Math 163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I wanted to respond to my last assignment. You wrote in response to my assignment:
Your solution:
Since I didn’t have a spring or empty containers, I used whatever I had available in my house. I looked around for something that would be sturdy enough to support weight and then I tried to come up with something that would be equal in weight. This led to the idea of tying forks to an artificial limb of a large plant.
I predicted the limb would get closer to the ground at an even pace. A spring would probably not stretch the same as a limb.
Very good. The behavior of the limb ought to be very interesting.
I was going to put the behavior in the assignment, but there was not a question that asked. I thought I would send it like this to see if I did it correctly.
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After tying the forks to the limb one by one, I marked the distance from the tip of a leaf to the floor on each fork. I ended up with the points
x = forks
y = distance
(1, 44.5) (2, 41.5) (3, 39.5) (4, 37) (5, 36.5) (6, 35.5)
I wasn't sure if I put the forks on the correct axis.
Then I drew a straight line through the points to see the best fit. There was only a slight variation from the line and the actual points on the graph.
Was that the correct way to do that? It did behave like I expected. I thought it would drop at a constant rate because the forks were all approx the same weight.
Everything is done very well. However the straight line really isn't the best model for your data.
The changes in leaf position relative to the floor are respectively -3, -2, -2.5, -.5 and -1. This indicates a decreasing slope. If graphed using an x scale from 0 to 7, and a y scale from, say, 30 to 45 the tendency away from a straight line will be clear.
This is what I would have expected. As the branch bends, the bent part moves more into the thicker part of the branch, closer to the trunk or stalk, where it's stronger. This isn't a physics class so we can leave it at that. In any case the same added force (i.e., the additional weight of another fork) results in progressively less displacement of the end of the branch.
I was curious about your data and I'm glad you've shared it. Excellent work.
It doesn't change anything, but note that force vs. distance for the spring would correspond to # of forks vs. distance from floor, which would in fact reverse your coordinates.