Does Paper Bend in Space with a Constant Force Applied?

[pete worthington]

Questions arise in my high school physics class about all sorts of things. A current thought question had to do with a piece of paper in space and a constant force being supplied at its center, perhaps by an alien or astronauts finger tip. Would the outer edges of the paper bend from the center of contact in the opposite direction of motion. There are no air particles distributing a resistance force, however would the localized force push the paper along in space as a flat sheet or more like what we would experience on earth. By bringing in Newtons III Law it would appear that the paper will move along as a flat sheet since there is no resisting force, however, earthbound experience and logic makes it hard to believe that this would be true. For sake of discussion, let's assume that there are no forces due to solar winds or gravitation towards another object.

 

[morry]

I reckon the paper would still bend. Paper is not a rigid body, so if a force is applied it will still deform. After this though it will travel forever. Or at least until it hits something. :D

Interesting question though.

 

[ZapperZ]

Questions arise in my high school physics class about all sorts of things. A current thought question had to do with a piece of paper in space and a constant force being supplied at its center, perhaps by an alien or astronauts finger tip. Would the outer edges of the paper bend from the center of contact in the opposite direction of motion. There are no air particles distributing a resistance force, however would the localized force push the paper along in space as a flat sheet or more like what we would experience on earth. By bringing in Newtons III Law it would appear that the paper will move along as a flat sheet since there is no resisting force, however, earthbound experience and logic makes it hard to believe that this would be true. For sake of discussion, let's assume that there are no forces due to solar winds or gravitation towards another object.

The paper would still "bend" because of its mass and thus, inertia, distributed over the size of the paper.

Zz.

 

[Nereid]

Welcome to Physics Forums, pete worthington!

How about some variations? What if the paper were an extremely thin sheet of plastic, sort of gladwrap on anorexia? What if it were super-hardened steel? How about something like putty, or glass just below melting point? What if the 'finger tip' force were a feather, or a stream of tiny glass beads? or a beam of cold neutrons? or photons?? What if the 'finger' was very hot, and raised the point of contact to above the 'paper's' melting point (or otherwise cause the 'point' of contact to suffer a drastic drop in 'mechanical strength')?

And how much 'flapping' would the paper do? What would that flapping depend upon?

 

[whozum]

I'm thinking it will bend regardless because the deformation has to propagate through the material. You are immediately pushing a point, and that point will pull its paper-atom buddies with it, but that pull isn't instantaneous, so there will be a brief bend. Come to think of it, I think some oscillating will be taking place.

 

[govinda]

i think the bend will be very small on an atomic level for the same reasons that whoozum attributed but i doubt whether there will be ossilation if the force is constant . if the force is instantaneous then i guess there will be oscillation since elastic forces(?) caused the deformation of the bonds in the first place.

 

[jdavel]

Suppose the force you apply accelerates the paper at g (9.8m/s2). Then the paper will do pretty much what a sheet of paper does when you set it on a finger that's pointing up.

Not bad huh?

 

[whozum]

True, but I think the initial problem was an instantaneous force, rather than a continued force. If the force is instantaneous then I proposed that the deformation would lead to oscillations where the center and the edges oscillate to a small extent in displacement from the CM.

That was genius jdavel :)

 

[nishant]

to me it seems,it will bend upward due to inertia

 

[whozum]

For the edges to bend upwards (farther than the deformation of the center) they would need a force applied greater than the force of the finger on the center, how is that feasible?

 

[nishant]

no,u did not understand me,they'll appear to bend upwards as seen from the centre of the paper.

 

[whozum]

I still don't understand your perspective.

Say the paper lies on the xy plane. The instant the force is applied in the positive z direction, the center is lifted above the xy plane, while the force still needs to propagate through the medium to lift the rest of the paper. Once the center has lifted, the force begins propagate and travels like a shockwave through the rest of the paper, lifting it in what looks like a conic fashion. Once the wave reaches the edges, the entire page will be moving with constant velocity in the positive z direction.

However, given some loss in energy transfer through the paper, the edges will not accelerate at the same speed as the center, even after the tiny time delay (of propagation). The effects of this I am not sure.

