# Monthly Archives - April 2013

## SpillNot: The Physics Behind the Slosh

Although the problem of why coffee spills might seem trivial, it actually brings together a variety of fundamental scientific issues. These include fluid mechanics, the stability of fluid surfaces, and interactions between fluids and structures (we’ll set aside the biology of walking for now). The SpillNot is a cool tool for getting your students interested in the everyday physics behind why drinks spill while we’re carrying them and what has to happen to prevent spillage.

Why spilling happens: When the rigid cup is accelerated horizontally the low viscosity fluid remains at rest and is left behind to rise up on the cup’s wall. The greater the acceleration is compared to gravity, the more fluid is left behind such that the ratio ahoriz/g is the same as the slope. Later, when the person stops walking forward, the cup is decelerated but the fluid (now in motion) remains in motion toward the other end of the container. In some cases there is an amplifying resonance when the accelerations match the natural frequency of the fluid’s back and forth sloshing. Try it!

Why the SpillNot doesn’t spill: Instead of accelerating the cup sideways, the handy lever tilts the base of the apparatus so that the cup’s walls are always perpendicular to the fluid’s surface. The device tips when you accelerate it so that the largest force on the cup comes perpendicularly from the base. Now, even when though the fluid has been sloped compared to the horizontal, the cup has been, too! Simply put, the SpillNot prevents spilling by rotating the bottom of the cup so that the sloshing of the fluid never falls over the edge.

Simply put, the SpillNot rotates the bottom of the cup so that the sloshing of the fluid never falls over the edge. Most teachers are familiar with the demonstration of centripetal force that involves a cup or water in the bottom of a bucket is maintained in the bucket even when the bucket is spun in a vertical circle that goes overhead. This is not a difficult demonstration to do, but the SpillNot makes it more fun and students can safely try the experiment themselves. Of course I recommend practicing with clear water first versus using hot coffee. For the most part spilling is nearly impossible unless one goes out of his way to jounce the string. So long as there is tension in the string, spills generally will not happen.

The SpillNot is best for qualitative demonstrations of centripetal force. The idea that it can successfully take an object through a vertical circle so long as its acceleration exceeds the acceleration due to gravity is well demonstrated. But quantitative measurements are technically nuanced and not as convenient. The radius of the circle is often hard to measure and is different for every case of spin. Additionally, the normal force N on the object is not the same as the force acting on the strap. Therefore, one will have to account for the added mass of the apparatus itself if one wishes to measure the force directly; for example by using a spring scale hooked to the loop. Otherwise, one can indeed use the SpillNot to make direct verification of Centripetal Force as being mv2/r.

B A sample procedure for the horizontal circle.

a) Hold the apparatus (loaded with ½ filled cup) out horizontally at an arm’s length
b) Hook a spring scale into the loop of the SpillNot (this can be used to measure m, the mass of the device and cup, and then later to measure the Tension, T)
c) Spin with the device in hand with a sufficient velocity such that the device raises
d) Have a partner time five full cycles with a stop watch, determine t for one cycle
e) During the spin, note the average value of the force on the scale (T)
f) Measure the horizontal radius (if the velocity is sufficient then Rhoriz = R is nearly true, otherwise Rhoriz = R cos θ)
g) Compute the velocity using the formula vcircle = 2πR/t or, more accurately, 2πRhoriz / t
h) Compare T with mv2/R, determine the percent difference, account for experimental error. (One such error is the assumption that either R or T is horizontal or that the mass of the apparatus is all the way out at R, which it is not!) Diagnosing errors is an important skill in physics. Note, that the centripetal force is only caused by Thoriz = T cos θ.

Alternatively, one could use the tilt of the SpillNot to determine the force. This can be accomplished by perhaps taking a picture or still-frame of a person swinging the apparatus. Then, with a protractor, measure the angle at which the rope falls below the horizontal. One can then compare a and v2/R by using tan(Ɵ)=a/g

This lab does not have much to offer pedagogically beyond what a ball on a string can teach, however the device itself is the hook that gets kids interested. It is novel and exciting to be spinning a cup ominously out with the plane of the fluid nearly perpendicular to the floor!

