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Category Archives: Physics
Everybody's Doing It
C’mon baby, do the polar motion!
I mentioned that I printed out several posters for some colleagues for our Open House. Since they were displayed to the public and not copyrightable (work of the US government), I feel free to share.
Earth rotates about an axis, but this axis does not always coincide with the (geographic) North Pole.
The plot shows the location of Earth’s spin axis over the past few years. The center of the spiral is not at the geographic North Pole: it’s about 9 meters (~ 27 feet) away.
Why: early-20th-century geodesists adopted the rotation axis position of 1900 as the geographic North Pole; the rotation (spin) axis has migrated to its current position since then.
Knowing the true location of Earth’s spin axis is important when using star locations for navigation and timing, because the true spin axis determines where the stars will appear in the sky (as opposed to where one would expect them to be, were the spin axis at the North Pole).
“Polar motion” – the difference between Earth’s true spin axis and geographic north – is computed by combining measurements from radio astronomy, GPS and satellite ranging.
Important Physics Public Service Announcement
Ten things to do In the Event That You Have Accidentally Swallowed the Higgs Boson
6. If the Higgs boson begins creating mass in your esophagus or stomach before you reach a hospital, you will need to perform an immediate bosonectomy on yourself. Luckily, surgical knowledge is not necessary. Just choose from the array of probable outcomes that will manifest themselves upon your decision to perform surgery, and make the one most favourable to yourself into reality. Be sensible—do not wait for the outcome in which you successfully remove the boson and win the lottery and grow wings.
Bosonectomies aren’t nearly as complicated as the corresponding operation, a Fermiplasty. The Pauli exclusion principle applies to the latter, so a hospital can only treat one patient at a time.
It's a Setup
When I taught I tried to instill the concept that you should be able to pass an exam without a single correct numerical answer, because the problem set-up was the most important part of the solution. Few of my students believed me, but I see that my experience was not unique. The First Excited State has Missing the Important Stuff, which sets up a response at Uncertain Principles, The Process Is as Important as the Answer
Chad points to the problem of giving a problem with only algebraic expressions
The problem with this method, of course, is that students hate it with the burning passion of a million white-hot suns. If you think they get unhappy when they don’t have the exact numerical answers to work toward, just wait until you see their reaction to no numbers at all.
Physics Malpractice
Via physics and physicists I see a story about how golf can be hazardous to your hearing. And the story botches the physics. (I don’t know if it’s the journalist or from the original journal article)
The coefficient of restitution (Cor) of a golf club is a measure of the efficiency of energy transfer between the golf club head and the golf ball. The upper Cor limit for a golf club in competition is 0.83, which means that a golf club head striking a golf ball at 100km per hour will cause the ball to travel at 83km/h.
Well, that’s just wrong. The Cor tells you about the kinetic energy, so it won’t be the same for the speed, because KE depends on v2. i.e. if a ball is dropped from 1 meter and bounces, returning to 0.83m, the impact speed is ~4.4 m/s and the return speed is ~4.0 m/s, which is 0.91 of the speed.
Another problem is that the mass of the clubhead is not the same as the mass of the ball. Even if the Cor applied to speed, the statement is incorrect. In the limiting case of Cor=1 and the ball’s mass being negligible, the ball would leave at twice the clubhead speed.
The actual equation is v = u*(1+e)/(1+m/M)
v is the ball’s speed, u is the clubhead speed, e is the Cor, m is the ball’s mass and M is the clubhead mass. (This is trivially derived using conservation of momentum and balancing the kinetic energy equation to account for the loss) Using e = 0.83, and assiming the M=4m, we see that v = 1.46u
Update — This is using a definition of Cor on terms of energy. I couldn’t find how the USGA was defining it when I was composing the post, but further research (and noted in the comments) indicates that it is indeed the fraction of the speed retained after the collision. That changes the details of the analysis, but the article’s numbers are still wrong — the ball’s speed is larger than the clubhead speed. I still haven’t found a mathematical definition of how the USGA applies this to a golf club
That makes e in the equation the square of the Cor (so e = 0.689), which means that the ball leaves the clubhead at v = 1.35u
Rolling, Rolling, Rolling
A few days ago I was relating the cans-in-a-blanket problem, and retelling the vacuum joke and story to someone who had not yet heard them. One of my colleagues commented on a problem he had been given during an interview, also involving cans of soda:
You have two cans, one filled with ice and the other with liquid, but otherwise identical. The cans are rolled down an incline. Which one reaches the bottom first?
