Posts with «physics» label

The Large Hadron Collider is smashing protons again after a three-year hiatus

The Large Hadron Collider, the particle accelerator that enabled the discovery of the Higgs boson, is back in action after over three years in hiatus. CERN shut the accelerator down for maintenance and upgrade work that was extended due to delays caused by the COVID-19 pandemic. Now, it's ready to smash particles for various research projects throughout its third run that's scheduled to last until 2026. In fact, two beams of protons had already circulated in opposite directions around the 27-kilometer collider as of April 22nd at 12:16 CEST (6:16AM Eastern Time). 

It's just a start, however: The beams contained a relatively small number of protons and circulated at 450 billion electronvolts. The LHC team will ramp up the energy and intensity of the beams until the accelerator can perform collisions at a record energy of 13.6 trillion electronvolts.

Mike Lamont, CERN's Director for Accelerators and Technology, said:

"The machines and facilities underwent major upgrades during the second long shutdown of CERN's accelerator complex. The LHC itself has undergone an extensive consolidation programme and will now operate at an even higher energy and, thanks to major improvements in the injector complex, it will deliver significantly more data to the upgraded LHC experiments."

Research teams using the accelerator for their studies are expecting to be able to perform a lot more collisions — one, in particular, is expecting a 50 times increase — thanks to the upgrade. The more powerful LHC will allow scientists to study the Higgs boson more closely and to resume their hunt for a particle that proves the existence of dark matter with a more capable tool at hand. 

At the moment, dark matter is but a hypothetical form of matter that's believed to be five times more prevalent than its ordinary counterpart. It's invisible, doesn't reflect or emit light, and all attempts at looking for it have so far been unsuccessful. LHC researchers have narrowed down the regions where the particle may be hidden, though, and the upgraded accelerator could bring us closer to its discovery. To note, CERN previously approved plans to build a more powerful $23 billion super-collider that's 100 km in circumference, but its construction isn't expected to begin until 2038. 

Hitting the Books: Why we can't 'beam ourselves up' Star Trek-style

Gene Roddenberry was a man ahead of his time, accurately predicting the development of fantastical gadgets like flip phones, tablet computers, Bluetooth and bionic eyes — even tractor beams. But one technology Roddenberry called for in the 1960s has yet to make it off the screen: teleportation. It's not only that "we just don't have enough power," as Scotty would say, we also lack the fundamental knowledge base to make it a reality. For now, at least. In their latest book, Frequently Asked Questions about the Universe, Jorge Cham and Daniel Whiteson delve into this and a host of other quandaries facing humanity — from whether there's an afterlife, why aliens haven't made contact with us yet, or if our observable existence is actually a computer simulation. 

Penguin

Excerpted from Frequently Asked Questions about the Universe by Jorge Cham and Daniel Whiteson. Copyright © 2021 by Jorge Cham and Daniel Whiteson. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.


If your dream of teleportation is to be here in one moment, and then be in a totally different place the next moment, then we are sad to tell you right off the bat that this is impossible. Unfortunately, physics has some pretty hard rules about anything happening instantaneously. Anything that happens (an effect) has to have a cause, which in turn requires the transmission of information. Think about it: in order for two things to be causally related to each other (like you disappearing here and you appearing somewhere else), they have to somehow talk to each other. And in this universe, everything, including information, has a speed limit.

Information has to travel through space just like everything else, and the fastest anything can travel in this universe is the speed of light. Really, the speed of light should have been called the “speed of information” or “the universe’s speed limit.” It’s baked into relativity and the very idea of cause and effect, which are at the heart of physics.

Even gravity can’t move faster than light. The Earth doesn’t feel gravity from where the Sun is right now; it feels gravity from where the Sun was eight minutes ago. That’s how long it takes information to travel the ninety-three million miles between here and there. If the Sun disappeared (teleporting off for its own vacation), the Earth would continue in its normal orbit for eight minutes before realizing that the Sun was gone.

So the idea that you can disappear in one place and reappear in another place instantly is pretty much out of the question. Something has to happen in between, and that something can’t move faster than light.