Another lab idea that you might try is the small vertical circle demonstration. In this case the radius is much easier to measure because, for all practical purposes, it is simply the height of the SpillNot plus the small rope. Assuming the cup has a fairly low level, one can determine the minimum speed required to spin the device without spilling. It may be wise and more fun – to do this lab outside. The slowest speed possible will be noticed when, at the top, the cup looses contact with the base. The free body diagram at the top of the spin generates Fnet = mv2/r = N+mg (down or centripetal taken to be positive). The statement “losing contact” implies that there is normal force coming from the base. Thus setting N=0 results in g=v2/r. Measure vcircle = 2πR/t similar to step g in the horizontal circle lab. In this case however I would recommend frame by frame video analysis of a video in which the students spin the device progressively slow until the cup falls off. By counting frames, t can be determined (frame rates can vary from camera to camera). Be careful however, the velocity changes throughout the circle. It will reduce error to use only the top half of the circle. In that case, vsemicircle= πR/t. Post lab analysis might involve comparing g with v2/r and accounting for error; which is usually about 15%.

Despite that the SpillNot does not offer itself easily to quantitative laboratory work, you will be impressed by how easy it is to use. It is not a quantitative demonstration tool. On the contrary, its best use is to demonstrate that the study of physics can be used to solve practical problems in ordinary life. The bonus is that it makes the classic centripetal force demonstrations much easier to perform.

In conclusion, the SpillNot’s ability to demonstrate centripetal force is not unprecedented. Many teachers will already be aware of the demonstration of the “Greek Waiter’s Tray” or water in the bottom of a bucket (both vertical and horizontal circles), and of course loop-the-loop rollercoasters. What is unique about the SpillNot is that you don’t spill whereas spilling is quite common among these other demonstrations, especially when a novice handles the apparatus. A novice, however, can successfully handle the SpillNot. Of course there is always the possibility that students will try to push the limits of the apparatus; but this is not a bad thing! In fact, having students learn what it takes to spill is a good lesson in the scientific method.

James Lincoln

Tarbut V’ Torah High School
Irvine, CA, USA

James Lincoln teaches Physics in Southern California and has won several science video contests and worked on various projects in the past few years.  James has consulted on TV’s “The Big Bang Theory” and WebTV’s “This vs. That”  and  the UCLA Physics Video Project.

Contact: [email protected]

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## Top 10 Demonstrations with the Plasma Globe [W/Video]

The plasma ball is an engaging and safe tool for studying high voltages and the electric field and can be used in middle school, high school, and college level physics courses. A very large voltage is created by a Tesla coil-like circuit and this creates a high electric field between the central electrode and the inner glass. The Field is strong enough to ionize the gases in the ball (it pulls their electrons off) and the freed electrons undergo collisions which liberate more electrons from other gas molecules. This process is known as cascade/avalanche or impact ionization. On first inspection, you will notice that the plasma ball responds to your touch. This is due to the polarization of your body (a decent conductor). As you approach the plasma ball you become polarized by the electric field and this attracts more charge to you.

1. Demonstrate plasma

Most physical science classes require that students have a cursory understanding of plasma as the “fourth state of matter.” This title is misleading because plasma is the most common state of matter in the universe and plasma was in fact the first state to exist after the big bang. Plasma is a gas-like collection of atoms that have a large number of free electric charges.  This means that newly created plasma has undergone ionization (the phase transition that is after melting and boiling). When the freed electrons are regained by ionized atoms the bonding energy is often released as visible light; therefore glowing is a signature of most plasma. Like a gas, plasma has no fixed volume and like other fluids it does not have a fixed shape.

Moving plasmas can usually be controlled by magnetic fields, but this will not be visible on the plasma of a plasma ball. In order to witness deflections of plasma, he charges must move for long enough times. A plasma ball operates on a high-frequency alternative voltage, and for this reason, the charges do not have much time to move in demonstrably measurable distances and get deflected.