Much like the previous problem, I think there is a common misconception at play here for some people who get the answer wrong, and I’ll get to the explanation below. One of the people in the conversation said his first impulse was the wrong answer, but when we discussed the physics, we all agreed on the solution.
I set up to do a demonstration, though my first attempt was thwarted — I filled up a can with water and popped it in the freezer, hoping the can would be strong enough to hold together and have the ice expand vertically. It wasn’t.
I think the problem being that since ice will freeze from the top down and outside-in, the ice adhered to the can too well to let it expand upward as much as I hoped. (BTW — Black Cherry Citrus? Blecch. I bought it by accident when they redesigned their color scheme and introduced the flavor)
So I did it again, adding a little bit of water and letting that freeze, repeating the process several times until it was full, and it worked. Here is the experiment to investigate the problem given above:
For those who think that the liquid-filled can will roll more slowly, I think I know what the misconception is: most of us have seen or done the experiment with spinning an egg, and a hard-boiled egg spins readily while the unboiled egg doesn’t. So the intuition is that since liquids don’t spin readily, the liquid-filled can won’t want to roll very fast. And, as we can see, that’s wrong.
The reason the intuition is wrong is from a misinterpretation of the reason the unboiled egg doesn’t spin — it’s because it’s difficult to transfer energy and angular momentum to the liquid by spinning the container; the coupling between them is weak. And angular momentum tells you the tendency for something to spin — it only changes when you apply a torque. With the soda cans it means that the work being done, adding energy (gravity acts on it, and there is a torque from the friction of the treadmill causing rotation)but this energy isn’t being added to the liquid, so it must be going into the can itself, which isn’t very massive — almost all of the energy goes into translational kinetic energy. The frozen water, though, does rotate with the can, so the gravitational potential energy has to be shared between translation and rotation of the can + ice system, so the translational kinetic energy (and therefore speed) is smaller.
I Can No' Change the Laws of Physics, Cap'n!
Quantum setback for warp drives
Bad news I’m afraid — it looks as if faster-than-light travel isn’t possible after all. That’s the conclusion of a new study into how warp drives would behave when quantum mechanics is taken into account. “Warp drives would become rapidly unstable once superluminal speeds are reached,” say Stefano Finazzi at the International School for Advanced Studies in Trieste, Italy, and a couple of friends.
Making Restitution
When two objects collide, the coefficient of restitution, or COR, is the ratio of the speed of separation after the collision to the initial speed of approach. A perfectly elastic collision will have a restitution coefficient of one, but almost all macroscopic collisions are inelastic, with coefficients less than one. A golf ball dropped on a concrete floor, for example, will bounce with a COR of around 0.8, and it can never be greater than one–despite golfers’ dreams–because some of the kinetic energy always goes into heating the ball.
[…]
[B]elow a certain threshold of cohesiveness some of the simulated events displayed a COR greater than one and as high as 1.05. The fraction of these anomalous rebounds increased with the cluster temperature. “When the temperature increases, more and more vibrating modes are excited,” Kuninaka says. These vibrations can sometimes give an extra kick to the collision, like a gymnast pushing off the pummel horse to get a greater lift.
IOW, when the particles are really small, you are more likely to see when they are expanding or contracting, a behavior that will get averaged out for larger particles. If you have a collision when the expansion happens, that internal vibration energy gets transferred to translational energy, and a COR > 1.
I don’t like how they say that the second law of thermodynamics doesn’t necessarily hold, because later on they explain how it actually does. There will an increase in entropy for the system, but you have to look at this stochastically rather than for an individual particle. It’s like a compressed spring which is at maximum compression just as it hits the ground, and snaps open on the impact (you can sometimes do this with a retractable pen) — it will rebound higher than the point from which it was dropped, because you convert the potential energy of the spring into kinetic energy, and this doesn’t violate any physical laws. But for an ensemble of springs for which the spring motion is random, the average rebound will be lower than the release point.
Just a Reminder
For the (statistically speaking) fraction of a reader within commuting distance of Washington, DC. Tomorrow (Saturday) is the Naval Observatory Open House
Though it is raining today, the weather looks like it’s going to be great tomorrow. Which means that no meteorologists will need to be strangled.
April Fool Forces
Fake Forces – sometimes they are Fantastic
[T]here are times when faux forces are awesome. Just to be clear, a faux force is needed to use normal newtonian mechanics when the reference frame is accelerating. To show this, let me look at the following problem. I will solve it without and then with fake forces.