We only address linear media in introductory physics classes, and really only focus on infinite or semi-infinite sine-wave-like disturbances. In the real world waves have a finite duration; this type of wave is often called a wave packet. If the wave is large enough, it can be affected by the nonlinear properties of the medium. The most dramatic example of this is the soliton, a disturbance that propagates with no loss in speed, size or shape over large distances.
Though first observed more than 150 years ago, solitons weren’t understood until the last few decades and are still actively investigated in mathematics, physics and engineering. This site gives an overview of current research as well as a historical account of the first description of a soliton on a canal in England.
Chemical engineers at the University of Minnesota filled a swimming pool with guar gum (which should be familiar to anyone who reads food labels) to answer the age-old question “Can you swim faster in goop than in water?”
High Reynolds number hydrodynamics (roughly speaking, the study of large, fast things in water, where Re>1) is considerably more complex than low Reynolds number hydrodynamics (roughly speaking, the study of small, slow things in goop, where Re<1). Since a swimming human operates in the complicated high Reynolds number regime (at Re ~ 4.5 × 106), there had been controversy about whether people would swim more or less quickly in viscous goop.
Short answer: it makes no difference whatsoever. But lest you feel disappointed, this research did earn Cussler and Gettelfinger one of the highest-profile prizes in the natural sciences: an Ig Nobel! Unfortunately, their goop only increased the swimming pool’s viscosity by a factor of two, which means that all else being equal (and, in fact, all else was equal because their test subjects swam at exactly the same speed as in water) the Reynolds number was only 2× smaller in the goop. This is still very far from the simple yet weird physics that occurs at small Reynolds numbers.
The Great Molasses Disaster. Caused by deregulation of the molasses industry, no doubt.
Cautionary note: this experiment is sometimes incorrectly compared to swimming in molasses. This is a dangerously bad analogy. You can swim in a swimming pool filled with guar gum goop, but you cannot swim in molasses. In fact, molasses are very dangerous.
This is an ad hoc list of physics-violating devices that have achieved sufficient prominence to make it onto the web. Many have associated comment streams where you can read paranoid posts about sinister energy or oil cabals (OK – the oil cabal actually exists and even has its own web site) suppressing inventions that would free the world from the tyranny of energy scarcity. In fact, the DARPA site for Breakthrough Propulsion Physics even includes a Cautionary Note:
“On a topic this visionary and whose implications are profound, there is a risk of encountering, premature conclusions in the literature, driven by overzealous enthusiasts as well as pedantic pessimists … Avoid works with broad-sweeping and unsubstantiated claims, either supportive or dismissive.”
Wikipedia has a short historical introduction to perpetual motion devices. I have included only a few examples here, mostly just for fun.
An ancient unworkable machine. Since this predates the theory of conservation of energy, it's understandable.
Eric Krieg has an extensive list of perpetual motion machines, but seems to have abandoned his compilation around 2003 after some hundred entries. Krieg seems to conclude that most of these devices’ “inventors” were nothing more than scam artists trying to bilk investors out of their money. Luckily, my students understand conservation of energy and won’t be so easily parted from their lucre. On a personal note: I had hoped the inventors were merely optimistic, or perhaps insane; apparently I’m naive.
Frustration with the whack-a-mole quality of these schemes is not new. As far back as 1775, the French Academy of Sciences proclaimed that it would no longer consider any purported perpetual motion devices, because
“This sort of research . . . has ruined more than one family, and in many cases mechanics who might have rendered great services have consumed their fortune, their time, and their genius on it.”
Back then, perpetual motion machines were all mechanical, like the folding wheel (see figure). Nowadays most – but not all – perpetual motion machines are electric or magnetic.
Please note that perpetual motion is possible, if you eliminate friction (for mechanical systems) or resistance (for electrical systems). We know of exotic materials that are (under appropriate conditions) superfluids or superconductors: these will sustain flow or current forever with no loss. However, these systems still do not produce any excess energy, and any energy extracted from them directly diminishes the amount remaining.
