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# Investigation into Relationship between Volume and Diameter in Sand Piles

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Introduction

25/09/01   -Physics Coursework 2 0 0 1-   Kajeynan Jeyaveerasingam 4D

Key Stage 4 - Assessment Ph2 – Sand Piles

i) Investigation into Relationship between Volume and Diameter

If sand is allowed to fall steadily onto a horizontal, level, and flat surface, it forms conical piles.

Our AIM, in this experiment, is to find the effects, on the diameter, caused by varying the volume these conical piles of building sand, and hence, find their relationship with one another, in terms of a graph showing all possible, plausible volumes, applicable in the laboratory, with their respective outcomes.

There are two predictions to discuss, the first being the qualitative prediction, explaining itself in simple, common sense terms, followed by a quantitative prediction.

Qualitative Prediction: As the volume of the pile increases, I would expect the diameter to increase; this I observed, when I was travelling to school, and saw piles of building sand, cement, grit, and other building materials on the sites. Everyday, when I passed, the piles would get smaller, as the materials were gradually used up, but not just in height and volume, but their diameter also.

Middle

2] The apparatus used were as follows: a small funnel, for steady constant distribution of the sand onto the piles; pieces of graph paper to measure the diameter with; a measuring cylinder for precise measurement of the volume of sand to be distributed.

3] When the volumes were measured out we were careful to look at the graduation of the cylinder from all sides as the sand does not self-level like water.

4] Our method for the equal distribution of the sand was to keep the flow of sand directly over the centre of the paper and consequently directly over the centre of the pile, to make sure that equal amounts of sand fell on each side of the cone. For the same reason we kept the angle of the funnel at a steady 90°. We then also kept the distance between the apex of the pile and the tip of the funnel constant, so that the force of the falling sand on the pile remained uniform, this distance was 5mm.

5] To measure the diameter,

Conclusion

[5] When we were measuring out the volumes in the measuring cylinder, we found that there were small pockets of air being formed where there was not enough force to collapse them from above. So, these would have significantly affected our results, had they been pockets of air near the centre of the cylinder, which we could not see, and therefore rectify.

[6] Then there was the fact that, however hard you tried, the diameters of no one pile, let alone two, could match up, again due to uneven distribution of sand, and the movement of the graph paper just as the sand piles’ diameters were going to be measured.

[5] Finally, there was the factor of human error and the commonly occurring parallax problem, when using the eye, to measure the volumes and diameters, which would have slightly affected our results, as well.

[6] Of course, if they were available, more accurate material-measurement, ~distribution, and result-measurement equipment would have helped to impede any mistakes occurring due to human error, in measuring and distributing the sand, like, for example, the case of the funnel’s angle relative to the paper, and the case of the hand’s steadiness.

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