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If a surrfboard has a fin, would it sink because it's heavier... or would it have to oppose less friction because the surface area is smaller, or how does that work??! Basically, how does a surfboard fin affect the speed of the surfer, and what's the situation like in terms of friction/surface area/ sinking? What would happen?

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First of all, the fin on the surf bored wouldnt be heavy enough to sink it. Second of all, take the fin of a shark or a dolphin for example, they dont sink. It actually helps the swim and go faster.
I didn't mean literally "sink"! So, technically the surfboard fin isn't only for stability and direction control purposes, but it would also be beneficial in terms of opposing friction and going at a faster speed?
Yes exactly.

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Alright then, a fin wouldn't be a negative thing in any possible aspect I guess :) Thanks a bunch! I'll ace this essay! :D
It's obvious that the fin slows down the surfboard. It's mainly there for stability. The extra stability more than compensates for the extra friction (which is nevertheless very small given the shape of the fin).

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