Fortunately, most of us aren’t such sticklers when it comes to the definition of “teleportation.” Most of us will take “almost instantly” or “in the blink of an eye” or even “as fast as the laws of physics will allow” for our teleportation needs. If that’s the case, then there are two options for making a teleportation machine work:

1. Your teleportation machine could transmit you to your destination at the speed of light.

2. Your teleportation machine could somehow shorten the distance between where you are and where you want to go.

Option #2 is what you might call the “portal” type of teleportation. In movies, it would be the kind of teleportation that opens up a doorway, usually through a wormhole or some kind of extradimensional subspace, that you step through to find yourself somewhere else. Wormholes are theoretical tunnels that connect points in space that are far away, and physicists have definitely proposed the existence of multiple dimensions beyond the three we are familiar with.

Sadly, both of these concepts are still very much theoretical. We haven’t actually seen a wormhole, nor do we have any idea how to open one or control where it leads. And extra dimensions aren’t really something you can move into. They only represent extra ways in which your particles might be able to wiggle.

Much more interesting to talk about is Option #1, which, as it turns out, might actually be something we can do in the near future.

Getting There at Light Speed

If we can’t appear in other places instantly, or take shortcuts through space, can we at least get there as fast as possible? The top speed of the universe, three hundred million meters per second, is plenty fast to cut your commute down to a fraction of a second and make trips to the stars take years instead of decades or millennia. Speed-of-light teleportation would still be awesome.

To do that, you might imagine a machine that somehow takes your body and then pushes it at the speed of light to your destination. Unfortunately, there’s a big problem with this idea, and it’s that you’re too heavy. The truth is that you’re too massive to ever travel at the speed of light. First, it would take an enormous amount of time and energy just to accelerate all the particles in your body (whether assembled or broken up somehow) to speeds that are close to the speed of light. And second, you would never get to the speed of light. It doesn’t matter how much you’ve been dieting or working on your CrossFit; nothing that has any mass can ever travel at the speed of light.

Particles like electrons and quarks, the building blocks of your atoms, have mass. That means that it takes energy to get them moving, a lot of energy to get them moving fast, and infinite energy to reach the speed of light. They can travel at very high speeds, but they can never achieve light speed.

That means that you, and the molecules and particles that make up who you are right now, would never actually be able to teleport. Not instantaneously, and not at the speed of light. Transporting your body somewhere that quickly is never going to happen. It’s just not possible to move all the particles in your body fast enough.

But does that mean teleportation is impossible? Not quite!

There is one way it can still happen, and that’s if we relax what “you” means. What if we didn’t transport you, your molecules or your particles? What if we just transmitted the idea of you?

You Are Information

One possible way to achieve speed-of-light teleportation is to scan you and send you as a beam of photons. Photons don’t have any mass, which means they can go as fast as the universe will allow. In fact, photons can only travel at the speed of light (there’s no such thing as a slow-moving photon).*

Here’s a basic recipe for speed-of-light teleportation:

Step #1: Scan your body and record where all your molecules and particles are.

Step #2: Transmit this information to your destination via a beam of photons.

Step #3: Receive this information and rebuild your body using new particles.

Is this possible? Humans have made incredible progress in both scanning and 3D printing technologies. These days, magnetic resonance imaging (MRI) can scan your body down to a resolution of 0.1 millimeters, which is about the size of a brain cell. And scientists have used 3D printers to print increasingly more complicated clusters of living cells (known as “organoids”) for testing cancer drugs. We’ve even made machines (using scanning tunneling microscopes) that can grab and move individual atoms. So it’s not hard to imagine that one day we might be able to scan and then print whole bodies.

The real limitation, though, might not be technological but philosophical. After all, if someone made a copy of you, would it actually be you?

Remember, there’s nothing particularly special about the particles that make up your body right now. All particles of a given type are the same. Every electron is perfectly identical to every other electron, and the same is true for quarks. Particles don’t come out of the universe factory with personalities or any sort of distinguishing features. The only difference between any two electrons or any two quarks is where each of them is and what other particles they’re hanging out with.*

But how much would a copy of you still be you? Well, it depends on two things. The first is the resolution of the technology that scans and prints you. Can it read and print your cells? Your molecules? Your atoms, or even your individual particles?

