Why not just make the wood an animated sprite that's bouncing/floating the way you want on a separate layer, with no collisions enabled?
Like, I know it's way dumb-ed down from the physics aspect but it seems like it would be pretty easy to have the animated wood sprites bobbing in the "water" and just have the water doing its parallax scrolling (or however you have it set). And if you wanted you could randomize the instances of the animated wood sprite.
Of course, I'm much better at the art side of things than the game development side, so creating the sprite itself is a whole lot easier for me.