 

[nishant]

what I have been saying is what u have been saying till
the wave reaches the edges

 

[whozum]

Until the wave reaches the edges, the edges are below the center, not above.

 

[nishant]

but in the starting,when the waves have just begun to travel,the edges are above

 

[whozum]

Can you do some explaining as to why the edges would be above. You say you are agreeing with my proposition but it looks like you are disagreeing with it. The edges can't be above because in the initial inertial frame where the paper was stationary and completely flat the force applied to the center displaces the center immediately and then travels to the rest of the paper. Saying the edges are above the center means that the force through the center got to the edges before the center (or were more powerful than the force at the center).

 

[pete worthington]

constant force is assumed. jdavel has a great thought analogy but what about atmospheric pressure. all those piled up molecules and dust particles pushing in on all areas/surfaces of the paper except where your finger tip touches? Isn't that point of contact creating an unequal force distribution on the paper?

 

[GOD__AM]

I think the paper would take on a wave shape, higher in the center (of where we touch it) and dropping off towards the edges. It would distort and be effected by the shape of the paper also;square, rectangular, round, etc. The wave size would be determined by how hard we push and for how far.

A question: how would the conditions in space effect the paper? I mean the extreme cold and lack of pressure specifically.

 

[strid]

i just read through this thread (breifly, so excuse me if I repeat something), and couldn't resit posting my opinion...

I believe that the paper will Not bend... argument are given that it has a distribution of mass, and that this will cause the paper to bend. But that isn't true at all, as mass itself doenst bend this, or is a force. It is with gravtitation (any acceleation) that makes the mass "get weight".

So, if a paper is in space, and there is actually no need to keep an alien finger or somethign to keep it up (whichever direction that is ), as there is no force exerting on it. But IF we now put a finger there, we are not "lifiting" but rather pushing it. See it as we have a block on a friction-free surface and it is at rest. It doesn't need any force or finger to remain at rest.

EDIT: didnt get expressed what i wanted to say :)... However, just thotght if a similar question. When Superman flies through space, should his hair "wirl" (dont know the english word really)... Like when you are driving a cab or motrobike, your har "wirls"

 

[Nereid]

OK, replace the paper with a whole lot of tiny balls of tungsten, each of which is welded to (say) six 'massless' springs (and no spring is a 'loose end'; each end is attached to a W ball).

You 'push' on one of the tiny W balls ... what happens?

 

[whozum]

The whole system will transfer the force.

Isn't that what's happening ot hte paper in the microscale?

For example take a sheet of dough and hold it up. Poke it at the center, it will most likely tear, however this is due to the local strength of the dough not being able to pull all the weigh of its 'neighbor-dough-cells' along iwth it, the body was trying to accelerate, the force wave was just too powerful.

 

[rygar]

if it's true that if you push at the center of a paper in space, the paper will bend, and continue on forever (or until it hits something)...

will it continue on forever in it's bent shape, or return back to it's rectangular shape? i would guess the former because i don't know what force would cause it to 'snap back into place'... but i don't know much of anything.

 

[Chi Meson]

Regular paper (writing paper) does have some "elasticity" to it, that is, uless you crease the paper there is a tendency to return to its original shape. I just tried this, you can too: hold a sheet of paper at one end, it will bend due to gravity. Now pull the bent-down portion further and let it go. The paper will rebound against gravity slightly. Take away gravity and it will probable return to a near-flat shape after a while.

Oh yeah, and I'm in the camp that says due to the inertia of the paper's edges and the non-rigid nature of paper, the edges will bend back as the alien pushes in the center. I'm still thinking aabout whether or not it will "flap." I'm thinking no.

 

[Cyrus]

To me it seems that the edges would fall back and stay back as long as the force is applied. (much like the example of holding up paper with your finger in a gravity field.) But once the force is relaxed, the paper will rebound. If you look at the paper where you push it locally, it will deform forward in the motion of the force slightly. Once you stop applying the force, it will rebound back, causing small waves to be transmitted towards the edges as it oscillates back and forth, (very minutely). It might be detectable by the time it reaches the edges though, so you could detect small vibrations at the very edge of the paper. Also, we assume that the force is applied to the center of mass of the paper. (Just a guess).

