Here are a number of projects which typify the spirit of Saturday Science: they are novel, they are playful, they get you doing practical things, give you a ‘feel for stuff’. The projects often bring out some fascinating science in the overall concept. But sometimes the fascination is in the details, details that you don’t get unless you actually a practical project. I love Einstein’s analysis, his gedanken experiments, ‘thought experiments’, but you miss out a lot of science if you only do the gedanken half.
They play around with technologies from different places, do different things with them, and offer a chance to learn some science that you won’t find in a textbook, and to have some fun !
- Sonic Molecular Mass Meter: Hear those Molecules ! see below, or for a Microbit readout version see the Microbit page
- Seeing Sound Waves in the Air #soundwave
- Cranky Crawler an ingenious sliding vehicle #crankycrawler
- The Ferrocraft, a Ferrofluid Rail Vehicle #ferrofluid
- Retroreflector Refractometer ! #refractometer
- The Three Laws Cannon: Newton’s Laws of Motion in Milliseconds #threelaws
- Pneumatic Drums, for percussion players who also like bagpipes ! #pneumaticdrums
Sonic Molecular Mass Meter: Hear those Molecules !
Remember those ‘I speak your weight’ machines? Once common, there are still a few around. You put in a small coin and the large accurate mechanical scales tells your body mass. This is just the same, only instead of measuring 50 to 100kg, it is 1000,000,000, 000,000,000, 000,000,000x more sensitive, measuring, as it does, molecules from 3 to 300 x 10-27 kg. We look here at how to make the meter. In the Microbit page of the website, we look at building a Microbit computer on to the meter to allow it to be calibrated and more linear.
If you put a light gas like helium into a flute instruments such as an ocarina, then it will sound a higher note. A friend of mine called Mark Williams made something like this, using a bagpipe chanter, into a musical (ish) instrument that he christened the ‘Heliracket’. The Heliracket has helium and air mixed with a bath mixer tap, and flows the mixture of gas through the ocarina. I’ve demonstrated a version of the Heliracket with an ocarina to many hundreds of people since that time. Mark appeared on a BBC TV programme with the instrument (I had an exotic drum tuned by air pressure in the same programme). *
You can generate a single frequency of sound by using the oscillation of sound waves inside a tube. Here we use electronics to maintain those oscillations, and measure the molecular mass of the gas inside the tube by measuring the frequency.
*We are all familiar with the effect, although it is more complicated than it at first seems, that if you take in a breath of helium gas your voice goes high and squeaky. (I don’t recommend this, by the way, on the safety grounds that we humans need oxygen to live, and just a few breaths of helium, which doesn’t normally have any O2 in it could kill you.)
Here we use the oscillation of sound waves inside a tube to measure the molecular mass of the gas inside the tube.
What you need
Battery box and batteries
45mm PVC pipe, 150mm long, end cap (eg.plastic jar top)
Condenser microphone (eg. standard 10mm diameter device), 50mm dia 64Ohm loudspeaker
Vero circuit stripboard, 2 transistors, eg. BC547B, resistors 4.7MOhm, 8.2KOhm, capacitor 1nF
6mm flexible plastic tube for connecting gas to device.
Wires, glue etc
Multimeter with frequency readout ( or Microbit )
What you do
Hook up a microphone to an amplifier to a microphone in a box and what have you got ? Feedback ! And positive feedback in electronics means oscillations !
Take a 150mm length of 45mm drainpipe and cap it off at one end by a plastic jar lid, the other end is taken by the loudspeaker, simply glued to the end. The microphone is glued into a hole near the loudspeaker end. That’s it !
It’s useful to be able to flush gas in and out of the pipe easily, and arranging the pipes as shown will help to do this. Put in heavy gases like CO2 or Butane with the Sonic MMM pipes upward, and put in light gases like methane with the Sonic pipes down and you should be able to get gases to flow without mixing too much of the previous gas in.
Now plug in and see what the Sonic MMM sounds like. With air, you should get a steady oscillation of a little over 1000 Hz.
If simplicity is good, then this circuit is seriously good. Only 5 components connect the microphone and speaker, all of them in themselves simple, elemental electronic parts. The two transistors are wired as a Darlington pair, with their collector load the 64ohm 50mm loudspeaker, a 4.7MOhm resistor providing stabilizing feedback, while a capacitor isolates DC component of the microphone output. A Darlington pair behaves like a single transistor with a super high gain. The microphone, a standard condenser microphone, is fed current by the 8.2KOhm resistor.