The even bigger question is how much your “you-ness” depends on the tiny details. What level of detail does it take for the copy to still be considered you? It turns out that this is an open question, and the answer might depend on how quantum your sense of self is.

Exploring a classic physics problem with Arduino

As described in this project’s write-up, “The brachistochrone curve is a classic physics problem, that derives the fastest path between two points A and B which are at different elevations.” In other words, if you have a ramp leading down to another point, what’s the quickest route?

Intuitively—and incorrectly—you might think this is a straight line, and while you could work out the solution mathematically, this rig releases three marbles at a time, letting them cruise down to the Arduino Uno-based timing mechanism to see which path is fastest. 

The ramps are made out of laser-cut acrylic, and the marbles each strike a microswitch to indicate they’ve finished the race. The build looks like a great way to cement a classic physics problem in students’ minds, and learn even more while constructing the contraption!

Make Physics Fun with a Trebuchet

What goes up must come down. And what goes way, way up can come down way, way too fast to survive the sudden stop. That’s why [Tom Stanton] built an altitude recording projectile into an oversized golf ball with parachute-controlled descent. Oh, and there’s a trebuchet too.

That’s a lot to unpack, but suffice it to say, all this stems from [Tom]’s obvious appreciation for physics. Where most of us would be satisfied with tossing a ball into the air and estimating the height to solve the classic kinematic equations from Physics 101, [Tom] decided that more extreme means were needed.

Having a compound trebuchet close at hand, a few simple mods were all it took to launch projectiles more or less straight up. The first payload was to be rocket-shaped, but that proved difficult to launch. So [Tom] 3D-printed an upsized golf ball and packed it with electronics to record the details of its brief ballistic flight. Aside from an altimeter, there’s a small servo controlled by an Arduino and an accelerometer. The servo retracts a pin holding the two halves of the ball together, allowing a parachute to deploy and return the package safely to Earth. The video below shows some pretty exciting launches, the best of which reached over 60 meters high.

The skies in the field behind [Tom]’s house are an exciting place. Between flying supercapacitors, reaction wheel drones, and low-altitude ISS flybys, there’s always something going on up there.

Dirt Cheap Muon Detector Puts Particle Physics Within DIY Reach

Subatomic physics is pretty neat stuff, but not generally considered within the reach of the home-gamer. With cavernous labs filled with racks of expensive gears and miles-wide accelerators, playing with the subatomic menagerie has been firmly in the hands of the pros for pretty much as long as the field has been in existence. But that could change with this sub-$100 DIY muon detector.

[Spencer Axani] has been fiddling with the idea of a tiny muon detector since his undergrad days. Now as an MIT doctoral candidate, he’s making that dream a reality. Muons are particles that are similar to electrons but more massive and less likely to be affected by electromagnetic fields. Muons rain down on the Earth’s surface at the rate of 10,000 per square meter every minute after being created by cosmic rays interacting with the atmosphere and are capable of penetrating deep into the planet. [Spencer]’s detector is purposely kept as low-budget as possible, using cheap plastic scintillators and solid-state photomultipliers hooked up to an Arduino. The whole project is as much STEM outreach as it is a serious scientific effort; the online paper (PDF link) stresses the mechanical and electronics skills needed to complete the build. At the $100 price point, this build is well within the means of most high school STEM programs and allows for a large, distributed array of muon detectors that has the potential for some exciting science.

We’ve covered quite a few subatomic detection projects before, from the aforementioned large-scale builds to more modest efforts. But we like this project because it has the potential to inspire a lot of citizen scientists.

Thanks for the tip, [deralchemist]


Filed under: misc hacks

Arduino data logger at Global Physics Department

My son presented the Arduino Data Logger he wrote for my circuits class to the Global Physics Department on 2013 May 15.  The sessions are recorded, and the recording is available on the web (though you have to run Blackboard Collaborate through Java Web Start to play the recording).