Energy for nothing
This person should know better.
Interestingly, proponents of these devices split into two camps: those who admit that they violate the known laws of physics, and those who claim to use only standard physical principles. The former seem to revel in rebutting conventional science, while the latter portray themselves as clever engineers who merely exploit obscure loopholes in “normal” science.
A clearing house for schemes that promise to produce more energy than they consume. These are apparently called over unity devices. Also weirder stuff that seems to veer toward UFOlogy.
Orbo: some kind of rotary mechanical / electromagnetic device. Proof that a nicely designed website doesn’t make something true. I’d like to give Steorn (the company responsible for this device) credit for submitting the Orbo for review by a nonpartisan jury, but a few months after jury concluded that the device “[has] not shown the production of energy“, Steorn claimed to have “resolved the key technical problems” and plans to market the Orbo in the near future.
Motionless Electrical Generator. Some kind of zero-point energy device (extracting energy from the vacuum). Proof that acceptance by the U.S. Patent Office doesn’t make something true. Bonus: the same guy who invented the MEG can also cure cancer.
Cold fusion: the claim that catalysts can cause deuterium fusion at normal temperatures and pressures. This is a completely different category of unconventional energy generation, since there is no fundamental physics reason why cold fusion cannot exist. Fusion certainly happens in the Sun and in the lab (in tokamaks), though at very high temperatures and pressures, and it certainly liberates large amounts of energy. Fusion may well also occur at STP, but under normal conditions the rate of cold fusion is negligibly small, and it’s hard to see why a catalyst or electric current would increase that rate. Most physicists would love cold fusion to be real; unfortunately, it appears that it’s not.
Hydrino power. Blacklight Power claims to have discovered a state of molecular hydrogen that has a lower ground state than the one we learn about in physics or chemistry: the hydrino. They have a simple, highly exothermic chemical reaction that produces hyrinos. This doesn’t violate any laws of thermodynamics – if the hydrino exists, it would be possible to build reactors that produce lots of cheap energy – but the hydrino is not an allowed solution to the laws of quantum mechanics as they are currently understood. Blacklight Power has a rebuttal for that, of course. Bonus: the company is located just down the road from my hometown of Princeton, NJ.
Too-simple ways to increase your car’s mpg:
Magnetic treatment of gasoline. Not a perpetual motion device, but claims to improve fuel efficiency (and reduce carbon buildup and improve cooling system performance). Apparently magnetism is so mysterious that people are willing to believe it can do just about anything.
Plug-in mileage enhancer. Insert in cigarette lighter and it increases fuel efficiency up to 30 percent, increases torque, and reduces emissions. Bonus: improves car audio quality, too!
Momentum for nothing
Don't ask me how this is supposed to work.
DARPA’s now-defunct “Breakthrough Propulsion Physics” Program reads like something out of The X-Files. DARPA’s official technical site is rather heavy; the layperson’s summary is more accessible but light on the science; Wikipedia does a pretty good synopsis. Bear in mind that DARPA attempts a lot of really weird stuff that never pans out so the fact that it launched a program like this should not be taken as U.S. government endorsement of any of the physics therein.
The Dean Drive looks like it falls under the DARPA category of “Oscillation Thrusters” characterized as “Non-Viable“.
EM-drive. Radiation pressure within a closed, tapered cavity supposedly causes the cavity to accelerate.
Though the initial press release reasonably touted this as a way to get power to street lights in remote, off-grid locations, the idea was seized on by people with no comprehension of energy conservation as a “free” way to generate power.
The “best” proposal combines not only capturing the passing cars’ energy in pneumatic storage tanks but also powering the cars themselves with air pressure. The logical next step is to eliminate the cars altogether and build a perpetual motion machine.
Note that there are some legitimate situations where you could produce net energy this way – basically, you can extract a bit of a car’s kinetic energy just before the car was going to brake anyway. Even if you did come out ahead in purely energy terms, though, it’s pretty unlikely that replacing the output of large, efficient, highly regulated power plants by that of poorly maintained, gasoline-burning internal combustion engines will benefit the environment.
