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Name: Tom M.
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Question:
we were doing a paper cone expt. in class but the results we got gave a curved line of best fit What we did was to get many equally sized paper cones, and , after loading weights on them, found that the graph curved downwards instead of being a nice straight line. Why?



Replies:
I am not sure I understand exactly what you did. If you filled equally sized paper cones to the top with the same material, assuming the material is fine and granular (e.g. sand) and not large chunks, the cones should all weight the same. If the weight you added -- again having a fine granular consistency -- was at different heights, then the weight of the partially filled cones will vary as the volume of the cone. For a circular cone the volume V=(pi/3)*R^2*H, where R is the radius, ie 1/2 the diameter, and H is the height FROM THE TIP OF THE CONE TO THE LEVEL OF THE SAND. Since R appears as the second power you would expect the weight to vary as the second power R. And a plot of weight vs. height should be curved.

A good way to analyze the data if it is what I have assumed is to plot the weight, W, (which is proportional to the volume) divided by (R^2*H). In this format not only should the line be straight, it should be a constant, i.e. have zero slope.

Vince Calder



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