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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.

*Spilling happens when acceleration is perpendicular to the normal*

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: James@PhysicsVideos.net**