I’ve been hearing about Mark Kasevich’s super fountain tower for a while (including someone who was involved in funding it who was trying dazzle me a little. It worked.) A 10m tall device is imposing; one might ask what you can do with such a device that you can’t do with something that fits in one room. The answer is some really neat interferometry:
Category Archives: Physics
About That Perfect Clock…
Physicist proves impossibility of quantum time crystals
Bruno’s proof demonstrates that setting a system of particles in motion around a one-dimensional magnetic ring always increases the ground-state energy of the system so that it’s no longer in its ground state, which prohibits the existence of a rotating ground-state system. The proof covers systems rotating at any finite angular velocity.
I had linked to this some time back because the press release was bad and made some overly bold extrapolations. Interesting that a periodic system as described can’t be in a ground state.
There are also probably a couple of “I reject quantum theory” crackpots who will be disappointed, as this seems to rule out some of the favorite classical atom models. Oh, who am I kidding. They are impervious.
Tackling the Block Problem Some More
More on the problem posted yesterday. Such a simple setup, and it’s generated a lot of positive discussion in the physics blogohedron (including twitter), which is a sign that I’m not the only one who thinks it’s a great demo.
As I stated, the kinetic energy of a particle of momentum p is given by p^/2m (since KE = 1/2 mv^2 and p = mv). We can estimate how much of the initial kinetic energy is lost; since momentum is the same before and after the collision, all we need to know is the mass of “moving things” before and after. The ratio of the initial and final KE is then just m/(m+M), where m is the mass of the projectile and M is the mass of the target. If this is a 10g bullet and a 1kg block of wood, then only 1% of the kinetic energy remains after the collision.
Let’s assume the block of wood went up about a meter in the video. To do that the speed is about 4.4 m/s right after the collision, which gives the bullet+block system a kinetic energy of 9.8 Joules (which is what you’d better expect to 2 digits for a ~1 kg system rising a meter). That means the bullet had a kinetic energy of 970 Joules! It was also traveling at ~440 m/s prior to impact.
Elastic collisions are different. KE is conserved, and the incident particle recoils. This gives you a momentum equation and a kinetic equation to solve, with the final velocities being the two unknowns, so you can solve for them in terms of the initial velocity of the projectile. Do a little math and you get the results.
If we solve for the final speed of the two objects but use the same masses and speeds, the block will start up at a speed of 8.7 m/s — almost twice as fast, so there is almost 4 times the kinetic energy (38 Joules). The projectile (more like a super-ball rather than a bullet, and probably a harder target) will end up going -431 m/s. The negative sign means its going down, as you expect — it will recoil, just not quite as fast. That’s 930 Joules, and 930 + 38 is about 970 (the same to the two digits I kept in the calculations)
If you play around with those formulas, you can see the target always goes in the direction of the projectile, but the projectile can recoil if the target is more massive, come to a stop if it has the same mass as the target, or will continue on in the same direction if it is more massive. I hope that matches intuition.
The rotating case is a little more complicated to work out, since you have more variables. Since the ball recoils and the block rotates, that’s another set of equations, and there’s the issue of the ball not bouncing straight down, which literally (and I literally mean literally; thanks a lot, OED) brings another dimension to the problem, though this effect is probably small for this problem and could be ignored.
After This, Veritasium Will Saw a Woman in Half
Some physics sleight-of-hand. I like it.
I have to admit, my first instinct was that the rotating block should not have gone as high, but I quickly realized why this was wrong. I don’t know if the folks in the video who are truly puzzled or acting that way for the sake of the video, because from other science videos I’ve seen, they are smart cookies.
There is not any extra energy that has to be “created” for the rotating case, because this is a completely inelastic collision. Kinetic energy is not a conserved quantity (!), total energy is. KE is only conserved in elastic collisions. There is more kinetic energy in the rotating case, and that’s just fine! And that’s the misdirection — everyone is puzzling over a quantity that’s not constant, implying that it should be. But this is why it’s a great demo — you have to identify and avoid a misconception to get the answer.
