Transcript lect3
http://www.physics.usyd.edu.au/teach_res/jp/fluids09 lect3.ppt ? BUOYANCY - FLOATING AND SINKING Why do ice cubes float on water? Why does a hot air balloon rise? What is wrong with the picture of the ship on the left? If I suspend a block on a rope, what force do we need to pull with on the rope to make the block hang steady? rope T=? m If I immerse the block in water, what happens to the tension in the rope? W Buoyancy A useful model: Immersion of the block produces an upward buoyant force, which at least partly counteracts the weight. T FB Apply Newton’s 2nd Law W – T – FB = 0 T = W - FB + W Archimedes’ Principle • When an object is immersed in a fluid, there is an upward buoyant force equal to the weight of the volume of fluid displaced by the object. • This applies to either full or partial immersion (i.e. a “sinking” or “floating” object) T = W - FB T FB m W Hung Tension T=W Weight Floating Tension FB T = W - FB Water displaced Weight Floating: buoyant force equals Water displaced weight Floating: fully submerged Some fish can remain at a fixed depth without moving by storing gas in their bladder. Water displaced Submarines take on or discharge water into their ballast tanks Why can ships float? A 200 tonne ship enters a lock of a canal. The fit between the sides of the lock is so tight that the weight of the water left in the lock after it closes is much less than the ship's weight. Can the ship float? T h e b u o ya n t fo rce is e q u a l to th e w e ig h t o f th e w a te r d isp la ce d , n o t th e w a te r a ctu a lly p re se n t. T h e m issin g w a te r th a t w o u ld h a ve fille d th e vo lu m e o f th e sh ip b e lo w th e w a te rlin e is th e d isp la ce d flu i d . V o lu m e o f w a te r d isp la ce d . T h is vo lu m e is n o t n e ce ssa rily th e vo lu m e p re se n t. W e ig h t o f sh ip = w e ig h t o f w a te r d isp la ce d So buoyancy is a force. Can we explain in terms of a push or pull ? top A rF h ro bottom F = (pbottom – ptop) A F = (patm + rF g h – patm) A F = rF g h A = rF VF g F = mF g = Weight of displaced fluid =Buoyant force ? A Two cups are filled to the same level. One cup has ice cubes floating on it. Which weighs more? B Two cups are filled to the same level. One of the cups has ice cubes floating in it. When the ice melts, in which cup is the level higher? ? A Two cups are filled to the same level. One cup has ice cubes floating on it. Which weighs more? cups weigh the same B Two cups are filled to the same level. One of the cups has ice cubes floating in it. When the ice melts, in which cup is the level higher? the level is the same A Cartesian diver can be made by completely filling an empty soft drink bottle with water. A medicine dropper is then placed in the bottle so that a small air pocket is trapped at the top of the dropper. When the bottle is squeezed, the medicine dropper sinks. When the bottle is release, the diver rises. Why does the dropper sink when the bottle is squeezed? Your answer should include a list of the important physical quantities involved, the names and descriptions of the physical principles involved. ? A giant clam has a mass of 470 kg and a volume of 0.350 m3 lies at the bottom of a freshwater lake. How much force is needed to lift it at constant velocity? m = 470 kg FT + FB = FG Vclam = 0.350 m3 g = 9.8 m.s-2 FT = ? N m FT + FB F = 0 a=0 rwater = 1.0x103 kg.m-3 FG FT = FG - FB FT = m g - rwater g Vdisplaced FT = m g - rwater g Vclam FT = (470)(9.8) – (103)(9.8)(0.350) N FT = 1.2103 N A ring weighs 6.32710-3 N in air and 6.03310-3 N when submerged in water. What is the volume of the ring? What is the density of the ring? What is the ring made of? air water Volume? density? What is the ring made of? air water FTair = FG FTwater + FB = FG know FTair know FTwater weight of ring FG know FG Mass of ring mring rring = mring / Vring calculate FB Archimedes’ Principle FB = weight of water displaced FB = rF Vring g Vring = 3.0x10-8 m3 rring = 2.2x104 kg.m-3 maybe gold A wooden raft has a density of 0.500103 kg.m-3 and dimensions of 3.05 m 6.10 m 0.305 m. How deep does it sink into the water when unloaded? What is the maximum number of 70 kg people can the raft carry before it sinks? A hydrometer is a simple instrument used to measure the density of a liquid by measuring how deep it sinks in a liquid. A particular hydrometer was made of a uniform cylindrical rod that could float vertically in a liquid. The length of the rod was 0.250 m and its cross sectional area was 2.0010-4 m2. The mass of the rod was 4.5010-2 kg. To calibrate the hydrometer it is placed into water that had a density of 1.000103 kg.m-3. How far from the bottom end of the rod should a mark of 1.000 be placed to indicate the relative density of the water? The hydrometer sinks to a depth of 0.229 m when placed into an alcohol solution. What is the density of the alcohol solution?