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There is this video about a tape peeling trick trending on the internet.

If you have a tape sticking on a paper, it rips off the paper if you perpendicularly pull on the tape. But when you stretch the tape before doing so (and if the tape is elastic), it peels off nicely. I tried it, and it really works. You can also get the same effect by pulling and raising one end of the tape while tightly holding the rest of it.

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I wonder why this works. How does stretching the tape prevent the paper from tearing off?

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The paper is stronger in the direction parallel to the plane of the paper than in the direction perpendicular to the plane. (It seems plausible to me that the fibers of the paper are for the most part aligned with the plane of the paper.)

When you pull perpendicular the force of the tape's adhesive is sronger than the cohesion force of the paper, and the paper delaminates.

When you stretch the tape the force that the tape's adhesive exerts is a shearing force. We infer from the demonstration in the video: the forces of cohesion of the paper are way stronger in the direction in the plane of the paper. The paper holds together; the stretching ruptures the tape's adhesive.

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First, let's consider how those interesting longitudinal wrinkles arise:

Mahadevan's group showed, in "Wrinkling of an elastic sheet under tension," Nature (2002), and "Geometry and physics of wrinkling," PRL (2003), that the wrinkles arise from the inability of the film to undergo Poisson contraction at its ends, near the rigid supports (in the tape video, the hands). This constraint produces a stress state that shears the film into wrinkles with predicted wavelength $\lambda=(tL)^{1/2}\varepsilon^{-1/4}$, where $t$ is the thickness, $L$ is the length, and $\varepsilon$ is the applied axial strain.

Let's now consider the difference between peeling the film before and after implementing this wrinkled state. It appears that the level of tape-paper adhesion needs to be intermediate for the trick to be effective; if the adhesion is low, then peeling is effective, whereas if the adhesion is high, then the paper would be pulled off by the out-of-plane wrinkling deformation.

We appear to have a state where (1) some parts of the paper stochastically stick strongly to the tape and (2) the paper cohesion is similar to the paper-box adhesion, so that pulling at a small point can expand to a triangle of ripped and delaminated paper. In addition, (3) shearing the interface detaches the tape effectively.

Thus, if we pull the adhered tape from one direction (left image below), small attached areas expand into a big ugly rip, whereas if we selective delaminate strips through the buckling method (right image below), any small attached areas are localized, the detachment at the connected, sheared regions is clean, and the damage doesn't propagate:

I would expect this trick to fail if the adhesion is strong enough that shearing becomes ineffective in separating the interfaces cleanly.

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I was a bit late to post my answer and seems like @Cleonis has already posted one along the same lines as mine. FWIW, I will post this as a summary then.

You are essentially asking why the tape tears off the paper when pulled vertically but not when pulled horizontally.

Let's view this from the viewpoint of a molecule of paper. When you pull on the tape, you apply a force to the paper molecule. Whether the paper tears or not depends on how strong your pull is and how hard the molecule holds on to the surrounding molecules. In a planar sheet of paper, there are many more molecules holding on to you along the plane of the paper than above or below it.

Consequently, a force perpendicular to the plane of paper can rip it off easier than one parallel to it.

So, in short, when you pull on the tape vertically, the glue on the tape rips off the paper as there is nothing much holding the paper back. When you pull it horizontally, the tape stretches out and tries to take the paper along with it. But since the paper has strong structural linkage in this direction, it refuses to go with the tape. As a result, the glue, which is sandwiched in between the tape and paper, has no other option than to let go of one of the surfaces (the one with lower adhesion). This results in the tape neatly detaching from the paper surface.

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