The circuit is so simple that you can assemble it by soldering parts to each other, or maybe using very small ‘choc bloc’ screw terminals. However, it is probably easier to solder up a small circuit board, using stripboard (Veroboard or similar).* You could maybe use a single power supply for the Microbit and circuit (it works at 3V too), but you can also use a separate battery pack for the resonator, and this makes it easier to test the circuit before connecting the Microbit.
Once all is wired up, connect batteries and you should get an immediate oscillation in the region of 1KHz, with air in the pipe. Try it on different gases. Note on H2 and Helium you will tend to find that the frequency jumps as the gas goes in, due to the pipe now sounding a different harmonic. Follow this process on a spectrum analyser and you can see what is happening – and if you track the harmonic you started on with air you can measure the correct relative frequency of He and H2.
*Because you are using only simple components, you can use the larger scale 3.8mm grid board – it is still made by Vero and comes from a few suppliers. The larger scale – it seems really HUGE, makes soldering very easy, even for the ham-fisted like me !
Things to Try
There are a few tricks to getting the best out of the Sonic Molecular Mass Meter. You will discover pretty quickly that the frequency of the oscillations will change if you pull the gas pipes out. You will also discover that ambient noises will upset the measurement process: so keep quiet ! Putting the whole gadget in a cardboard box lined with something sound absorbent like blanket or packing material may help – and also means the noise from the Sonic MMM won’t drive you and your neighbours crazy quite so quickly !
Look at the waveform produced by the Sonic MMM. Also, try using an audio spectrum analyser on it. (You can use the Spectrum Analyser on a ‘app’ on your mobile phone – one is ‘FrequenSee’.) The waveform, and particularly the spectrum analyser, will usually show a lot of complexity.
The easiest gases to test are probably from air (freely available on one planet in the Sol star system), and CO2, most easily obtained from a Sodastream lemonade machine. The latter just needs one of the tubes pushing over the CO2 lance, and then press as gently as you can, squeezing just enough to get a modest flow of CO2, repeating short bursts of CO2 until the Sonic MMM is clearly heard to have stopped changing frequency after a burst.
The Theory: the Science of Relative Molecular Mass – RMM or ‘molecular weight’
The number of protons and neutrons in the nucleus of an atom make up its atomic weight, since the electrons are very light. The number of electrons is the same as the number of protons, and determines the chemistry of an atom. The relative molecular mass depends upon the atoms which make it. The noble elements like Helium, Neon and Argon exist as single atoms in gases, so their gas RMM = atomic weight. Many other gases are made of two atoms, like nitrogen, N2, and oxygen, O2, and their RMM is =2x atomic weight. Other gases have multiple atoms, and their RMM is simply the sum of their atomic weights (=atomic masses)* of their atoms. So butane (lighter and BBQ fuel) has the formula C4H10, so its RMM is (4×12 + 10×1) = 58.
The Simple Science of Gas Density
Gases at the same temperature and pressure vary in density in direct proportion to their Relative Molecular Mass (RMM). So if we can make a density meter we can use it to measure the Molecular Mass. We have to correct the measurement for pressure(P) & absolute temperature (T), because density is proportional to P and to 1/T.
The More Complicated Science of speed of Sound
Gases at the same temperature (the pressure doesn’t matter much) have a speed of sound which is more-or-less proportional to one over the square root of their molecular mass. Or, in other words:
Speed of sound = constant x 1/(square root RMM).
Just like with density, however, there is a temperature correction, and this also involves absolute (Kelvin) temperature ratios, although this time square rooted. There is also a correction due to whether a gas is made of molecules of 1 atom, 2 atoms, or many atoms, which is called the Cp/Cv ratio or γ (gamma).
*There is history in the use of the words weight and mass, in atomic weight/mass and molecular weight/mass: they are still widely used interchangeably, although of course ‘mass’ is the correct word.
Try building a Sonic MMM differently
Try a different length – that will change the frequency of course. Using a different ‘aspect ratio’ of pipe (radio of length/diameter) will affect the tone of the oscillations to some extent, and may give a tone which is easier / more accurate to measure the frequency.
Tuning the oscillator so that it has less ‘gain’ (amplification factor) may give a purer note, and less tendency to jump to a different harmonics, as seen with Helium.