A tsunami is an unusually large wave triggered by a major force (usually an earthquake) applied to the ocean. In the open ocean a tsunami does not have a particularly large amplitude, but its wavelength is enormous. As it approaches land, the amplitude of a tsunami can increase dramatically, leading to catastrophic flooding.
Several sites, some more media-rich than others, present conclusion about the physics of tsunamis. The origin of tsunamis is well understood (though, because most are caused by earthquakes, impossible to predict). Any short, sharp excitation of sufficient size can cause a tsunami; as in many wave-bearing media, the specific details of the excitation are not as important as its total size.
My reconstruction of the major practical difficulties in tsunami warning is
Since the tsunami has a small amplitude in the open ocean, it is difficult to detect before it nears shore, and
Whether a small amplitude open-ocean tsunami turns into a large amplitude wave near shore (called “shoaling”) depends critically on the details of the shoreline and the direction of approach of the wave. During the time between the triggering of a wave and its arrival on land, there is often not enough information to precisely calculate the threat to populated areas and then to communicate an appropriate warning. After the fact it is possible to reconstruct the path of the wave, but this is small consolation to the survivors.
Since the funnel drops towards the center, the potential energy of a coin rolling on the surface decreases; since energy is conserved, kinetic energy must increase and the coin speeds up. This happens in planetary orbits as well, and – assuming the coin funnel shape is similar to the gravitational potential, i.e., proportional to 1/r2 – the coin funnel is a good representation of this part of celestial mechanics.
In Newton’s law of gravitation, the force of gravity is purely central and therefore produces no torque, so angular momentum is conserved. This is not the case for the coin funnel, since frictional forces between coin and funnel do produce a torque on the coin; in fact, if you measure the angular momentum of a coin in one of the funnel videos above, you will find that it increases with time. This is a clear violation of conservation of angular momentum and is dramatically different from planetary motion. It’s not a huge effect but it is definitely measurable. I don’t see any way to fix this without making the funnel frictionless.
An artist's depiction of the Mars Orbiter actually orbiting Mars.
You’re probably calculating everything in MKS units (meters, kilograms and seconds) and I could probably guess what units you are using, but if you neglect to actually write down the units explicitly then
You’re giving up a chance to catch algebra errors, and
This could happen to you, causing international embarrassment.
We often need to consume energy at a different time or place from where the energy is generated. We therefore store energy in the interim. My subjective ranking from least to most interesting modes of energy storage is:
Batteries. When (or if) most people think of energy storage, they think of batteries. Batteries store energy chemically; this energy can be converted into electricity pretty efficiently, and then into mechanical energy moderately efficiently. The drive to smaller computing devices and to electric cars has produced an explosion in battery research.
Biomass and petroleum. Fusion in the sun produces lots of energy; a small fraction of that energy arrives at the Earth as sunlight and by plants to grow. We can liberate that energy by burning the plants, but this usually requires large volumes of material: think of the huge stack of firewood outside a house that’s heated with a wood-burning stove. Over very long times, some buried plant material is converted into petroleum. Petroleum is more energy dense than wood, is easier to transport (since it is a liquid), and is “free” (since it represents energy harvested from sunlight in the distant past, it doesn’t require any acreage be set aside today). Petroleum used to be abundant, but the most accessible sources have already been depleted; the first oil well in the U.S. was in Titusville, PA, at a depth of 69 feet (!) and Pennsylvania dominated worldwide oil production for the next 40 years; the giant refinery complexes in northern New Jersey are a legacy of those early days of when the mid-Atlantic states dominated oil production. Other combustible liquids, such as ethanol, share some of the advantages of petroleum.
Hydrogen. Molecular hydrogen can be combusted or used to generate electricity in fuel cells. If technical and safety hurdles can be overcome, it could function as a relatively high-energy-density, clean, transportable form of stored energy. Despite its proponents’ careless rhetoric, hydrogen is not a source of energy: since there are no preexisting pools of molecular hydrogen, we have to make the stuff, which requires more energy as input than is present in the product.