Plasma is also an excellent conductor so, once one filament forms, it becomes generally stable allowing for more current to flow through it (similar to a lightning strike). This is more obvious when you bring a finger to the plasma ball. It is important to remember that plasma is very hot and it will slowly conduct heat through the glass.

2. Touch lightning

The very high voltages of the plasma ball can easily polarize a coin (or piece of aluminum foil) placed on top of the plasma ball.  By bringing your finger only a few millimeters above the penny, you will be able to elicit a spark from the top of the coin. This spark will not cause pain, or electric shock, but will be hot and if you hold your finger their long enough it might begin to hurt. The tip of the finger will now show a few harmless burn marks that will rub off in a day. Let the students touch lightning too and use this sparking technique to explain how lightning forms due to the Electric Field ionizing the air. You can also have fun burning small pieces of paper with the spark.  If you are too shy to touch the spark with your hand, you can touch a metal key (or any conductor) to the coin and the spark will still form while providing additional insulation. You should avoid touching the spark with your fingernail. Fingernails conduct electricity better than the skin and underneath it is a tissue that is dense lined with pain nerves.

3. Demonstrate convection

The plasma threads are very hot and they will rise due to their buoyancy in the other gases inside the plasma ball. For this reason, it is difficult to get a horizontal streamer to remain unbroken for more than a second – not unlike a Jacob’s Ladder. However, a vertical streamer at the top will be stabilized by the buoyancy. With practice, you should be able to get just a single vertical thread. Once again, be cautious because the glass will heat up.

4. Investigate  the oscillating electric field

The Electric Field created by the Tesla coil reaches beyond the glass dome and into the air surrounding the plasma ball. This Electric Field can easily be investigated with a small neon bulb or light emitting diode (LED). Bring either of these near the plasma ball and they will light up when aligned radially, but not circumferentially. This demonstrates that the voltages are decreasing with radial distance or (equivalently) that the Electric Field is radial. You will also notice no directional dependence of the diode because the field is oscillating rapidly.

The LED bulb (far right) is not lit at this distance

The LED bulb glows brighter as it approaches the plasma globe

The circuit is providing a high-frequency alternating voltage which is necessary to “step up” the voltage to the levels needed to operate the plasma globe. Study the voltage directly by simply connecting a probe to one of the channels on an oscilloscope and you can probe the changing voltage spatially. Some experiments include determining how rapidly the voltage decreases with radial distance or whether the voltage differences are established radially or circumferentially (the answer is the former).

For fun or if you don’t own an oscilloscope, you can also use an audio cable as a probe and listen to the frequencies on an amplifier. These will sound louder up close and quieter far away or when probed circumferentially (along an equipotential line). The human body can serve as an excellent antenna for picking up the signal so be sure to touch the tip of the cable.

One last technique is to investigate the voltage differences directly by using a digital voltmeter set to read AC. Through this investigation, one can most easily verify the distance dependence of voltage as it decreases with radial distance.

5. Illuminate a fluorescent lamp

This demonstration is normally done with a Van de Graaff generator but often results in you getting mild shocks. However, there is no pain or danger if you simply use the plasma ball!  Borrow a long fluorescent tube from your overhead lights, or buy one from the hardware store and bring it near the plasma ball. You will notice that once a part of the mercury gas in the tube gets glowing that it can stay glowing even as you extend it. There is essentially no limit to how far you can pull the tube. It also works on the household small tubes.  Emphasize that the fluorescent tube holds ionized mercury (plasma) and that plasma is a conductor (because of the free charges) and for this reason, the tube’s light can be drawn with no apparent increase in resistance (no decrease in brightness).

Also, note that the starting point of the tube must be close to the plasma ball where the Electric Field is largest (the voltage is changing the most rapidly). This can be demonstrated by moving the tube closer then further radially to the globe. At certain distances, the tube will not glow. There is a minimum Electric Field required to ionize the mercury gas and if the field is not strong enough the tube will not light.

