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AlexChandler
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Homework Statement
I was looking through my notes, and I saw that my professor solved a propellor blade problem in a way that I don't understand. I took this class two semesters ago, so I cannot ask the professor himself. The problem that I am having is with his setup of a differential element in the propellor blade. He considers a small section of the propellor blade "dm" and does a force analysis on it. The blade is rotating at constant angular speed. So he finds two radial forces: a tension "T" directed radially inward, and a tension "T+dT" directed radially outward. I have attached a drawing of this setup. We are assuming the blade is uniform, even though I have drawn it as growing wider with greater radius, it should be the same width all along the blade.
Homework Equations
F=ma
ac = m*v2/r
We find: T+dT-T=dm v2/r
The Attempt at a Solution
My attempt in understanding this setup leads me to think that tension should not be increasing with radial distance. I think this because if you consider the force analysis on the section of the blade "dm" there is greater force directed radially outward, and thus how can we have a centripetal acceleration on that chunk if there is greater outward force than inward force! But at the same time, I see that for each chunk "dm" centripetal acceleration will be increasing with radial distance, as the velocity increases with radius. However at the same time, as we move along the blade at further and further distances, the tension force is responsible for accelerating less and less of the mass of the blade.
So there are two things here that make me think that the tension should decrease with radial distance from the center, and one thing that says it should increase.
Any ideas?
I hope I am communicating myself well here.. I am a bit confused
Thanks
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