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Mathematicians Explain Tape's Tendency to Tear

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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.

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.

"One of the nightmare situations that I start to dread more and more is each time I have to move, that sound of the Scotch tape unpeeling from the roll," he says.

He relives this nightmare by giving a little demonstration in a studio. He works some tape up with his fingernail. The strip starts peeling OK. 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.

"I'm having a little trouble here myself, unpeeling a little bit with my nail. You see exactly what we studied is happening now — I can't get the full piece," he says.

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

"I ended up with a nice, triangular, useless piece of Scotch tape on my finger, and I have to start over again."

If you've peeled a grape or a tomato, or removed wallpaper, or tried to get that 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. Now the mathematicians can tell you why: "Sin theta is equal to the square root of B tau over 2 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 says, "Go slow — that's my advice."

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



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