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Surface Area vs. Side Length: What controls object height?


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Purpose: In this experiment, Scientific AmeriKen will examine what has the greater influence on the height several stacked objects can reach before it topples over. Three factors that will be examined are total surface area, shortest side length and average side length.

Hypothesis: It is the hypothesis of this experiment that the deciding component of object size is the shortest side of the object as objects will have an increased chance of toppling over along the short side as it offers less support.

Equipment: Used in this experiment was a Jenga® game, pen, paper, calculator, and ruler.

Procedure: The first step is to measure the dimensions of the Jenga® block. Essentially the experiment is performed by stacking the blocks as high as possible. Measuring the length and width of the base of the stack will give surface area by which the stack stands. Measuring the height of one block and multiplying by the number of blocks stacked will suffice in measuring height. The Jenga® block has different measurements for its length, width, and height so that by rotating which side the block sits on will create varying amounts. Record results from different surface area/height test and compare.

Results: The experiment yielding the following
 
Experiment Length Width Height Surface Area Blocks used Total Height
Exp 1a
75 mm
14 mm
25 mm
1050 mm²
15
375 mm
Exp 1b
75 mm
14 mm
25 mm
1050 mm²
16
400 mm
Exp 1c
75 mm
14 mm
25 mm
1050 mm²
14
350 mm
Exp 2a
75 mm
25 mm
14 mm
1875 mm²
24
336 mm
Exp 2b
75 mm
25 mm
14 mm
1875 mm²
30
420 mm
Exp 2c
75 mm
25 mm
14 mm
1875 mm²
32
448 mm
Exp 3a
25 mm
14 mm
75 mm
350 mm²
8
600 mm
Exp 3b
25 mm
14 mm
75 mm
350 mm²
9
675 mm
Exp 3c
25 mm
14 mm
75 mm
350 mm²
7
525 mm
Experiment
Ave. Total Height (H)
Surface 
Area (A)
Ave. Side Length (AS)
Shortest Side Length (SS)
H/A
H/SS
H/AS
Experiment 1 375 mm 1050 mm² 44.5 mm 14 mm .38 mm/mm² 26.8 mm/mm 8.40 mm/mm
Experiment 2 401 mm 1875 mm² 50 mm 25 mm .21 mm/mm² 16.0 mm/mm 8.02 mm/mm
Experiment 3 600 mm 350 mm² 19.5 mm 14 mm 1.71 mm/mm² 42.9 mm/mm 30.8 mm/mm

Conclusion: The results demonstrate that surface area is inversely proportional to an objects maximum height and stability. In other words greater surface area decreases maximum height. Because this obviously does not seem right, other factors must be at work in deciding total height. If we look at the column which examines the influence of the shortest side (H/SS), we find that its numbers inversely reflect surface area. This means that the shortest side has a large influence in dictating structure stability. However, because experiments 1 and 3 had the same height, however not the same H/SS values, then it is apparent that this is not the only factor. The most telling column is H/AS which demonstrates that structures seem to gain in stability when the difference between the size of the sides is small.  One factor which may have influence in this experiment is the fact that in experiment 3, only 8 blocks were stacked while in experiments 1 and 2, 20 to 30 blocks were stacked. Error in stacking may have caused the objects to topple sooner, then in experiment 3 where the chance of this error is less. Small details aside, it is shown in this experiment that the hypothesis was shown wrong, and the deciding factor seems to be difference between the length of one side verse the other. In other words, stacking more "square" objects will obtain more height then stacking rectangles.




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