Anyone do Maths Modelling in College (if no you might still be able to help!)?

irish life

I haven't a clue where to put this topic. Believe me though, while it is under the heading of Maths it really hasn't a lot to do with maths so please give it a look. Its about how tying a knot in a rope will shorten it.... Bit obvious, I know.

I am doing a computer science degree and have a Maths modelling question to do for tomorrow. I only got the sheet today from someone in my course. Anyway, I don't really know what I'm supposed to do. I've asked a few people in college and they are stuck too (there isn't many in as all lectures are finished). I've typed up the sheet I was handed so I would really appreciate if anyone could take 2 minutes to read it and make any suggestion at all as to what you think I'm supposed to do.

Also, I was told it was only supposed to be a page or so long (more if needed of course).

What my sister thinks I do is put seperate headings for Diameter of rope, stiffness, etc. and explain how each makes the rope shorter. ie. The bigger the diameter, the shorter the rope will be with a knot.

Any suggestions welcome, please.

D

http://www.boards.ie/vbulletin/forumdisplay.php?f=380
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or here
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nesf

1) Do your own homework

2) This isn't mathematical modelling really. So posting it to the maths board won't help you, it is more of a physical model really. Actually, I object to the use of the word model in this question, since it isn't one. But I'll try to not be a pedant about it.

It's not a particularily tough question either, I'll give you a few tips you can solve the rest of it yourself, ok?

You have all the data you need on the particular ropes in question, this is good, now all you need is a formulae for each specific type to provide the "model".

Ok, now you have the dimensions of this particular not for each type of rope, and you know the shape of the "gap" in the knot if it is present.

We know the shape of the knot, and the size of the knot, and if we given three seperate catagories to divide the materials into (again really nice).

The easy way to solve this, and the least accurate by far, but to be blunt, I doubt you'll be expected to return anything actually accurate, innovative or complex (ie you're doing computer science, not applied maths or physics, so you shouldn't be expected to be capable of great feats of modelling prowess, the part that you need to be good with is implimenting the model in an efficient manner).

All you need do is, by using the shape of the knot, and the sizes you are given for each specific knot is to calculate the volume of the knot. From the volume you can calculate the mass of the knot, and from the mass calculate how much rope is in the knot, and from that the lenght difference.

The whole thing about gaps is that you need to factor in the gap space when calculating the volume for the knot.

I am not going to tell you how to calculate the volume of the knot, it's not difficult but I don't feel like doing your homework for you.

Now the EXTREMELY IMPORTANT PART!

These are your assumptions for the above model:

The ropes are all incompressible. IE when tied in the knot their density does not change (I'll get back to this)
The knots are the same for all ropes of the same type
There is no human error in tying the knots so they are identical


Now, for improving the model.

After working out the lenghts of rope used up by different materials, compare this table to a table of material stiffness. The results should be related. Linerally I think off the top of my head, but I could be wrong.

For soft ropes, the rope is obviously compressable. To accurately model this, you need to calculate, a) the pressure on the rope in the knot, b) the reaction of the rope in question to pressure, and c) how this pressure is absorbed by a lack of cross-sectional rigidity.

This is more complicated, but not by much. Again, I ain't going to solve it for you.

Hoep the above helps, (but not too much )