I thought he did a pretty good job of presenting the features of the data logger.

Now that school is beginning to wind down, he’s started looking at making modifications to the data logger code again, and has updated it at https://bitbucket.org/abe_k/arduino-data-logger/

He’s down to only three classes now (US History, Physics, and Dinosaur Prom Improv), though he still has homework to catch up on in Dramatic Literature and his English class.  He’s still TAing for the Python class also.

On Thursday and Friday this week, he’ll be taking the AP Computer Science test and the AP Physics C: Electricity and Magnetism test.  He’s having to take both tests in the “make-up” time slot, because we couldn’t get any local high school to agree to proctor the tests for him during the regular testing time.  Eventually his consultant teacher convinced the AP coordinator to let her proctor the tests, but by then it was too late to register for anything but the makeup tests. We’re way behind schedule on the physics class, so he’s just going to read the rest of the physics book without working any problems before Friday’s exam—we’ll finish the book in a more leisurely fashion after the exam. He won’t be as prepared for the physics exam as I had hoped, but at least the CS exam looks pretty easy to him.

One thing I didn’t realize is that schools can charge homeschoolers whatever the market will bear for proctoring the tests:

  • Depending on the reasons for late testing, schools may be charged an additional fee ($40 per exam), part or all of which the school may ask students to pay. Students eligible for the College Board fee reduction will not be charged the $40-per-exam late-testing fee, regardless of their reason for testing late.
  • Schools administering exams to homeschooled students or students from other schools may negotiate a higher fee to recover the additional proctoring and administration costs.

[ http://professionals.collegeboard.com/testing/ap/about/fees ]

We’re paying $145 per exam (not just the $89 standard fee and the $40 late fee), but I’m glad he gets to take the exams at all this year.

Tomorrow he and I are doing another campus tour—this time at Stanford. He managed to get an appointment with a faculty member, but we noticed that the faculty member is scheduled to be teaching a class at the time of the appointment—I wonder what is going to happen with that. I’ll report on the visit later this week.


Filed under: Data acquisition Tagged: Advanced Placement exams, Arduino, data logger, Global Physics Department, physics

Arduino data logger at Global Physics Department

My son presented the Arduino Data Logger he wrote for my circuits class to the Global Physics Department on 2013 May 15.  The sessions are recorded, and the recording is available on the web (though you have to run Blackboard Collaborate through Java Web Start to play the recording).

I thought he did a pretty good job of presenting the features of the data logger.

Now that school is beginning to wind down, he’s started looking at making modifications to the data logger code again, and has updated it at https://bitbucket.org/abe_k/arduino-data-logger/

He’s down to only three classes now (US History, Physics, and Dinosaur Prom Improv), though he still has homework to catch up on in Dramatic Literature and his English class.  He’s still TAing for the Python class also.

On Thursday and Friday this week, he’ll be taking the AP Computer Science test and the AP Physics C: Electricity and Magnetism test.  He’s having to take both tests in the “make-up” time slot, because we couldn’t get any local high school to agree to proctor the tests for him during the regular testing time.  Eventually his consultant teacher convinced the AP coordinator to let her proctor the tests, but by then it was too late to register for anything but the makeup tests. We’re way behind schedule on the physics class, so he’s just going to read the rest of the physics book without working any problems before Friday’s exam—we’ll finish the book in a more leisurely fashion after the exam. He won’t be as prepared for the physics exam as I had hoped, but at least the CS exam looks pretty easy to him.

One thing I didn’t realize is that schools can charge homeschoolers whatever the market will bear for proctoring the tests:

  • Depending on the reasons for late testing, schools may be charged an additional fee ($40 per exam), part or all of which the school may ask students to pay. Students eligible for the College Board fee reduction will not be charged the $40-per-exam late-testing fee, regardless of their reason for testing late.
  • Schools administering exams to homeschooled students or students from other schools may negotiate a higher fee to recover the additional proctoring and administration costs.

[ http://professionals.collegeboard.com/testing/ap/about/fees ]

We’re paying $145 per exam (not just the $89 standard fee and the $40 late fee), but I’m glad he gets to take the exams at all this year.