Try the microphone in different places – are there other positions which work, and do they work better ? You could try moving the loudspeaker, but that is trickier, since it fits neatly onto the end of the pipe, but rather less neatly anywhere else.
What is the use of measuring the Molecular Mass of Gases for ? Two examples…
Purging: before you can use gas in a system of pipes and pressure vessels – anything from welding workshops to an oil refinery – you need to check that the air originally inside the pipes and vessels has been replaced by the correct gas. If you are using hydrogen, for example, you check that RMM=2 before using the system – like lighting up a burner, or starting a fuel cell – if the meter said RMM=29, then you know that it is full of air and needs H2 purging. In the case of a burner, if you start it up before it is full of fuel, there may be an explosion inside the pipes – not necessarily dangerous (the pipes are usually very strong), but noisy, scary and possible a long term problem causing damage to ancillary equipment.
Natural Gas: The RMM of natural gases varies with where the gas has come from, and what has been added to it. Pure methane NG has RMM=16, but it may, in Germany, contain added H2, which reduces the RMM, maybe RMM=14. NG in the USA from ‘fracking’ will often contain ethane, which increases the density, so RMM= 17 or 18. Why does this matter ? Well, in a large furnace burning these gases, the flame length and intensity will change with the gases in the mixture, and the furnace would have to be adjusted to avoid over-firing pottery or wrongly heat-treating metals. A molecular mass meter will check that you have got the mixture right.
Mixing Gases: more generally, wherever gases are used in mixtures, the Sonic MMM can be used to check that the mixture is approximately right. Mixtures of gases are used for dispensing beer (CO2 and nitrogen), for welding (Argon or Helium with CO2 and even a little oxygen) and in hospitals (N2O and oxygen for easing of pain, eg. in childbirth).
Andrew Baker-Campbell Andrew; Justin Buckland Justin; Harry Bullivant Acoustic Sensor, European Patent EP 3230727 (2014)
Abdul WAJID, Clarence HURD, Melvin C HETZEL, Acoustic sensor with resonator cell for in-line continuous monitoring of gases, European Patent EP0813060 (1996)
Seeing Sound Waves in the Air
It is possible to show a sound wave travelling through the air in real time. A set of low cost microphone-LED units planted over a long line (150m or more) across a field and can demonstrate the movement of a pulse of sound as it lights up LEDs along its path.
You can’t normally see sound except in extreme and extraordinary circumstances. Large explosions can reveal the movement of a sound wave as a ‘wobble’ in the appearance of the region near the bang. The explosion compresses the air, changing its refractive index. But this isn’t a practical way to demonstrate sound waves !
The speed of sound is about 340ms-1 at room temperature. Human perception is such that we can’t see movement – or intervals in flashes of light – which take place in less than a few tens of milliseconds. To perceive a wave of light travelling, that wave needs to take a reasonable fraction of a second – perhaps half a second or so – to go across our field of view. By arranging for LEDs to respond sensitively to sound, and arranging those LEDs across a long distance – 100m or 200m – you can see where a pulse of sound is as it goes through the air. Here is a video of a See a Sound Wave setup, with microphones over 170 metres. https://www.youtube.com/watch?v=SwEtnostzEs
What you do: how to make microphone/LED units
The microphone goes via a two stage amplifier to the LED. The circuit can be constructed on strip-board, using the circuit diagram shown below, and will end up looking something like the picture underneath. The low cost electret microphone has a built-in FET device supplied with power via a 1k resistor. Signal from this is taken to a simple transistor amplifier and then to another similar stage. The potentiometer provides a variable gain to the whole system. The second of these stages then feeds a transistor whose load includes the LED. The base of this final transistor is connected to ground via a diode, which has the effect of rectifying the current and ensuring that LED will illuminate only when an AC signal is present. The amplifier stages are DC isolated with capacitors.
Operation of the microphone-LED units – seeing sound waves
You will need 8 or more microphone-LED units to show the progress of a sound wave well. Mount each one on a pole, such as a bamboo pole 1m or so tall, which can be easily pushed or tapped with a mallet into the ground. The potentiometer needs to be adjusted on each microphone-LED unit so that it is sensitive enough, but sufficiently insensitive to ignore background noise from wind, for example, or distant traffic. Turn the potentiometer on each one until the gain is the maximum that is consistent with this – although the nearer 2 or 3 units could be set up with a lower gain. To see the LEDs flashing at a long distance, you want a day without sunshine, and ideally the demonstration should be done at dusk or in the dark.
