SpillNot: The Physics Behind Slosh

SpillNot: The Physics Behind Slosh
by James Lincoln, MS, MEd
[email protected]
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!
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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
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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
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)
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g) Compute the velocity using the formula vcircle = 2πR/t or, more accurately, 2πRhoriz /
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
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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.
Product # P4-2500
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