Tomorrow he and I are doing another campus tour—this time at Stanford. He managed to get an appointment with a faculty member, but we noticed that the faculty member is scheduled to be teaching a class at the time of the appointment—I wonder what is going to happen with that. I’ll report on the visit later this week.


Filed under: Data acquisition Tagged: Advanced Placement exams, Arduino, data logger, Global Physics Department, physics

Nerf gun prototype 1

The Santa Cruz Robotics Club met again today, for the first time in over a month.  The current project is not the underwater ROV (we’re all getting very tired of waterproofing problems), but an automated Nerf gun.

The club members came up with some very ambitious plans for the Nerf gun (which included getting a Raspberry Pi and doing image processing to have a self-aiming gun), but I’m making them build quick-and-easy prototypes to try out their ideas one step at a time.  I don’t think I can get an Raspberry Pi this summer—the companies doing the distribution aren’t taking more orders (just expressions of interest) and they don’t expect to clear the current backlog until September at the soonest.  They are doing batches of 100,000 units, and that doesn’t seem to be enough to shrink the lead time—if anything, the lead time is growing.

So, giving up on image processing for this summer, there are still a lot of things to build.  For today’s four-hour meeting (which included a 1-hour trip to the hardware store and a fifteen-minute snack break), the goal was simply to test out the basic launcher concept: an air reservoir pressurized by a bike pump, a solenoid valve, and a barrel.

The first prototype. The air reservoir is about 18″ of 1-½” PVC pipe on the left, and the barrel is about 24″ of ½” PVC pipe on the right.

The biggest problem was that the valve has ¾” male pipe threads, but we wanted 1-½” PVC pipe for the reservoir (because we had a piece handy—we may build a bigger reservoir later) and ½” PVC pipe for the barrel (because Nerf darts just fit inside—probably Nerf guns were prototyped with PVC barrels).  Our hardware store run was to get threaded adapters to make things fit.We wanted everything to be joined with screw threads, so that we could disassemble the components and replace them or add elbows as needed.

Note that the ½” PVC pipe is also a good size for compressed-air paper “rockets”.  The term “rocket” is a misnomer here, as all the acceleration occurs while the rocket is on the launcher—it is modeled more like a gun than like a rocket. (But my soda-bottle rocket simulator can model these paper bullets also.)  It would probably best to have a shorter barrel for doing rocket launching—just the length of the rocket and no more, since the longer barrel results in more pressure loss with no gain in launch speed.

The bicycle valve glued into a ½” female-threaded end cap was one I’ve had for a long time, as part of a soda-bottle rocket launcher. I had two of them, and both failed in testing today (the Barge cement holding the valve stem in failed—we’ve now reglued them with a different cement), though we managed some testing before the failure.

The solenoid valve we used was the same model (sold by Sparkfun) as the one used for the vacuum bottle on the ROV.  It has ¾” male pipe threads on each side.  To make it air-tight we had to disassemble it and grease the rubber membrane thoroughly with vaseline or faucet grease, but we had done that months ago, so it did not need to be done today.  The valve only works in one direction, but the high-pressure side is clearly marked by a metal intake screen, so assembling it the right way around is easy.

I was not sure that the solenoid valve would work in this application. It is not the model of valve that the compressed-air “rocket” people have used—those valves cost about twice as much and have female threaded ends rather than male threaded ends. I think that the mechanism they use may open up a bigger channel for air or water than the cheap solenoid valve sold by Sparkfun.

My first concern was that I did not know whether the valve would open up wide enough and fast enough to let a blast of air through to get a clean launch.  Second, I did not know whether we could open and close the valve fast enough to retain pressure in the reservoir for doing multiple shots.

We controlled the solenoid valve with an Arduino and the Hexmotor motor-control board (which is really overkill for one solenoid—a single power transistor would be enough to interface the Arduino to a solenoid, but I did not have one handy).  My son wrote an Arduino program to allow us to experiment with the duration of the solenoid pulse.  If it were too short, the Nerf dart would not leave the barrel.  If it were too long, air pressure would be wasted.  He allowed for 100 µsec increments in pulse duration, under control from commands on the USB serial line.