There are different ways of setting out the microphone-LEDs. The simplest geometry is side view: aiming the LEDs back to a viewing point well away from the long line of them (see below). With the explosion or sound pulse set up at one end, you will see the wave progressing across if you stand at the viewpoint. If your viewpoint is, say 100m from a 150m line there will be a little compression of the angles between the LEDs at the two ends, but nothing too serious – the wave will show a linear progression along the LEDs. However, the wave will progress at 150 degrees per second across the observer’s point of view.
A better geometry in some ways is to view the LEDs close to along the line of LEDs, watching the wave progress away from a sound pulse, aiming each LED sideways towards the viewpoint. For this near-axial viewpoint geometry a straight line is not the best. In order that the viewer will see the LEDs evenly spaced in angle the layout should be approximately a straight line, but with a slight parabolic curve.
Suppose the LEDs are spaced 17m apart and you wish them to be visually separated from each other by a small angle, 1.5 degrees. Below is a table which gives some values of deflection from straight line at different distances. With a little geometry you can figure out similar tables for different spacings.
You don’t need to measure all this out accurately. You can simply pace out the distance and place the poles by eye from the viewing point, shouting “left a bit” or “right a bit”. Once you have a layout, put your poles or bamboo canes into the ground and fit a microphone-LED circuit on the top of each one, pointing in the right direction. If all is well, you are now ready to See a Sound Wave !
For shorter distances in areas of low ambient noise a loud hand-clap or similar will work. However, the system really does work better with something louder. We tried a drum and an acetylene cannon. Acetylene cannons are a rather rare toy, but they can still be purchased (see Reference). They use the reaction of a measured charge of calcium carbide with water to produce acetylene gas, which explodes when mixed with air. Small gunpowder charges – firework ‘bangers’ – also work, although they are louder than needed.
Ultrabright LEDs show up nicely even in daylight on a cloudy day. At night, the LEDs are visible at huge distances, far more than the microphones will pick up a hand-clap !
The human eye has a time constant of around 50 milliseconds, which determines the time between frames of video, for example. For this reason, to see the travelling sound wave the microphone-LED units should be located about 17 meters or more apart.
What else could you do with the microphone-LED units ? Could you set them up to figure out from what direction sounds were coming from ? What sort of layout of microphones would you need to see sound waves from multiple directions ? There were projects in the early 20th century to do this kind of thing, because there was a strong military interest in knowing where noisy and dangerous things like guns and bomber aircraft are. To this day, some equipment based on sound waves is used to locate gunnery positions in war. And what about echoes ? You would have probably already seen the effect of echoes from buildings on the system, unless you were lucky enough to have tried it out in the middle of a very large field. If you can identify a place with just one single building with a large flat face on one side, miles from any other buildings, then you might be able to study the echoes nicely: the beginning of a kind of acoustic radar !
The author would like to thank Stuart Williams of Air Products & the Overton Scout Group, Overton, Hampshire for ‘field-testing’ the prototype microphone-LED units – in a very large field.
A longer write-up of this project appeared in Neil A Downie, Seeing sound waves, Physics Education, volume 48, Number 2 (2013)
The Conestoga Company of Pennsylvania can supply Big Bang Cannon – an acetylene cannon. See www.bigbangcannons.com
At first glance, you might think that the Cranky Crawler would not go anywhere. As the crank wheel goes round and round, you might expect it to just push it’s two wooden ‘feet’ apart, then pull them together again, going exactly nowhere !
First take a look at the video clip. https://youtu.be/sMaCIH-EkOg
The Cranky Crawler works because of geometry, forces, and friction. Of these, geometry and forces can be figured out exactly, and are used everywhere in science and engineering. The laws of friction, however, are more rarely used. Although enormously important in engineering, they are inexact laws which seem often to be relatively neglected.
What you need
- electric motor with reduction gearbox, eg. by 50 or 100:1 (eg. 30-60rpm)
- batteries, battery box, wires, switch
- crank / wheel push fit onto motor shaft
- conrod, bracket for second foot, eg. Meccano/Erector strip
- wood for ‘feet’ and for motor support on first foot
- sundry hot-melt glue etc
What you do
The geometry of the Cranky Crawler is important, as we see in the analysis section below.
It is possible to build a Crawler with 3 segments instead of 2, but still using the same crank geometry and friction effects.