Explain also how the fluorescent light is produced: the low pressure, ionized mercury gas releases mostly UV and violet light when it regains its electrons. This light falls on the fluorescent paint that coats the inside of the tube.  The paint then glows white. The UV light is blocked by glass, so harmful UV light does not escape the glass tubes. Thus, the process does not work in reverse: if you shine UV light on the tube from the outside the paint won’t fluoresce.

6. Create a human short-circuit

While you have the fluorescent tubes out, demonstrate that the Electric Field can be diverted to a grounded, shorter circuit if a lab-partner grabs part of the tube. This will reinforce the idea of lightning and currents (perhaps later on) taking the path of least resistance. It will also awaken students to the reality that their bodies are paths through which electricity can flow. (A valuable lesson in electrical safety!)

Fluorescent tube lights at point of contact continues with no obstruction

Touching the fluorescent tube diverts the current

7. Analyze the spectrum of the gases within globe

When it comes to analyzing the spectrum of the gases in your plasma ball, a good place to start is to analyze the point where your finger touches. Looking straight at the plasma globe, place a finger as far to one side as possible. This should create what looks like a vertical (pink?) stripe. Analyze this with your diffraction grating and compare the spectrum to known inert (noble) gases. Since there is often more than one gas, this can be difficult but is worth the effort.

To analyze the (bluish white) streamer filaments, it is helpful to create the vertical streamer from experiment #3. This vertical column will be ideal for analyzing its spectrum. It is best to have a partner supply a free hand and beware once again of the plasma heating up the glass. This may also be a good time to break out the digital spectrometer or other spectrum-analyzing equipment to get specific wavelengths measured. Different plasma globes use different gases and in different amounts, but they are almost always noble gases.

8. Hold ionized gases in the palm of your hand

Neon gas tube near plasma globe

Ionizing gases and observing their spectra is normally associated with dangerous, high-voltage equipment that only instructors can handle. But now you can put ionized neon tubes in the hands of eager students because your plasma ball ionizes them safely. No longer is a black box needed to confuse students as to what is happening. The plasma ball’s strong Electric Field rips the electrons off their atoms and unique colors are produced as electrons are reacquired by the various orbitals. Teaching about the emission spectrum of ionized gases can now become a hands-on activity.

9. Power up your cathode ray tube

A plasma ball provides a safe source of high-voltage that can allow you to investigate the properties of cathode rays safely. A typical concern with doing cathode ray tube experiments is that you have to connect your CRT to a dangerous high-voltage source. Teacher and student alike can now safely and easily demonstrate the magnetic deflection of electrons and relive the discoveries of J.J. Thomson thanks to their marvelous plasma globe.

10. Demonstrate an absorption spectrum

A plasma globe provides a rare chance for you to demonstrate that light is absorbed by ionized gases.  Send a beam of collimated, white light into the plasma housing and you will be able to observe the absorption spectrum. Collimated light is produced by sending a bright beam through two holes on either side of a box; this guarantees that the light that emerges is a narrow column. Note that projectors that mix RGB will not suffice as a white light source – the light has to be a full rainbow.  The best source is a bright incandescent flashlight or an overhead projector.  Focus the beam so it passes through the plasma, then separate it with a diffraction grating or prism and project the rainbow on a screen or wall.  When the plasma globe is off, the white light will split into a full rainbow.  When the globe is on, some of the colors will be missing as thin bands. Most notably will be the yellow and reds observed in the emission spectrum from earlier. This will verify that emission and absorption spectra have the same wavelengths.

conclusion:

In conclusion, the plasma globe is an under-utilized and relatively familiar piece of lab equipment. I strongly recommend that every physics teacher include one in his or her laboratory and use them to make electrostatics as hands-on as possible.

James Lincoln

Tarbut V’ Torah High School
Irvine, CA, USA

James Lincoln teaches Physics in Southern California and has won several science video contests and worked on various projects in the past few years.  James has consulted on TV’s “The Big Bang Theory” and WebTV’s “This vs. That”  and the UCLA Physics Video Project.

Contact: [email protected]

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## 1 KM = 1 MI?

Somebody at the Department of Transportation doesn’t understand that a kilometer and a mile are NOT the same!

Hmmmmm…