Because the glue they used takes 24 hours to set properly, we only tested at low pressure today (20–30 psi).  At those pressures, a 16 msec pulse was not long enough for the dart to clear the barrel, but a 19.2 msec pulse was easily long enough. We were also able to launch a 14g paper “rocket” left over from Maker Faire, though it did not go as high as the approximately 1.6g “Nerf” darts (I think several of the foam darts we have a different brand). We would not have expected it to go as high, since it was only accelerated for its 11″ length, not the 24″ length of the barrel for the darts, and it weighed a lot more.

One thing I thought about was monitoring the air pressure in the reservoir electronically. I doubt that we’ll put a pressure sensor in the reservoir, though, as the sensors I have only go up to 250 kPa absolute (about 21 psi above atmospheric pressure—about as low as we could fire with).  Freescale makes a 145psi (1000 kPa) sensor, the MPX5999D, but it is a differential sensor without port tubes (so would be difficult to mount) and it costs $13.

Perhaps the other thing worth doing today is to analyze how fast the Nerf dart should be going as it leaves the barrel, and how high it should fly if we shoot it straight up.  The physics here is fairly simple, if we assume that opening the solenoid valves connects us to a constant-pressure source. (In practice, we saw about a 10psi or 70kPa drop in pressure after one shot. If the pressure is P, then the force on the dart is P*area.  The cross-sectional area of the foam dart is a little hard to measure, because of the squishiness of the foam, but the inside diameter of the barrel is 1.45cm, for a cross-sectional area of 1.65 cm^2. At 140 kPa (about 20 psi), the force on the dart would be 23 Newtons.  That force is applied for about 60 cm (the length of the barrel), for a total energy of about 14 Joules.

We can use the kinetic energy of the dart to get its speed (E = ½ m v2), so for 140 kPa, the dart should leave the barrel at about 130 m/s or 290 mph. I suspect that we are not getting anywhere near that speed, for several reasons, including leakage of air around the dart, limited speed of air moving through the valve, and friction of the dart in the barrel (mainly from the pressure wave in front of it, but also from rubbing on the sides of the barrel).

We can also use the kinetic energy of the dart to estimate how high it would fly (ignoring air resistance, which is obviously hugely important for a low density object like a foam dart). The potential energy of a mass at height h is , so the height it would go without air resistance is . For 14 Joules and 1.6 grams, that would be almost 900m. I think that 20m is a more reasonable estimate for the height the dart went, though I never could see it near the top of its trajectory.

I tried adding the specs for the Nerf dart and a 60cm barrel to my rocket simulator (to get a crude estimate of the effect of air drag), and for 140 kPa I got an estimated max speed of 132m/s and an estimated max height of 52.6m. I don’t know if that height is reasonable—certainly it is better than the no-air-resistance estimate. The 6.78 second estimated time of flight seems to be fairly reasonable, though we never timed it.

Doubling the pressure increases the maximum velocity by a factor of 1.414, but only increases the maximum height to 60.8 m, a 16% increase. Doubling the barrel length has about the same effect. Air drag is what determines the speed of the dart, and that is the least well-modeled part of my simulation.

On Thursday, when they club meets again, they’ll try experimenting with higher pressures, and see whether 17 or 18 msec pulses are long enough—the shorter the pulse the less air will be wasted, and the more shots they can make from the reservoir.  It may be necessary to design a bigger reservoir or add a compressor to the design, since they eventually want a fully automatic Nerf gun, not the one-shot muzzle-loader that they made as the prototype today.  They’ll also start designing a pan-tilt mechanism for the Nerf gun, probably prototyping it out of Lego Technic components.