The Three Segment Crawler can push out the front segment at low angle, while simultaneously pulling in the rear segment at high angle, then, as the crank turns, doing the opposite. Take a look at the video clip: https://youtu.be/5CV-zDFIY4A
Again, correct weighting is needed. Can the Three Segment Crawler go backwards with the wrong weighting ?
How the Cranky Crawler works:
The secret lies in the angle of the pushrod. When the rod is at the top of the wheel, the rod is pushing down at a steep angle, increasing the downforce Fn on the trailing segment at the same time as pushing forwards with force Fp. When the rod is at the bottom of the wheel, the pushrod is pulling horizontally, with virtually zero downforce. Now the Laws of Friction say that the maximum horizontal force Fp you can get on a block with downforce Fn is given by :
Fp = μ Fn
Curiously, this law of friction says that the area of the block does not matter, which is not quite true, but is a good approximation. The value of μ is roughly a constant, a little larger for a stationary block, ‘static’ friction. It is a little less for the case of block that is sliding, ‘dynamic’ friction. The vertical component of the force from the wheel Fw can be as much as ~ Fw.sinθ, to which must then be added the weight Mt.g of the trailing block. This gives a horizontal force of:
Fp = μ Fn = μ (Mt.g + Fw.sinθ)
This horizontal force must be sufficient to overcome the friction of the leading block Fa due to the weight Ma.g of the leading block less the vertical upward reaction
Fa = μ (Ma.g – Fw.sinθ)
You can see that it is important that the angle is large, θ, as this both increases the trailing block friction and decreases the leading block friction.
So far, however, we have only proved that the leading block can advance by pushing downwards and sidewards on the trailing block. Can the trailing block be slid forwards to ready itself for another push on the leading block ? Here we can take θ to be small, for simplicity, say zero: Then we can say that if μ.Ma.g > μ.Mt.g, or Ma > Mt the trailing block can be pulled back to the leading block without pulling it backwards. Suppose that Mg = 2m and Mt = m, so that the trailing block can go definitely forwards then we can look at the result of the for leading block going forwards. If Fp must be > Fa, then we have
μ (m.g + Fw.sinθ) > μ (2m.g – Fw.sinθ) OR
Fw.sinθ > ½ mg
The maximum angle θ is tan’-1(2R/L), which is but a more reasonable view is to take the value sin-1(2R/L), 30 degrees. If we put 2R/L at 2, then this gives a maximum θ of . Let’s put θ at 30 degrees on the average, then sinθ = 0.5, so if Fw > mg forward progress can happen. But will the leading block flip up ? Its weight is 2mg, and it has an upward reaction equal to the downforce of Fw. sinθ, which is 0.5 x mg, which is much less than its weight 2mg. Phew ! Here is a plot of how the push distance varies with the angle of the motor wheel (can you do the geometry of this ?):
Furthermore… So we can prove that the Cranky Crawler is expected to work. But can it be made to work better. If the trailing segment is weighted heavier, or, equivalently, the leading block is lighter, then maybe a longer forward progress move is possible. Look at extending the theory above, and then try this out on an actual Crawler.
More coming soon…
Ferrofluid Rail Vehicle or Ferrocraft
Ferrofluid hovercraft or Ferrocraft: taking friction out of physics
Hovercraft are rare in the world of vehicles. However, hovering is a mainstay of physics laboratories. Hovering minimizes friction and allows free movement, showing physical phenomena in a clearer form. Usually compressed air is supplied to a track via small holes, or a powerful fan is mounted on the vehicle. Two relatively new additions to materials science – ferrofluids and rare earth magnets – have enabled the birth of a new addition to the hovercraft family: the ferrofluid hovercraft. This is a kind of ferrofluid linear bearing or slider bearing with extraordinary low friction properties. A ferrofluid hovercraft demonstrates interesting physics of itself, but is also an enabling technology for demonstrating other physics. Here is a video of one we made… https://www.youtube.com/watch?v=8EsyKJVE8_E
Ferrofluids have been around while1, and are now readily available, although you can make your own, for example, by dissolving magnetic tape. A typical ferrofluid comprises nanoparticles of a ferromagnetic material, often an iron oxide like magnetite (Fe3O4) suspended in a runny oily liquid. The particles are so small that they are retained in suspension by Brownian motion.
