

Cones
Name: Tom M.
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
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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Update: June 2012