Filed under: Robotics Tagged: Arduino, Nerf gun, nerf guns, physics, rocket, simulation, SparkFun Electronics

Pendulum lab went well

In today’s lab we derived the formula for the period of a simple pendulum (assuming the small-angle approximation), , then measured both circular and simple pendulums.  For the circular pendulum we measured the radius of the cone on the first orbit and the last orbit, the length of the string (the slant height of the cone), and approximated the period by timing 10 or 20 periods and dividing.  For the simple pendulum, we used the photogate setup described in More on pendulums, to get very precise and repeatable measurements of the period.  The hardest part for us was measuring the length of the pendulums, since the center of mass for the bob was not obvious and the exact position of the pivot was not obvious—these uncertainties probably resulted in length measurements being ±5mm, making a large contribution to inaccuracy.

Here is a table of the measurements (and calculated g) we made for the circular pendulum:

Length cm radius cm num orbits period sec g cm/sec^2
 212.4  48.6–46.6 10 2.90  970.8–972.6
 212.4  38–52.4 20 2.601  959.8–974.7
 161.5  58–60.5 20 2.501  938.7–984.2

The range of estimates for g is larger than I would like.  I think that the decay of the oscillation of the pendulum makes quite a difference.  The average of all the estimates of g is 967 gm/sec^2, which is rather low.

And for the simple pendulum:

Length cm num ticks mean period sec standard deviation g cm/sec^2
207.2 47 2.8958 0.0050 975.4
171.3 74 2.6272 0.0065 979.8
95.5 89 1.9565 0.0025 984.9
54.7 58 1.4809 0.0042 984.7
28.7 44 1.0730 0.0019 984.0

The pendulum ticked reliably for quite a while, and the periods were remarkably consistent.  The estimates of g from the simple pendulum are good to about 0.5%, which is the limitation of accuracy on our pendulum length measurements and close to the limit of the accuracy of the small-angle approximation.  The average of the 5 measurements looks good to about 0.2%, which seems pretty good to me, since we certainly weren’t measuring the lengths that accurately.

I looked up the gravitational field in Santa Cruz on Wolfram Alpha’s gravitational fields widget:

total field | 9.7995 m/s^2  (meters per second squared)
angular deviation from local vertical | 0.00322°  (degrees)
down component | 9.79945 m/s^2  (meters per second squared)
west component | 3.4×10^-4 m/s^2  (meters per second squared)
south component | 0.0316 m/s^2  (meters per second squared)
(based on EGM2008 12th order model; 11 meters above sea level)

While the lab was running, one of the students wrote a Python script (using numpy for mean and standard deviation) to read the data and compute the numbers in the table.  We could have talked directly to the Arduino, but it was simpler to cut the numbers from the Arduino serial monitor and paste them into a file for the script to read. That allowed us to keep the Arduino running throughout, and just cut and paste the good numbers, discarding the junk from starting or stopping the pendulum.

I’m quite pleased with the photogate setup, which was very simple to build and worked reliably during the experiment. Crudely wrapping tape around the string made a lumpy opaque object, whose rotation probably contributed to the standard deviation of the  period—having a smoother cylinder for the optical blocker would probably make the period measurement much more consistent.  But that would not improve the mean estimates much since errors in adjacent period measurements cancel.  I believe that our mean periods are much more accurate than the standard deviations suggests, with errors less than 1 per thousand.

I had to make one change in the Arduino code during the lab to accommodate all the different pendulum lengths—I had a dead time before recognizing the next pulse, to prevent getting 2 pulses per period as the string passed through the beam twice.  I started with a dead time of 1 second, which as a bit too long for the smallest pendulum.  Reducing the dead time to 500 msec for that pendulum made it count reliably.  Note that for the 2nd and 3rd pendulum, we measured for about 3 minutes without a bad time measurement, and could have gone longer if we had had the patience.


Tagged: AP physics, Arduino, circular pendulum, g, gravity, high school, Newton, pendulum, photogate, physics

More on pendulums

In Newton’s measurement of g, I described a failed experiment to measure g with a motorized circular pendulum. Further experimentation on my own lead me to adopt for this week’s lab the standard approach using an unpowered circular pendulum.  The cone formed by the string can be described as having height , base radius , and hypotenuse , the length of the string.  If the circular pendulum has period , then (derived in the Newton post).  If we make the string long and push the pendulum with the right speed to get a nearly circular (rather than elliptical) motion, then is nearly constant for many orbits, and we can estimate the period with just a stopwatch by counting 20 or 30 periods.  Using a large enough mass means that neglecting air resistance is now reasonable (which it was not for the tiny mass I started with).