This is not enough to make a ferrofluid, however, because the nanoparticles could clump together to form larger particles which would be big enough to settle under gravity or a magnetic field. So ferrofluids are stabilised by the addition of surfactants, molecules which have a hydrocarbon-like end and an ionic end like a –COOH (organic acid) group. The surfactant coats each nanoparticle with hydrocarbon ends sticking out and prevents them from clumping.
Ferrofluids are most commonly used to provide a low-friction seal for bearings, bearings which depend upon ordinary lubricants or ball-races. They have rarely been used for providing the bearing itself. This has been tried2, but engineering tests have related to bearings under high load, when friction coefficients are higher, and apparently the phenomenon has not been used in physics equipment. One book3 described the low friction bearings, but the authors didn’t give details because of the limited load pressures, only 1N/cm2, then available. It ignored the many applications that would work perfectly well with such load pressures. Here we describe a simple way to demonstrate and use the very low friction that ferrofluids confer.
What you need:
- 1 small bottle of Ferrofluid
- 4 neodymium magnets
- PVC or similar plastic track, eg. plastic channel, with sides and/or grooves/ridges
- long board of wood to mount track on
- double-sided adhesive tape
- wood/plastic parts for vehicle
- motor + propeller
- wires; battery box; switch
- sundry hot-melt glue etc
What you do: setting up a ferrofluid hovercraft
A ferrofluid hovercraft – which we might call a ferrocraft for short – has a set of 3 or more powerful Neodymium-Iron magnets attached, projecting out underneath it. The magnets are then coated in a ‘cushion’ of ferrofluid a couple of millimetres thick, and the vehicle placed on a smooth surface. Surprisingly, the vehicle doesn’t sit down hard on the magnets. Rather, the magnets continue to be covered in their cushion of ferrofluid, which largely resists squashing under the vehicle weight. It is as if the vehicle is sitting on soft rubber, but with an important difference: it is almost frictionless. The ferrocraft can slide effortlessly down the least slope or with a tiny applied force.
A ferrocraft is not completely frictionless: the ferrofluid has a finite viscosity, although this is low, only a few times that of water. The drag force seems to follow roughly the law of normal viscous liquids :
F = μ A v / t
where μ is the viscosity, v is the velocity, A is the area of the cushion of liquid and t the thickness. Thus if the support area A goes up (lower power magnets) the friction will go up, which explains why NdFe magnets are important, since allow a smaller area. And as the ferrofluid thickness goes down, the drag will also go up, which again points to using powerful magnets and also to ensuring sufficient ferrofluid.
The ferrocraft will tend to coat the surface supporting it, losing ferrofluid. If the ferrocraft is set up to run along a linear track then less ferrofluid is lost. We tried a plastic extrusion, intended for wiring, which had two wide flat-bottomed grooves to act as a guide for the vehicle. You can fix it on to a long length of flat wood with double-sided tape to make a rigid linear assembly. The vehicle has a magnet at each corner to match the track. A motor and propeller is mounted suitably on a small piece of wood or plastic. A battery box hooked up to the motor via a switch completes a simple vehicle to try. The fluid will stain clothes, so be careful when setting up.
Figure 1. A ferrofluid hovercraft with coated magnets on base with track above
Effective coefficient of friction and other investigations
With the system working, you can now measure its properties. The static coefficient of friction (‘stiction’) and the dynamic coefficient of friction can be estimated.
With no solid-to-solid contact, the static coefficient should be zero, and in practice we did find it difficult to show any stiction. A ferrocraft will slip down a slope of less than 0.1 degree or so, albeit at a snail’s pace. This demonstrates static friction <0.002, which is stunningly low, lower than skates on ice.
The effective dynamic coefficient of friction can also be measured using an inclined track, but in this case measuring acceleration. This is a challenge. The ferrocraft is nearly frictionless at low speeds. And measurement of the ferrocraft’s dynamic friction at high speeds is difficult too. The effective friction at high speed increases due to the effect of ferrofluid viscosity. Neglecting air drag, the vehicle will tend to a ‘terminal velocity’ at which the dynamic friction equals the component of the vehicle’s weight down the slope. If you have light gates and timers, set them up to measure the acceleration of the ferrocraft.
Figure 2. A ferrofluid hovercraft on track
Using the Ferrocraft as an enabling technology
Once you have ferrofluid hovercraft system working well, you can use it for other investigations. The addition of a BBC Microbit or similar credit card computer would allow you to add data collection and control functions to the vehicle. The low friction of a ferrocraft would allow you to test the drag due to eddy currents in materials, for example. You could fit the ferrocraft with an additional magnet at the side, perhaps, with a track of the test material alongside. Copper sheet would provide strong eddy currents and high drag, while less conductive materials or thinner sheets or foils would give lower drag.