So it’s possible they are just playing to the audience to try and get you to think something mystical is going on here, or they “got it” soon after the first reaction was taped.
Now, what is conserved in these interactions is momentum, both linear and angular, since at the moment of impact there are no external forces or torques we have to worry about; we ignore gravity, since the effect during the short time of impact is very, very small. The impulse would be mgt, where t is the time of impact, and that’s small compared to the momentum of a fast-moving projectile. We’re physicists, and we set small effects to be zero. Too messy otherwise.
In the straight-on case, we have a linear momentum p, and momentum and kinetic energy have a simple relationship: KE = p^2/2m. So the kinetic energy is dictated by the momentum of the bullet (nail) just before it strikes the block, and it will go to whatever height where the energy has changes to potential energy, because in that case, mechanical energy is conserved: KE + PE is a constant when no work is done.
Concluding: If the nail has the same momentum in each case, the block must rise to the same height, rotation be damned.
Rotationally, it’s similar. The angular momentum is L = r X p, (or rp, at the point of impact), and angular momentum has a similar relation to rotational KE as the linear case does. Mass becomes moment of inertia, and you have L^2/2I as your rotational energy.
But the rotational energy does not come at the expense of the linear (which is different experience than rolling a ball or disk down an incline, where they must share). Because of the collision, KE is not conserved, and all we are doing in the rotating case is turning little less of the lost KE into sound, deformation of the wood, and a temperature increase, and using it to rotate the block.
Leon's Getting Laaarger
Why Do Solids Expand When Heated?
Higher temperatures mean higher energy levels. At higher energy levels, the average atom separation is also larger. When you increase the temperature for most objects, they expand. Of course, this assumes that the more complicated ball and spring model works for solids as well as for molecular hydrogen, but it mostly does.
There’s this as well, which is a snapshot of how physicists think:
The simple spring model is much easier to use and works for some things. Like all models, if it works we us it.
It explains why we e.g. model things as harmonic oscillators all the time. It works.
Weirdness, TBA
TBA = tert-Butyl alcohol. At the triple point, where it freezes and boils at the same time.
It's Not Einstein Against the World
New York Times Wants to Fight Einstein, Einstein Declines
Short, snarky version: Everyone should be shocked, SHOCKED! that general relativity doesn’t work where quantum theory is needed.
Matthew also rightly points out that framing a relativity experiment as a cult-of-personality exercise is a bad idea.
Newer theories supplant older ones conceptually, but every theory is provisional, constantly tested by experiments and observations. Einstein, important as he was in 20th-century physics, is not the ultimate authority even on his own theories, and refinements to his work should not be framed as proving him right or wrong.
Of MOTs and ZOTs
I know I already linked to the beginning of Chad’s series on the Tools of the Cold-Atom Trade, but Tools of the Cold-Atom Trade: Magneto-Optical Traps is good stuff, MOTs are also the workhorse of research I’ve been doing for 20+ years, and I was short of time last night as a fire alarm in my apartment building (kitchen/cooking incident, minor damage but 7 trucks plus support vehicles showed up) performed an act of bloggus interruptus.
Mrs. Schrödinger's Cat
The internets tell me it’s Erwin Schrödinger’s birthday, so here’s a reminder that it wasn’t actually his cat.
More Mirrors
In the last post I explained that mirrors do not flip left and right, and the example (also used in the Feynman video) was seeing an image of yourself.
I thought of another example — written words. They look backwards in a mirror as well, but if a mirror doesn’t flip left and right, how can that be? As I demonstrate, it’s because we always rotate whatever the words are written on. If we don’t do the rotation, the words are unchanged.
(I apparently started talking a second or two before the recording actually began, but this isn’t Hollywood, so I only did one take)
It may be a little tough to see the uninverted image in the mirror in the tiny youtube video, so here’s a still
