equal to the weight of the liquid displaced, which in turn is equal to the density of the liquid times the volume of the object displacing the liquid. Calculating buoyant force is very similar to the formula for calculating mass (weight) using density and volume, except that buoyancy is upward, and weight is downward. If the downward force is greater, the object will sink, and the net, in-water weight will be its air weight minus the buoyant force. If the density of the object is less than the density of the water (or other fluid), the object will float. The submerged portion of a floating object will be equal to the ratio of the density of the object to the density of the liquid (or the ratio of the weight of the object to the weight of the liquid displaced if the object were completely submerged). Expressed as equations: Buoyant force = Volume of object x Density of liquid In-water weight = Air weight – Buoyant force (a negative answer means the object will float) Submerged portion of floating object = Density of object Density of liquid Many find it useful to visualize buoyancy problems by drawing pictures, labeling objects to show weights, buoyant forces, and volumes, and drawing arrows to indicate the direction of the force (down arrows for weight, up arrows for buoyancy)(figure 3-5). Sample Problems: SI/metric 1. A concrete block one-half meter on a side weighs 200 kg. What will be its in-water weight in the ocean? Answer: The dry weight of the block (200 kg) and the density of seawater (1.025 kg/L) are known. The volume of the block in liters is: (0.5 m x 0.5 m x 0.5 m) x 1,000 L/m3 = 125 L The weight of an equal volume of seawater (the buoyant force) is the density of seawater times the volume of the block: 1.025 kg/L x 125 L = 128 kg The buoyant force is less than the weight of the block of concrete, so the concrete will sink. The inwater weight of the block is the air weight minus the buoyant force: 200 kg – 128 kg = 72 kg The concrete block does not float, but under water its effective weight is only 72 kilograms rather than 200 kilograms. 2. A fully equipped diver, excluding her lead ballast weight, weighs 80 kilograms. Diving in fresh water, she requires 8 kilograms of lead weight to hover comfortably during her safety stop at the end of a dive. How many kilograms of lead weight will the diver require in order to hover comfortably in the ocean? Answer: In fresh water, the diver is able to hover, so she is “neutrally buoyant.” The upward, buoyant force of the fresh water is equal to the weight of the equipped diver, including her 8 kilogram weight system. In the ocean, the denser seawater will exert a greater buoyant force, so the diver will have to add weight to counterbalance the increased buoyancy. There are two ways to solve this problem. The first is to compute the volume of the diver using her total weight and the density of fresh water. Then knowing her volume, compute the buoyant force of seawater on her. This will be the total weight she must achieve to be able NAUI Master Scuba Diver 78 Diving Physics In water weight of a 1 liter 1.5 kg object immersed in seawater dry weight = 1.5 kg V = 1L buoyant force in water weight = 1L x 1.035 kg/L = 1.025 kg 1.5 kg - 1.025 kg = 0.475 kg FIGURE 3-5. MANY FIND IT USEFUL TO VISUALIZE BUOYANCY PROBLEMS WITH PICTURES
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