The effectiveness of low power propulsion systems is another example. Low thrust propulsion is of strong in interest in the space industry, where there is a lot of effort going into low thrust but highly efficient propulsion for changing orbits of satellites already in orbit. Low thrust effects with an electric motor with a propeller as above is one method: by using a single cell supply and a resistor or regulator to further reduce the current, electric motors can be tuned down to very low thrust values (although there is a point at which the motor simply doesn’t go around: we found that beyond about 20 or 30 Ohms resistor with a typical toy motor, this happens). Compressed air in a soda bottle emitted from a nozzle would be another method. Such studies can utilise the possibility of very low accelerations, as little as 10-3 ms-2 or 0.001g.
With two Ferrocraft, you could try collisions, perhaps trying materials like plain rubber or superelastics or pneumatic buffers. What about a Ferrocraft which goes around bends, or even in circles ? You probably need to bank curves in a track: what angle does the banking need to be: for low speeds, for high speeds ? Could you do get a Ferrocraft going fast enough to do a ‘Wall of Death’ with vertical walls ? Can you get more lift from the magnets by using Ne/-Fe magnets of large pole diameter or more powerful magnetization ? And what about Samarium-Cobalt magnets ?
- Anon., “Dispersions of ferromagnetic metals”, Patent GB974627, 1964 (California Research Corporation).
- Wei Huang. Cong Shen, Sijie Liao, Xiaolei Wang, “Study on the Ferrofluid Lubrication with an External Magnetic Field”, Tribol Lett (2011) 41:145–151, available on line by searching on the title.
- B. M. Berkovsky, V. F. Medvedev, and M. S. Krakov, Magnetic Fluids, Engineering Applications (Oxford University Press, Oxford, 1993)
Retroreflector Refractometer !
Coming Soon !
The Three Laws Cannon
The Three Laws Cannon might be thought of as a the ultimate solution to human warfare, offering the chance to attack both sides simultaneously by firing a projectile both forwards and backwards. In fact, however, human history being what it is, actually there was a kind of Three Laws Cannon which fired both ways – and it didn’t stop anybody fighting, quite the opposite. It was used to arm aircraft of several kinds with a very large (for an aircraft) cannon, avoiding the problem that a large cannon’s recoil might both wreck the lightweight airframe and stop the aircraft flying if fired in a forward direction. It didn’t work very well. But that doesn’t make it a bad physics demonstration… we had a lot of fun with the Physics World magazine team doing some science demonstrations, one of which was the Three Laws Cannon. Take a look at the video here… https://physicsworld.com/a/amazing-science-demo-two-newtons-three-laws-cannon/
First, just a reminder of Newton’s Three Laws:
- Any physical object continues in its state of rest or motion at constant speed in a straight line unless a force is impressed on it
- If a force F is impressed on the object mass M, then it will accelerate as a rate of a, where F = M a
- Any action has an equal and opposite reaction. If I push you with a force F, then you push back at me with force F.
These are all you need, of course, for doing a ton of physics, on anything from atoms to space rockets. The demonstration here deploys a compressed air cannon based on a soda bottle with a bursting disk, and fires, simultaneously, in opposite directions, two projectiles.
What you need
- Soda bottle
- drain pipe
- wide ‘Sellotape’, the thinnest type of clear or brown parcel self-adhesive tape
- car tyre or bike tyre air pump
- car tyre filler valve
- 2 projectiles: eg. lightweight wood (‘deal’ or pine, or even balsa) or champagne corks with clay weighted nose, or even just well-calibrated cylinders of carrot
- 2 large cardboard boxes with large cushions, or stuffed loosely with cushion fibre
- long hat-pin, or length of thin (<1mm) piano wire with sharpened tip
- clamp stand (‘retort stand’)
What you do
Join two lengths of plumbing tubes with a T-piece in the middle.
drill a small hole in the T-piece so that a pin going through the hole can pierce the tape at the end of the soda bottle. Mount a car-tyre valve (the are check-valves) into the base of the soda bottle. The easiest way to do this is to drill a small hole, then a larger hole, then a larger one again until it is just a little smaller than the diameter of the tyre valve at the point it normally fits into the wheel. Measure the size of the hole in a wheel if you want to make certain of the hole size. With the large sizes of drill, you can try doing it ‘backwards’, mounting the drill in a bench vice and rotating the bottle (wear gloves). Then make a large hole in the bottle’s screw cap and stick a piece of tape over the top of the open bottle, before screwing the cap back on. The neck of the bottle also needs a small adaptation: a ring of the drain pipe so that the bottle fits the side-arm of the tee, and seals. Cut a short length of drain pipe, cut it one place, and then snap the resultant nearly closed ‘C’ shape onto the bottle just below the cap.
