LECTURE 3 BUOYANCY (ARCHIMEDES’ PRINCIPLE) Lecture Instructor: Kazumi Tolich Lecture 3 2 ¨ Reading chapter 11-7 ¤ Archimedes’ principle and buoyancy Buoyancy and Archimedes’ principle 3 ¨ The force exerted by a fluid on a body wholly or partially submerged in it is called the buoyant force. ¨ Archimedes’ principle: A body wholly or partially submerged in a fluid is buoyed up by a force equal to the weight of the displaced fluid. Fb = wfluid = ρfluidgV V is the volume of the object in the fluid. Demo: 1 4 ¨ Archimedes’ principle ¤ The buoyant force is equal to the weight of the water displaced. Lifting a rock under water 5 ¨ Why is it easier to lift a rock under water? ¨ The buoyant force is acting upward. ¨ Since the density of water is much greater than that of air, the buoyant force is much greater under the water compared to in the air. Fb air = ρair gV Fb water = ρwater gV The crown and the nugget 6 Archimedes (287-212 BC) had been given the task of determining whether a crown made for King Hieron II was pure gold. In the above diagram, crown and nugget balance in air, but not in water because the crown has a lower density. Clicker question: 1 & 2 7 Demo: 2 8 ¨ Helium balloon in helium ¨ Helium balloon in liquid nitrogen ¤ Demonstration of buoyancy and Archimedes’ principle Floatation 9 ¨ When an object floats, the buoyant force equals its weight. ¨ An object floats when it displaces an amount of fluid whose weight is equal to the weight of the object. ¨ An object that is denser than fluid can float if it displaces enough fluid because of its shape. Fb = wfluid Demo: 3 10 ¨ Battleship ¨ Board and weights Clicker question: 3 & 4 11 Example: 1 12 ¨ What is the minimum area of the top surface of a slab of ice with thickness, h = 0.30 m, floating on fresh water that will hold up an automobile of mass mc = 1100 kg sitting on top? The density of water and ice 3 3 are ρw = 0.998 × 10 kg/m 3 3 and ρi = 0.917 × 10 kg/m , respectively. Example: 2 13 ¨ A block of an unknown material weighs Wa = 5.00 N in air and Ww = 4.55 N when submerged in water. What is the density of the material? Example: 3 14 ¨ You decide to enroll in a fitness program. To determine your initial fitness, your percentage of body fat is measured. Assume the average density of fat is 3 3 ρf = 0.90 × 10 kg/m , and lean tissue is 3 3 ρl = 1.10 × 10 kg/m . Your apparent weight in water is 5.0% of your weight in air. What fraction, f, of your body mass is fat? .