1. A study of the load-bearing ability of folded paper By Susan Wang A21
Introduction
Load-bearing ability means the mass a substance can hold before it breaks.
It is a common sense that folds the paper with different ways will greatly influence its load-bearing
ability. We also know that a paper with a sawtooth styled folding will have the greatest load-bearing
ability.
However, a question came up in my mind, ‘what is the relationship between the number of time a
paper is folded and its load-bearing ability?’
I folded pieces of paper different times and measure their load-bearing ability respectively by put 1-
yuan coins on the paper. It was beyond my expectations that the number of coins the pieces of paper
could bear seemed to have little with the number of times it was folded.
Therefore, another question came up, ‘does there exist a relationship between the area of the paper
and its load-bearing ability?’
I then folded each piece of paper for eight times but controlled the load-bearing area. In the
experiment, I found the number of coins the paper could hold was increased when the area of paper
decreased. I discovered that there should be an inverse proportional relationship between the load-
bearing ability and area of the paper, though I could not deduce the accurate mathematical
relationship.
Concept
Load-bearing ability means the weight of mass a substance can hold before it breaks.
The experiments
Experiment 1: investigate the relationship between the number of time a paper is folded and its load-
bearing ability.
Equipments: 1-yuan coins, paper, books, blocks
Variables
Independent: the number of times a paper is folded
Dependant: the mass it can hold
Constants: height of books, mass of a coin, type of paper
Procedure
1. Set up the equipments as shown in the diagram. Stack up the books into two piles. Ensure the
height of both piles of books is the same.
2. Fold the paper for 5 times. Put it over the two piles of books. Use two blocks to ensure the area
2. of the paper keeps unchanged during the whole experiment.
3. Put 1-yuan coins one by one onto the folded paper until the paper breaks.
4. Count the number of coins put.
5. Repeat step 2-4 with different number of times the paper is folded until a set of data is gained.
Experiment 2: investigate the relationship between the area of the paper and its load-bearing ability
Equipments: 1-yuan coins, paper, books, ruler, blocks
Variables
Independent: area of the paper
Dependent: the mass it can hold
Constants: height of books, mass of a coin, type of paper, number of times the paper is folded
Procedure
1. Set up the equipments as shown in the diagram. Stack up the books into two piles. Ensure the
height of both piles of books is the same.
2. Fold each piece of paper for 8 times. Use the ruler to measure the width of the gap between the
two blocks for 15 centimetres, ensure the width keeps unchanged during this experiment. Put
the piece of folded paper between the blocks over the two piles of books.
3. Put 1-yuan coins one by one onto the folded paper until the paper breaks.
4. Count the number of coins put.
5. Repeat step 2-4 with different width of gap until a set of data is gained.
Summary of results
No. of times the paper is folded No. of coins the paper can hold
5 24
6 54
8 50
10 50
12 52
16 56
Width of the gap between blocks (cm) No. of coins the paper can hold
10 37
12 34
14 29
15 27
Discussion of the results
3. relationship between the number of time a paper
is folded and its load-bearing ability
60
No. of coins the
paper can hold
50
40
30
20
10
0
0 5 10 15 20
No. of times the paper is folded
Fig.1
relationship between the area of the paper and
its load-bearing ability
40
No. of coins the
paper can hold
30
20
10
0
0 5 10 15 20
width of gap between two blocks
Fig.2
From Fig.1 we could find out that except the paper was folded by 5 times, the number of coins a
paper could hold was roughly unchanged when the paper was folded by different times. The main
reason for this is because that when the paper was folded by 5 times, only two rows of coins could
be put on the paper whereas in other situations three rows of coins could be put on it. Therefore,
when the same number of coins was put on the paper, the piece of paper folded by 5 times held more
mass in average than other pieces of paper.
In Fig.2, the number of coins a piece of paper could hold followed roughly inversely proportional to
the width of the gap between two blocks. The reason for the fact that number of coins held in the
4. second experiment was much less than that in the first experiment was that instead of put the coins
evenly on the paper in the first experiment, in the second experiment, I put the coins on the same
point to make the paper easier to break so that data could be gathered quicker.
Discussion of errors and suggestions
Errors in the number of coins could be hold by a piece of paper
1. Using 1-yuan coins is reasonable though it worried me a bit before the experiment that whether
a single piece of paper could hold such a heavy weight. However, it leads to a major problem
that the weight of load then becomes discrete and one could not gather a specific value of result.
This problem could be negligible when the required accuracy of the experiment was not high
because the difference between mass of n coins and (n+1) coins was a small value compared to
the mass of the total coins. In fact, one single 1-yuan coin weighs 3.8 grams. The greatest error
according to this reason in the two experiments was 1/25 = 4% - it is acceptable.
2. The number of coins a piece of paper could hold depended greatly on the way how the coins
were put on it. In the discussion before, we have already known that the main reason for the
number of coins a 5-times folded paper held was much less than other pieces of paper was the
different rows of coins could be put on the pieces of paper. In order to reduce this error, I tried
to put coins in the same way and order in every experiment in Expt.1 and Expt.2.
3. The number of coins a piece of paper could hold differed when the same experiment was
repeated. This problem was observed during the experiment that the more times the same
experiment was done, the larger the number of coins a piece of paper could hold. It might
depend on the fact that I got more familiar with the experiment after times of trials. To avoid
this error, all the data I used came from the first time I did the experiment, instead of the usual
way, using an average of data gathered from repeating the experiment for several times.
Other errors and suggestions for the experiments
1. Choose a table with large smooth working area. It is because when the paper breaks, coins are
easy to drop on the ground and roll around the room, it would make the work of counting the
number of coins difficult when some coins was lost and it would certainly make errors in data.
2. Instead of choosing some types of strong paper so that a large enough number of coins could be
held, I found that the pieces of paper seemed to be too strong that I nearly ran out of coins. I
suggest to use some thin paper or even not to fold the paper to diminish the load-bearing ability
of the pieces of paper into a more acceptable range.
Conclusion
From the data we gained, one could surprisingly conclude that load-bearing ability of a piece of
paper seems to have little relationship with the number of times it is folded. However, there is a
relationship between the area of a piece of paper and its load-bearing ability that I have found from
the experiment. That is, the load-bearing ability is inversely proportional to the area of the piece of
paper.
