Mathematicians Explain Tape's Tendency to Tear If you've ever peeled a strip of tape off a roll with your fingers, you know that it doesn't usually come off the way you really want it to. A strip may start out nice and even, but eventually it narrows into a useless triangular strip. This phenomenon may seem trivial, but not to some curious mathematicians.

## Mathematicians Explain Tape's Tendency to Tear

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Mathematicians Explain Tape's Tendency to Tear

# < Mathematicians Explain Tape's Tendency to Tear

## Mathematicians Explain Tape's Tendency to Tear

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RENEE MONTAGNE, host:

And here now a story about something that's holding together a little too well. If you've ever peeled a strip of Scotch tape off a roll with your fingers, you know it doesn't usually come off the way you really want it to. A strip may start nice and even, but eventually it narrows into a pretty useless pointy-ended triangle. Hardly a trivial matter - at least to me. I don't know about you, Steve, but definitely to me - nor to some curious mathematicians. NPR's Christopher Joyce tells us what they found out.

CHRISTOPHER JOYCE: Pedro Reis is from Portugal, and he traveled a lot before joining the faculty at the Massachusetts Institute of Technology in Cambridge. He knows a lot about unpeeling rolls of packing tape.

Dr. PEDRO REIS (Faculty Member, Massachusetts Institute of Technology): One of the nightmare situations that I'm starting to dread more and more is each time I have to move. Okay? So it is that sound of the Scotch tape unpeeling from the roll, right?

JOYCE: Reis relives this nightmare by giving a little demonstration in the studio. He works some tape up with his fingernail.

(Soundbite of Scotch tape tearing)

JOYCE: The strip starts peeling okay, but soon, a tear - or, as he calls it, a crack tip - starts on one edge. As he pulls, the tear creeps inward, and the strip of tape narrows.

Dr. REIS: I'm having a little trouble here myself, unpeeling a little bit with my nail. Exactly what we studied is happening now. I can't get the full piece.

(Soundbite of laughter)

JOYCE: Perhaps it's not a nightmare, but annoying.

Dr. REIS: So now I ended up with a nice, triangular, useless piece of Scotch tape on my finger, and I have to start over again.

(Soundbite of laughter)

JOYCE: Now if you've peeled a grape or a tomato or removed wallpaper or tried to get that darned sticky tape off the edge of a new CD, you know about this peeling problem. It just won't come off in nice, even strips. But now an MIT mathematician can tell you why.

Dr. REIS: Sin theta is equal to the square root of B tau over 2 eta gamma.

JOYCE: Yes, you heard it right. Sin theta is equal to the square root of B tau over eta gamma. What that equation means is that three things determine when and how the tape will tear: how tough the tape is to bend, how firmly it's stuck onto an object, and how much energy it takes to rip it.

Reis says knowing this actually could help engineers test thin films for strength and reliability. As for the rest of us, he saysâ€¦

Dr. REIS: Go slow. That's my advice.

JOYCE: And if you want to double-check that equation, you can find it in this week's issue of the journal, Nature Materials.

(Soundbite of Scotch tape tearing)

JOYCE: Christopher Joyce, NPR News.

Dr. REIS: And I managed to get - oh, no. Okay, I'm sorry about this. I'm making a mess. (unintelligible)