rotating wheel.
The linear speed of the wheel is equal to the speed that I’m bicycling at. That means that the water droplet should theoretically be travelling at the same speed at which I am bicycling.
Now all that I have to do is use conservation of energy to find that speed, given the height.
There are two types of energy involved, linear kinetic and gravitational potential. Here are the equations:
Here, m is the mass of the object, v is its velocity, h is its height above the surface of the earth in meters, and g is the acceleration due to gravity (approximately 9.8.)
The idea here is that energy is never created or destroyed. It just changes forms. In this case, it changes from kinetic energy to potential energy.
(I’m making several simplifications here. I’m assuming no air resistance, and no energy lost to deformation of the water droplet.)
Ok, here’s the calculation:
This equation at the end you can use to find your velocity. Just plug in the height your head is above the wheel when you start getting mud in your face.
Now for some numbers.
My usual head height is 3 feet, 3 inches above the midline of my wheel (I’m making another simplification, assuming that my head is directly vertical above the back edge of the wheel:
I’ll need to convert that to meters. For that I’ll just use google’s handy conversion feature.
Apparently 3’3″ is .9906 m
Plug this in to my equation:
And convert to miles per hour:
Here’s a table of head heights versus bike speed:
The cool thing is that it doesn’t matter how big your tire is, or how big the water droplets are, or how much dirt the droplets have in them. All that matters is how fast you’re going and how high above the wheel your face is.
There is probably a cutoff point, where if you’re going slower than that the water isn’t lifted at all, and of course if you’re going too fast you won’t be tall enough to reach the height of the water. Also, you can’t have fenders on your bike.
But, that’s how you can tell how fast you’re going based on how much mud you get in the face!
There’s something kind of awesome that happens when you realize that things you’ve learned in the classroom might actually have real-world applications. Like, when you go to a foreign country and can sort of communicate with the locals because you took Spanish 101.
I was watching Shark Tank recently, and these guys came on with this thing they invented. I don’t know anything for sure about how it works, but I could make some educated guesses, and I think that looking at their invention is a really interesting way to introduce thermodynamics.
I couldn’t find the clip of them on shark tank, but here’s their kickstarter campaign video, which according to youtube raised $306k in 37 days!
Anyway, it’s a pretty genius invention and I kind of want one. They’re these big metal things shaped like coffee beans and you put them in your coffee. They immediately cool it to the perfect (still hot) temperature for drinking, and then keep your coffee at that temperature for several hours.
Being a coffee drinker, extreme appreciater, addict, myself, I was like “wow, that’s genius.”
Here’s my guess at how it works: The inside is some metal that has its melting point at a good temperature for coffee. When you pour coffee over it, the excess heat goes into melting the metal. (This phase change absorbs energy, (called Joules, hence the name Coffee Joulies.)
Then, as the coffee starts to be cooled by the outside air, the metal inside starts to phase change back, solidifying and transferring heat back to your coffee. (Phase changes can absorb tons of energy, and they will stay at a constant temperature while they do so.)
We could even guess at what metal or material might be inside. It would be something with a melting point around the perfect coffee drinking temperature.
The National Coffee Association says this temperature is 180-185 Fahrenheit, which is 82-85 Celsius. But, drinks.seriouseats.com says 110-120 is ideal, which is 43-49 C. Coffee Joulies says they keep your coffee at exactly 140, or 60 C.
Then we can check the melting points on the periodic table. Sodium (Na) is 98 C and Potassium (K) is 63 C, Rubidium is 39 C. Potassium is basically right on, so it could conceivably be made of that.
I just checked their website for more clues. They call it PCM (for potassium? Maybe it’s a mixture of potassium and something else.) Other than that they don’t say what it is, only that it’s natural, edible, and already found in food (potassium again?)
Anyway, fun mystery, and an awesome invention! And, a really awesome example of how you can use physics to invent useful things.
One of my favorite things about physics is thinking about real world applications. I think the king of this was probably the physicist Richard Feynman. (From the awesome book Surely You’re Joking, Mr. Feynman.)
You can find him on youtube- there are videos of him talking about these weird puzzles, or just interesting things like how rubber bands work. My favorite: Why does a mirror swap left and right but not up and down?
Another favorite: how fire works.