Gravitational potential energy. Flowing water can become a source of energy. As it runs downhill, the gravitational potential energy of water is turned into kinetic energy, which can be harvested by a turbine. Historically, mills and factories were situated next to streams and millwheels provided energy for everything from grinding grain to turning lathes (except in Holland, which everyone knows is flat: since the Dutch don’t have fast-moving streams they had to use windmills). Nowadays we don’t rely on natural streams for energy: we build dams to store potential energy in artificial lakes, and extract the energy by draining the lake through a turbine in the base of the dam. During the night, when they have spare generating capacity, the British pump water into an old quarry at the top of Electric Mountain in Wales; during peak demand (for instance, at halftime on soccer game day, when everyone turns on the electric kettle to make tea), they release the water and recover its energy through a turbine as electricity.
Mechanical energy. The kinetic energy of a rotating flywheel can be used as storage. On a small scale, flywheels are used as reservoirs to accumulate bursts of energy and release the energy slowly. A spinning wheel contains a large flywheel what is pumped intermittently by a foot pedal; in a car, combustion in the cylinders spins a flywheel which then delivers it to the transmission; some versions of regenerative braking systems (typically used on buses) shunt translational kinetic energy (of the bus) into rotational kinetic energy (of a flywheel). On a larger scale, I once worked in the Princeton Plasma Physics Laboratory, which uses giant flywheels to store energy to be used to initiate fusion reactions. Drawing the necessary power directly off the grid would brown out central New Jersey, so instead they gradually spin up a pair of enormous flywheels over several hours, and then harvest the entire accumulated energy within minutes. The rim of each flywheel weighs 600 tons, and at full charge the outer edge spins at 329 mph, producing a centripetal acceleration of 800 g.
Obviously, most people study hydrodynamics for its many practical benefits in everyday life, viz., understanding shear-thinning colloidal fluids allows one to escape quicksand.
I particularly recommend this literature to students majoring in physics. Should one of you die a slow, agonizing quicksand-induced death, you would have only yourself (or, more precisely, your ignorance of the rheology of saturated granular beds) to blame. This would be particularly embarassing for the dual geology / physics major, who is not unlikely to encounter such perilous situations during field work.
Everyone knows it’s hard to push a heavy object on a rough surface. Most of the resistance comes from friction, a force between object and surface that resists motion (for kinetic friction) or attempted motion (for static friction). The standard model describing the amount of friction posits that
fk = ?kN (for kinetic friction), and
fs ? ?sN (for static friction)
where N is the normal force between object and surface and ?k,s are unitless constants that depend on the surface / object interaction. This site has a nice introduction to friction, including a section focusing on the coefficient of friction between car tires and road. I suggest you read it now, since you won’t have much time later while you’re skidding across a rain- or ice-slick road. In particular – just to pick an example – while you’re driving back to Amherst from South Hadley over the Notch on a wet day when the temperature is just above freezing in the lower parts of the Valley.
Although different tires behave differently, typical static coefficients of friction vary dramatically with road conditions (see table). For normal tires, the maximum braking force drops by almost a factor of 2 in rain, by another factor of 2 on snow, and by yet another factor of 2 on ice. Note that the stopping distance is inversely proportional to braking force; check your constant acceleration formulas to see why.
There is a whole discipline devoted to deducing vehicle speeds from skidmark length, primarily for use in court cases; this requires knowledge of the kinetic coefficient of friction for a skidding tire. If you are unlucky enough to be in a rollover accident, apparently the police may drag your car around on its roof to measure the kinetic coefficient of friction between roof and road.
We only address linear media in introductory physics classes, and really only focus on infinite or semi-infinite sine-wave-like disturbances. In the real world waves have a finite duration; this type of wave is often called a wave packet. If the wave is large enough, it can be affected by the nonlinear properties of the medium. The most dramatic example of this is the soliton, a disturbance that propagates with no loss in speed, size or shape over large distances.
