# Atomic Physics with Sticky Tape

## Atomic Tape Physics 101 – Atomic Physics with Sticky Tape

In addition to making a toy model to show the tipping-point behavior of charged pieces of sticky tape, I spent some time on Tuesday trying to do something quantitative with this. Of course, Tuesday is the one day of the week that I don’t teach, and I didn’t want to go to campus to do the experiment, so I put it together from the incredibly sophisticated materials I had available at home: Lego bricks and a tape measure belonging to SteelyKid and The Pip.

Having built this high-tech rig, I set up my new video camera on the tripod, and shot some videos of the key phenomena. First, there’s the attraction between two tapes with opposite charges:

In this, you can see the tipping point thing I mentioned– as I push them closer together, there’s an extremely narrow range where the electrostatic attraction pulls the tapes together by a perceptible amount without them flying up and sticking to each other. Once I managed to find that range, I used it to demonstrate the effect that set this whole thing off, namely that when you stick another object in between the tapes, the net electrostatic force on each increases.

I wanted video of this because I used it as a discussion question when talking about the polarization of matter in response to electric fields. The seemingly intuitive answer is to say that the force should decrease because it’s partially “blocked” in some sense, but that’s not how electromagnetism works. The electric field from a charge is not directly impeded by any intervening matter– the net field can change because of new sources of fields, but the original charge still contributes exactly the same field and thus force.

So why the change? Because you can think of neutral matter as being made up of atoms with an electron cloud outside a positive nucleus. In an electric field, these polarize, and become little dipoles aligned with the local field. If the tap on the left is positively charged, the electrons in a piece of paper stuck between the tapes will shift a little to the left. When they do that, the paper is no longer perfectly inert from the perspective of the tapes, but produces its own field.

The effect of that field is to attract both of the tapes. The electrons have shifted left by a tiny amount, exerting an attractive force on the positive tape on the left, while the positive nuclei don’t move at all, and end up a bit more to the right, where they exert an attractive force on the negative tape on the right.

My original hope with this was to see if there is a measurable difference between an insulator like paper and a conductor like aluminum foil. Unfortunately, as you can see, both of them just increase the attractive force to the point where the tapes cross the tipping point, and get sucked onto the paper or foil. There isn’t much difference between them.

The same effect, though, happens between charged and neutral tapes, so I repeated this with one charged tape and one neutral:

The tape on the left has a charge on it, which makes it attracted to my hand, while the tape on the right is uncharged, and not attracted to my hand. When I bring the two tapes close together, though, you get the same tipping point effect– they twitch a little, then get sucked together. The distance involved is much smaller, though– cranking these into Tracker Video, I estimated about a factor of 4 difference (roughly 3cm between the support points for only one charged, and about 12cm for both charged). So, what can we get from that?

Well, the equations giving the forces are pretty straightforward. In the case where both tapes are charged, we just have a Coulomb’s Law sort of thing:

$F_{both} = \frac{1}{4 \pi \epsilon_0} \frac{q^2}{r^2}$

(where I’ve assumed that the two tapes have the same magnitude of charge, q but opposite signs– this is a pretty good assumption, as the charging process involves quickly separating a neutral pair of tapes, so whatever charge one picks up had to come from the other). If only one tape is charged, the force comes from the polarization of the neutral tape, which is generally expressed in terms of a “polarizability,” which gets the symbol $\alpha$, because physicists are lazy and don’t want to go any farther into the Greek alphabet than they have to. The force between a charge and a polarizable object is something we derive in class, and is given by the formula:

$F_{one} = (\frac{1}{4 \pi \epsilon_0})^2 2 \alpha \frac{q^2}{r^5}$

This depends on the fifth power of r, so it’s a much shorter range force than the case where both tapes are charged– if you double the distance, the force between charged tapes drops by a factor of 4, but the force between one charged and one neutral tape drops by a factor of 32. So the qualitative behavior in the videos above is exactly right.

Can we get something quantitative out of this, though? Well, if we make some simplifying assumptions, sure. And this is physics– we’re all about simplifying assumptions…

The main assumptions to make are 1) that the charges involved have the same magnitude in both cases, and 2) that the force at the “tipping point” is the same in both cases. I think these are both fairly reasonable– the charging process is the same in both cases, so the q should be pretty similar, and the range of the effect is small enough that I think it’s not completely ridiculous to say that the force needed to start the tape moving by enough to get tipping point behavior is the same in both cases.

If we do that, then we can just set the two forces above equal to each other, with two different values of r:

$\frac{1}{4 \pi \epsilon_0} \frac{q^2}{r_{both}^2} = (\frac{1}{4 \pi \epsilon_0})^2 2 \alpha \frac{q^2}{r_{one}^5}$

The q is the same on both sides, so we don’t need to worry about those. which means the only thing in this that we haven’t measured is $\alpha$, the polarizability of the tape. So, we can solve for that, and get:

$\alpha = \frac{1}{2} 4 \pi \epsilon_0 \frac{r_{one}^5}{r_{both}^2}$

Using the fact that the tipping point for the case where both tapes were charged was about 12cm and the tipping point for the case with only one charged was 3cm, we get a value of:

$\alpha = 9.4 \times 10^{-17}$ C-m/(N/C)

Which, um, yeah. That’s a number all right. Is it a reasonable number? Well…

We’re saved, though, by the fact that the textbook makes several references to the polarizability of a single carbon atom, which is about $\alpha = 2 \times 10^{-40}$ C-m/(N/C). That might actually seem disastrously wrong– we’re 20-odd orders of magnitude off– but that’s the value for a single atom. A piece of tape is made up of quite a few atoms, and that would scale the effective polarizability of the tape up by roughly that number.

