Designing an oceanographic mooring. A mooring is a platform for placing scientific instrumentation in the water at a range of depths for extended periods of time. At its most basic, it consists of an anchor, a piece of cable, and a buoyant float (which remains submerged) which keeps the mooring line taut (we then attach scientific instruments to the cable). Choose also little flotation, and the mooring gets “blown over” in strong currents, and the instruments do not remain at the correct depth. Choose too much flotation, and the anchor can’t hold the mooring in place. Let’s suppose we have a mooring with the following specifications, pretty close to what we utilize for work in Lake Superior: Water depth: 220m (fresh water). Anchor: 0.6m3 of concrete (suppose that concrete has a density of 2900kg/m3). Cable: 210m, so that the float is 10m below the surface once deployed (for this exercise let’s suppose the cable is mass less). Float: A hollow steel sphere of radius 0.50m, by walls 5.0mm thick (suppose that steel has a density of about 7900kg/m3).
1. What is the apparent weight of the float?
2. In this case, what is the angle of the cable to the vertical?
3. In a 100cm/s current, what is the drag force on the sphere (assume C=0.47)?
4. What is the tension in the cable? The cable we use has a breaking strength of 5500lbs. Is this okay?
5. What is the apparent weight (i.e. weight MINUS buoyancy force) of the anchor when it is in water?