Make a 8x11 piece of paper stand 1 meter?!?

Question

im taking physics and one of our tasks is to turn a blank piece of 8x11 paper into a FREE-STANDING tower, we can use 1 ft of masking tape!!! how is the best way to go about this?!

Answer 1

a meter is 1.1 yards (39.6 inches) I do believe. You need to cut the paper into 4 sheets of 2X11 inches each. Fold the sheets into 11Hx.5wx.5l inches. Any excess use for the base.

Answer 2

The physics you should be addressing here is how to make the flimsy sheet of paper support its own weight when somehow extended to a height of 1 meter.

The only way paper can be made strong is through folding it.  If you have looked at corrigated cardboard end on, you will have seen the interior cardboard looks like WWWWWW with dozens of folds per linear.  That's where the cardboard gets its strength...the folds.

So I'd start the project by experimenting with sheets of paper, by cutting them into snippets and folding them in various fashions.  You want to see just how much folding is needed for the paper to support itself as layers of folded paper are built up to reach the requisite 1 meter.  

From what I read in your specifications, experimenting with sheets of paper and with masking tape is allowable.  That results because you specify only that one sheet and one foot of tape can be used in actually building the tower.  You do not specify that other sheets and tape cannot be used to test design issues.

Self support is one constraint, the height of the tower is another, and the amount of paper you can use in the tower is the other.  At just over 36 inches in the 1 meter, you need N >= 36/h layers of paper with a folded height of h inches each.  h is the height from the fold apex to its base.  For example, if h = 1 inch, you'd need over 36 layers of folded paper...all from that one 8 X 11 sheet.

h = (L/2) cos(theta); where L is the length of a piece (snippet) of paper before it is folded to an angle omega = 2theta between the two sides of the fold.  For example, if you use a snippet of paper L = 4 in and fold it to have an interior angle qmega = 60 degree, the height of the fold would be h = 2*cos(30) = 1.732089372 inches.  In which case you'd need N >= 36/1.732 = 20.7 layers.  That's a lot of layers from one sheet of paper.  

Clearly, the snippets must be quite small in depth (D) if their length must be used for the h dimension.  The number n of snippets from an 8X11 = A square inch sheet of paper cannot exceed n <= A/(LD).  By example, that means, when N ~ 21 layers if each layer consisted of only 1 snippet, we'd need n = 21 = 88/(2D) snippets of D = 88/(42) ~ 1/2 inch depth if each one is 2 inches long.  That's clearly not feasible, paper that thin will not support much and, further, we can't build a tower of one snippet each layer.  But now you can see whet needs to be considered during your design phase.

Another  issue is the stabiliity of a 1 meter tower.  With that many layers, your tower would need a fairly wide base; otherwise, it would topple because the center of gravity would invariably fall outside the base line with just a slight lean.  That means your lower layers will need to be relatively wide spread...taking up even more paper.

A bit of masking tape, to hold the snippets together in each layer would help make the tower an integrated whole.  That will also add to the strength of the tower as the individual snippets would not collapse when held in place by the bit of tape.  But beware of using too much tape, it will add to the weight that must be supported by the paper.

If this project is doable, it is clear a lot of trade offs must be made.  You have the three major constraints that are at odds with each other: strength, height, and paper availability.  But, for testing feasibility, you can start by seeing just what kind of snippets (size and shape) and snippet folds are needed to support the 1 meter tower.

Lots of luck; sounds like a challenging project.