Thanks to John Burk for suggesting that I forget about the motor—that seems to be the best approach, even though I then can’t use the photogate to time the period.  I’m hopeful that we can measure the height and the period accurately enough to get within about 2% of the right value for .

This week in addition to doing the circular pendulum right, I wanted to do simple pendulums.  I’ve assigned problem 4.P.89 in Matter and Interactions, which seems to be the only place in the book that simple pendulums are done.  It is a computational problem, since there isn’t an analytic solution (though the small-angle approximation works pretty well up to about 45°).  I hope the students have done that by tomorrow!

I wanted to measure the period of the pendulum directly (not averaging over many periods), to demonstrate that the amplitude does not matter much.  Unfortunately, I’ve not yet built a sensor that works for this. I tried using the photogate, but I could not hit the 1 cm gap consistently, even with a shorter pendulum.

I also tried using a magnetic sensor (using the circuit I used for the speed-of-sound lab) with a magnet for the pendulum weight, but that triggered at random times as the magnet came close.  Even 20cm away the field was enough to trigger the detector, and I got almost random timings.  A magnetometer was no better than the coil and comparator, as the magnetic field varied chaotically (from movements of the magnet other than the simple pendulum swing, such as twirling on the string).  The magnetometer was usable as a compass, though, which is good, because I originally bought it for the robotics club to use as a compass.  There are some tricky points to using it as a compass, which I’ll talk about in a different post.

I then tried marking the top of the string with a bit of electrical tape and using the photogate there.  That was the most successful so far—if I hold the photogate steady enough, I can get readings repeatable to ±20msec, which is much better than I can do with any other approach I’ve tried.  For one pendulum hanging from the edge of my desk, I either got  two pulses at about 1.11 and 0.45 seconds or one pulse every 1.56 seconds, depending on whether the marker on the string passes all the way through the beam or blocks it continuously at the end of the swing. The random variation I get is probably because of holding the sensor by hand (to align with the string).

If I had a more rigid way to mount the sensor, I should be able get more consistent readings, so my main engineering task was to get a rigid pivot point on the ceiling beam (without making any holes) and mount the photogate in a rigid, but adjustable, way.  Of my two standard mechanical engineering techniques, duct tape and Lego, I chose Lego:

A view of the photogate mounted on the Lego beam next to the pendulum string.

Closeup of the photogate, showing the breakout board and sensor wedged between a plate and a beam, with a 2-plate spacer.

Having come up with a nice way to grip the photogate and still be able to swing a pendulum string into the gap, I connected the beam holding the photogate to the same right-angle platform that we had used last week for the motorized pendulum. This left a little gap that I could rest the Arduino board in, so that there was no tension on the wires to the photogate.

I was a bit worried that I might have to put my laptop on top of a ladder, since the USB cord is not very long, but I have a spare pair of USB-to-Cat5 converters (one set is for the robotics project), so I was able to make an extension cord out of a flexible Cat-5 Ethernet cable, giving me enough length to put my laptop safely on the desk.

The same Lego that holds the photogate can also support the Arduino, so I don't need to hold anything in my hands.

I had two other ideas I haven’t tried: using one of the ultrasonic range finders to track the pendulum motion and using a video camera to time the motion.  These require interpolation of position data to estimate the period, so I’d rather avoid them for now. The top-of-string photogate will work (I think) for the simple pendulum, and the circular pendulum can be timed with a stopwatch averaged over many periods.  (I could even use the photogate timer as a stopwatch, though the resolution of the stop watch on my Casio wristwatch is 0.01 seconds, and human reflexes make anything less than 0.1 second pretty much noise.)


Tagged: AP physics, Arduino, circular pendulum, g, gravity, high school, Lego, Newton, pendulum, photogate, physics