The Physics of Tubing

Every summer, I visit my grandmother and her boyfriend in California. They live in a small town in Northern California on a lake. They own a speedboat that they keep on the lake. Whenever I visit them in the summer, I go tubing on their boat. The above picture is from the summer before sophomore year. It is quite fun. When I tube, I lie down on a tube attached by a sixty foot rope to the back of the boat, which zooms around the lake at speeds approaching 45 mph. The rope creates an angle of about 30 degrees above the horizontal. Thus, when the boat pulls the tube, it exerts a force roughly equivalent to cos 30 X mass of me and tube X g. The weight of the tube with me on it was probably equal to 50 kilograms. This means that the boat exerts 424 Newtons of force as it pulls me. When I tube, I try to steer the tube outside of the wake when the boat makes sharp turns. When this happens, I shift my weight such that the tube leans to one side. It then speeds up. This is the equivalent of a car making a banked turn. When the tube leans over, it reduces friction by theta, which allows the tube to move faster.