So, how many atoms in a piece of tape? I didn’t measure these specifically, lacking a milligram scale in Chateau Steelypips, but as part of the lab we did last week, the students measured the tapes they were using, and a fairly typical mass is something like 300 milligrams. If I assume the entire thing is carbon atoms, that would be around $1.5 \times 10^{22}$ atoms, each with a polarizability of $\alpha = 6.4 \times 10^{-39}$ C-m/(N/C).

“You’re still wrong by a factor of 32,” you say. And that’s true. But, dude, look at how many crude assumptions went into this measurement– you only need five factor-of-two errors to account for a factor of 32, and I’ve got at least three assumptions (the identical charge in the two different experiments, the identical force at the tipping point, and the mass-to-number-of-atoms process) that aren’t any better than that. I’d say this does remarkably well.

So, it turns out you can measure fundamental atomic properties using Duplo blocks and sticky tape. I think that’s pretty awesome. If you don’t, why are you reading this blog, anyway?

ORIGINAL SOURCE FOR THIS AWESOME ATOMIC TAPE ARTICLE:  http://scienceblogs.com/principles/2014/01/17/atomic-physics-with-sticky-tape/

Thanks to Chad for keeping science AND tape cool!

# Atomic Yellow Tape

## Atomic Tape by Duck brand Duck Tape!

This Atomic Yellow Tape is part of Henkel’s new X-Factor series of high performance tapes.  With a thicker poly layer and more agressive adhesion, this atomic yellow tape will make repairs fast and stick on longer.   Strength is also superior with a thicker cloth and more fibers per square inch.  This new atomic tape yellow duck tape tears easy by hand for easy use.  And, unlike silicone tapes which only stick to itself, this new Atomic Yellow Tape sticks to anything in traditional “Duck” quality and strength.

Atomic Tape Duck Tape is a professional-grade tape that features excellent adhesion to a wide variety of surfaces like cloth, leather, plastic, vinyl,  all metals, and laminates.

5.0 out of 5 stars best and cheapest duct tape out there June 14, 2013

Tape Review By Alvin Ray:

Amazon Verified Purchase

This is the cheapest and most durable duct tape in the market. I’ve tried other cheaper brands but they are not as durable. I use this to wrap big heavy boxes and packages. Aside from being durable, it’s also water-repellent.   And it comes in a variety of colors for different uses and purposes.

Buy Atomic Tape Yellow Tape now on Amazon.com:

Size:  1.88″ Wide x 20 Yards
Color:  Atomic Yellow
Brand:  Duck Tape

Not the kind of atomic tape you were looking for?  If you are looking for a silicone tape try here: http://www.atomictape.com/silicone-tape.htm

Here at Atomic Tape . com we love to show you all the cool things you can do with tape.   Uniquely colored tapes such as the Atomic Yellow Duct Tape allow you to be very creative with your tape applications.  Check out this video of how to make an Atomic Yellow Duct Tape Wallet:

# Atomic Design Sells TAPE!

Atomic Design sells TAPE!  At Atomic Tape .com you can find all sorts of info about tape.  Atomic Designs does a whole lot more than sell tape but in case you are looking for gaffer tape here’s what they have to say about it:

“Gaffer’s tape is used for the temporary mounting of lighting fixtures and reflectors; for the moisture and dust-proof sealing of equipment cases and film containers; for bundling and positioning of floor cables; and floor marks for actor’s positioning. Gaff tape is an economical, high strength vinyl impregnated cloth tape with a matte finish, available in a host of colors. It has a high performance adhesive system and is highly conformable to irregular surfaces. Pro-Gaff is waterproof, tear and abrasion resistant, and has a smooth, controlled unwind, and is hand tearable. It is one of the most popular tapes on any stage. ” Silicone Tape is also popular amongst gaffers and stage electricians, and is useful for many on set repairs.

They also sell a bunch of other varieties of tape for all your taping and repairing needs. Check out their cool “About Us” video here:

Atomic Design

# Atomic Tape X-Rays from Scotch Tape

## Atomic Tape – Scientists say standard Scotch Tape can produce atomic X-Rays!

Here is one of the coolest articles on Atomic Tape . com!  One of the joys of physics, and science in general, is that even seemingly mundane objects occasionally yield physical surprises.  A great example of this made the news about a month ago: the observation that, under the right circumstances, x-rays can be generated by the peeling of Scotch tape!  The phenomenon is an extreme example of the phenomenon of triboluminescence, and I thought I would take a closer look at the research results, which appeared in Nature.

First, a quick but important notice:  THERE’S NO REASON TO WORRY ABOUT USING STICKY TAPE AT HOME!  As we will note below, the x-ray effect is only significant when tape is peeled in a high vacuum.  Such a condition obviously does not occur without special preparation.  So the wrapping of Christmas packages can continue without fear.

It’s worth taking a moment to explain why this seems like such a surprising result in the first place.   Interaction energies in normal chemical interactions tend to be no greater than 10′s of electron volts; for instance, it takes 13.6 eV to ionize a hydrogen atom.  If the reaction releases a photon, this puts the wavelength of the photon at best in the ultraviolet or visible range, with an energy several orders of magnitude lower than the keV or MeV of x-rays.  X-ray emission from atoms under normal circumstances comes only from nuclear processes, e.g. the decay of an atomic nucleus.  Chemical reactions seemingly don’t have enough ‘oomph!’ to generate x-rays.

At Atomic Tape .Com we try to bring you all the cool atomic tape stories on the net.  No, Atomic Tape .com didn’t write the article but the source is given here.  See the whole atomic tape story here on the original atomic news story . . .

ORIGINAL SOURCE:  http://skullsinthestars.com/2008/11/20/x-rays-from-scotch-tape/