You can then pump air into the bottle to build up pressure inside it, the weak point in the pressure vessel being the tape. (This prevents an accident through over-pressurizing the bottle, although this is unlikely anyway, as the bottle cap will tend to leak as the pressure rises much above 10 bar.
Pressurize the soda bottle until it reaches a pressure of 4–5 bar. Then plug the bottle into the T-piece, fixing it into position with tape. Next, use a retort stand and clamp to hold the two pipes, T-piece and bottle in place. Finally, place your two projectiles in the opposite ends of the pipe before pushing each of them right down to the T-piece with a stick. Now don your safety goggles, pierce the tape with the long hat-pin or length of piano wire – and KaBOOM !
With luck, the two projectiles will simultaneously whizz out and blast into the cushioned cardboard boxes, but the cannon itself will not move much. If you repeat the experiment with only a single projectile and the other end of the pipe blocked, the cannon and stand will recoil backwards.
The Math and the Analysis
The air in the soda bottle will follow the Ideal Gas equation:
P V = n R T
At constant temperature, this reduces to PV = constant, or P = constant/V , which is Boyle’s Law. A compressed gas in a vessel is a store of energy. You can easily estimate how much energy if you integrate Boyle’s Law. Assume that you start from pressure / volume Pi / Vi and end up at Po Vo, then
Energy E = Pi Vi loge(Pi/Po)
When the pin punctures the tape, the tape will tend to shatter into fragments, since it is under severe stress, and high speed crack growth is the rule – the minimum size of hole for which this is true – the critical crack length – depends upon stress.
Once compressed air is released, it flows into the tee-piece and pushes the two projectiles in opposite directions. Some of the energy is lost because air expands rapidly and the expansion is not isothermal, but is closer to adiabatic, in which the air temperature falls, and less energy is available to accelerate the projectiles. With equal projectiles, equal lengths and diameter of barrel, the whole system is symmetrical, so you expect the two projectiles to have the same amount of energy (half of that stored less the adiabatic losses) and the same momentum. So with projectiles of mass m, the maximum speed V leaving the barrel must be less than Vmax, where 2 (1/2 m Vmax^2 ) = Ead, where Ead, the energy stored reduced but adiabatic effects is itself < Pi Vi loge(Pi/Po)
Vmax < sqrt (Ead/m) where Ead < Pi Vi loge(Pi/Po).
What more can you do ? Can you measure the speed of the two projectiles ?
Can you make the system with two projectiles of uneven mass ? What happens to the recoil then ? What happens to the speed of each projectile – how much energy does each get ? Momentum must be balanced, it must the same for each projectile, or does it ? Don’t forget that the faster projectile will leave the barrel first and stop accelerating – but does the expanding compressed air stop pushing the second one at the same time ? And what happens if you combine two projectiles of different mass with a barrel of different length, or even different diameter.
References Neil A Downie, Exploding Disk Cannons and Slimemobiles
L V Kurchevskij DRP / APK Recoilless Cannon for Aircraft (1930s) inI V. B. Shavrov The History of Aircraft Construction in the USSR
Take a drum, add a pipe, blow into the pipe and beat the drum. What happens? The BBC Television series Local Heroes had a challenge for viewers to demonstrate an entirely new musical instrument. Adam Hart-Davies, the presenter, and his colleagues found a dozen or two contestants or little teams of contestants with novel devices. The challenge was to play the melody Twinkle Twinkle Little Star on this entirely new instrument. Once contestant was Mark Williams, who came up with the Heliracket, a kind of bagpipes with two bags – one of air, the other of helium – and a mixer tap. I have worked with Mark, and know just how hard it must have been for a superb musician, which he is, to play such a terrible instrument ! There were others broadcast to the waiting world, however, which made an even worse sound, including one which I played on the broadcast with my daughters Helen and Becky: the Pneumatic Drum…
References: Neil A Downie, Ink Sandwiches, Electric Worms.