# Interesting Activity with a Paper

I request you all to perform this activity now (it will take less than a minute)-

1)Take a rectangular piece of paper.
2)Make two holes of the size or your fore-finger in it - equidistant from the edges (refer the figure attached.
3)Insert the fore-fingers of your two hands in the holes.

Now try to tear the paper along both the lines shown within one jerk.

I'm sure none of you will be able to tear both the sides together - no matter how many times you try.
Explain me what could be reason behind it.

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Are you kidding us, or you really don't understand why this happens?

If this is really true the reason is likely:

One hole/side will ALWAYS be slightly weaker than the other and will start to tear first. It immediately becomes much weaker and the other side will be subject to insufficient force to make it tear at all.

I'm not kidding offcourse, just seeking a possible explanation for the observation.
One hole will be slightly weaker than the other? Weak in what sense?

DarioC's answer can be expanded as "material and geometric imperfections", the same reasons for buckling of thin objects under compression. I would add the thought though that tearing of paper happens when it is either in tension or in shear, and your finger holes don't enable either of those actions to be accomplished, do they?

Paper is made of fibers from wood. Any two areas on a given sheet of paper will never be exactly alike and one will will always be less strong than the other. That is the edge of one hole will have a weaker tensile (stretch) strength than the other. Never a perfect match. One will tear first.

You could do this with aluminium sheet, or steel, or fiberglass and get the same result. Not with your fingers though. LOL Chuckle.

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Paper is made of fibers from wood. Any two areas on a given sheet of paper will never be exactly alike and one will will always be less strong than the other. That is the edge of one hole will have a weaker tensile (stretch) strength than the other. Never a perfect match. One will tear first.
I don't think that will be a strong reason. Those imperfections are of microscopic level and they might not play a big role in variation of tensile strength. In other words, the tensile strength of the paper (of good quality) can be taken as uniform. If you tear a big sheet of paper from different sides, you don't have do apply different amount of forces to tear it.

Even if I agree to your point for the sake of argument, why only one edge tears and the other not even a millimeter?

I would add the thought though that tearing of paper happens when it is either in tension or in shear, and your finger holes don't enable either of those actions to be accomplished, do they?
If they don't enable either of them to be accomplished, you can't tear the paper (no tension according to you). But one side is always torn.

Try this. Sheet of paper. Make a very small (short) tear in one edge and then tear it more, pulling from the ends of the sheet, noticing the resistance. Now pull on the ends of a sheet of paper that does not have any tear at all started on the edge.

You can do this in your mind and even then you will realize what the difference is going to be. Once even a small tear begins that point becomes MUCH weaker. So the tear strength of the other hole is never exceeded. One hole tears through.

Now if you want to attribute this to some mysterious unknown force that has no connection to the strength of materials, I guess that is your privilege too, but I sure hope you don't become an airplane designer.

So the tear strength of the other hole is never exceeded. One hole tears through.
I realised that my last reply to you was wrong. Timing is important. If you time the movement of your two fingers correctly, one edge gets torn for sure - the other tears by some amount.

I agree with you that once any part tears, its tensile strength decreases and it continues to tear. Consequently the other edge has greater tensile strength.
This happens because one of the fingers starts tearing the edge before the other. If we time our movement of fingers such that they both start at the same time ( not even pico seconds interval ) then I guess both the parts will be torn. But it is impossible to achieve without the use of machines. Do you think the use of a machine can tear the paper from both sides within one go? But then again there might be some forces operating. Not sure.

If your motion is quick enough that each finger is pulling against the inertia of the paper instead of pulling against the force created by the other finger then I'm pretty sure both holes would tear.

If your motion is quick enough that each finger is pulling against the inertia of the paper instead of pulling against the force created by the other finger then I'm pretty sure both holes would tear.
Did you try it?

IF you moved quickly enough you could use one finger and tear the paper. More realistically a spring loaded finger substitute could do it.

I don't think timing actually makes a difference. I think the weak side will tear first even if you hold one finger still. It would be difficult to prove as the variation in angle, contact, and who knows what else, might have significant effects.

You have piqued my curiosity now. I may try it tomorrow.

DC

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russ_watters
Mentor
Even if I agree to your point for the sake of argument, why only one edge tears and the other not even a millimeter?
Because structural failure is all or nothing. Once something starts to fail, it loses strength rapidly and the difference in strength between one side and the other suddely gets very large.

russ_watters
Mentor
If your motion is quick enough that each finger is pulling against the inertia of the paper instead of pulling against the force created by the other finger then I'm pretty sure both holes would tear.
True, but it would have to be extremely fast - much faster than a human is capable of.

Not sure if you've ever done target shooting with a BB gun, but even a bb at a few hundred fps will not necessarily always punch a nice neat, clean hole.

Danger
Gold Member
even a bb at a few hundred fps will not necessarily always punch a nice neat, clean hole.
Hell, my .44 magnum wouldn't do that. There is, in fact, a special sort of ammunition for just that purpose, to make things easier for target shooters. They're called "wadcutters". Claiming a touch of artistic license, I'll say that the slugs look quite a bit like itty-bitty oil drums. Their specific purpose is to make nice clean round holes in paper.

There is, in fact, a special sort of ammunition for just that purpose, to make things easier for target shooters. They're called "wadcutters".
I agree with you, got this image on google-
Mickey Mouse with a wadcutter lol.

Danger
Gold Member
I'm afraid that I'll have to Google that for myself, Abdul. Your picture shows up on my MacBook as just a small square with a question mark in it. Hang on a sec...

Okay... got it. I was expecting to see some sort of cartoon with Mickey using wadcutters, as opposed to the photo of Mickey "drawn" with wadcutters. Anyhow, I assume that the accompanying description adequately explains the ammo.

edit: I just checked back to page one, and your photo now shows up just fine. Was that just a time-delay thing, or did you modify your link?

edit: I just checked back to page one, and your photo now shows up just fine. Was that just a time-delay thing, or did you modify your link?
Haha no...I didn't modify anything. May be it required some time to load.

Danger
Gold Member
Haha no...I didn't modify anything. May be it required some time to load.
Hmmm... in that case, I should perhaps revisit some porn sites that I thought were dead-ends...