Take the holding the piece of paper one step further. Very carefully raise the piece of paper with that finger and then stop. You will have given it an acceleration and then a deceleration. You can see the edges of the paper flapping, well a better word would be oscillating very minutely. Can you neglect air resistance, since the speeds are low, and the area of the paper sees roughtly equal effects from the air all over its surface?

Heres an easier way of doing it i think. Hold the paper at its center of mass with one finger from the top and one from the bottom. Then you can give it a force up or down, which ever you choose, and not have to worry about the paper falling off your finger. Then you can easily see the edges osciallate very small amounts. When the force you applied suddenly stops.

 

[Nereid]

Suppose we take a pair of tiny W balls, connected by a massless spring.

We push, briefly - an impulsive force - on one W ball, along the line of the spring. What happens?

We push, briefly, perpendicular to the W ball-spring-W ball direction. What happens?

For the purposes of this thought experiment, to what extent are the bonds between the molecules in the paper different from massless springs? the molecules different from tiny W balls?

Let's assume that you conclude that there will be some 'flapping' (oscillation and/or rotation) of the two-balls+spring; what would cause the flapping to die out and eventually stop?

In what way is a sheet of (very thin) paper different from a system of tiny balls (with mass) connected via (massless) springs?

 

[pete worthington]

The flapping will die out due to the fibers of the paper resisting the bending moment. Fibers are not massless, they have inertia. Even if the tree fibers are cut up into little pieces the papers composition (like fiber or pulp board) will behave similarly.The inertia thread taking place on this forum is a good parallel for this one.

I'm still processing jdavels post about assuming the constant accel being 9.8 m/ss and comparing this to the papers shape on the tip of a vertical finger on earth. I'm having a difficult time letting go of air pressures effect. (This is important since most all of our observations undergo 14.7 psi). It should act equally on all surfaces of the paper. How about the area where the paper is touched, this is under the paper. Does this matter? Imagining air pressure without gravity is a real thought experiment. Any ideas here ?

The smaller a point the paper is contacted by will effect the bending in two ways 1) increase the bending due to a more localized force being applied therby creating a larder bending moment. 2) less of an area under the paper where 14.7 psi is acting thereby creating....

OK imagine that there is no gravity and just air pressure. The paper is supported by: 1) a thin string running horizontally,
2) by a 1 inch wide ruler on its side suspended horizontally in the air
3) a 1 inch wide vertical wall with the paper placed horizontally on top...like the
ruler but no air pressure acting underneath

...Compare the bending now ?

 

[Cyrus]

Here is a question I have. At first I was going to say that you can neglect the air pressure because it is essentially the same on the top and bottom, and thus cancels out. But I got a tank of water and put a sheet of paper in there and held it at its center of mass with my finger. And the paper did not bed. It stayed nice and flat when fully submerged. So it seems that the bouyancy effect must be an issue. Any thoughts?

 

[pete worthington]

Aha ! I perform a demo where I drop a book and a piece of paper side by side then drop the paper and the book together with the paper directly on top of the book. I use a paper with the same cross sectional area. This is a great demo to illustrate drag force and what it would be like to drop something on the moon or some other planet with no atmosphere (realizing thet gravity would be different)

As I was describing this paper in space problem to a group of students I brought out the vacuum pump and belljar and started to brainstorm about setting up a collision with paper in a vacuum ( all be it not a perfect one) Then one student suggested that we set up a experiment like the book and paper but put it in the vertical plane so that Earth's gravitational force does not contribute (considerably) to the bending of the paper. So, we have a 15cm by 30 cm piece of stiff foam-board with a strip of paper 2cm by 15cm thumbtacked to the foamboard at the center. We made a simple handle with paper and tape on the otherside so that we can slide one hand in and accelerate the board, being held in a vertical plane, horizontally. Guess what happens ? Try it out. This will serve as a great demo for physics class (H.S.)