Published on November 6, 2007
Chapter 19: Chapter 19 Liquids Liquid Pressure: Liquid Pressure A liquid in a container exerts forces on the walls and bottom of the container Pressure is force/area How much pressure depends on the density of the liquid For the same volume, a denser liquid exerts more pressure For liquids of the same density, the pressure will be greater at the bottom of a deeper liquid Think of diving deep into a pool, you feel the increased pressure in your ears Liquid Pressure: Liquid Pressure Pressure of a liquid at rest only depends on the density of the liquid—not on the shape of the container or the size of its bottom surface Bottom, sides of container The surface of an object submerged in liquid This is because liquids are incompressible (cannot be squeezed into a smaller volume) therefore their density is the same at all depths Pressure due to liquid = weight density x depth = ρgh Total pressure = pressure due to liquid + atmospheric pressure Normal atmospheric pressure is 1.01 x 105 Pa Pressure due to a liquid depends on DEPTH, not volume! Forces produced by pressure are equally exerted in all directions Net force exerted by a liquid against a surface is perpendicular to the surface If there is a hole in the surface the liquid will initially move perpendicular to the surface Liquid Pressure: Liquid Pressure Where is the pressure the greatest—at the bottom of the large, shallow lake or at the bottom of the small, deep pond? Wanda watches the fish in her fish tank and notices that the angel fish like to feed at the water’s surface, while that catfish feed 0.300 m below at the bottom of the tank. If the average density of the water in the tank is 1000. kg/m3, what is the pressure on the catfish? Liquid Pressure: Liquid Pressure Why is the water level the same in each vase? Water seeks its own level…because of pressure! Which teapot can hold more tea? Buoyancy: Buoyancy Why is it easier to lift something that is submerged in water? The object has an apparent weight loss due to an upward force exerted on the object by the water…this upward force is called the buoyant force Why does buoyant force push upward when forces are exerted all around the object? Horizontal forces cancel out Upward forces (against the bottom of the object) are greater than downward forces (against the top of the object) because the bottom of the object is deeper Buoyancy: Buoyancy When the weight of the submerged object… is greater than the buoyant force, the object will sink to the bottom is equal to the buoyant force, the object will remain at any level (like a fish) is less than the buoyant force, the object will rise to the surface and float In terms of density, if the object is denser than the fluid, it will sink the same density as the fluid, it will neither sink or float less dense than the fluid, it will float Buoyancy: Buoyancy What happens to water level when something is placed in it? It rises How much does it rise? The amount of displaced water is equal to the volume of the submerged object A completely submerged object always displaces a volume of liquid equal to its own volume. This is a good way to find the volume of irregular shapes Archimedes’ Principle: Archimedes’ Principle An object completely or partially immersed in a fluid is pushed up by a force that is equal to the weight of the displaced fluid Buoyant force equals the weight of the fluid displaced by the object In general cases: Fb = ρg∆V Buoyant Force = density x acceleration due to gravity x volume In terms of Newton’s third law: If you put something in water that pushes 100 N of water out of the way, then the water pushes back with a force on 100 N. The buoyant force is equal and opposite to the weight of water you displace. 1 liter of water = 1000 cm3 = 1 kg = 9.8 N Archimedes’ Principle: Archimedes’ Principle A object weighs less in water than air A 500 gram mass weighs about 5 N in air. Suppose the mass displaces 3 N of water when it is submerged. The buoyant force on the mass will also measure 3 N (pointing up). The mass will weigh only 2 N in the water (5 N – 3N). What happens it the mass is in deeper water—where there is greater pressure? As long as it is submerged completely, the depth will not make a difference because the difference in pressure between the bottom and top of the mass at different depth will be the same The difference in the upward and downward force acting on the submerged object is the same at any depth. The density of water near the surface is practically the same as the density of the water far beneath the surface. Greater variation occurs due to temperature difference. Waterlogged objects that lie submerged, yet above the bottom, are slightly denser than the warmer surface water and not quite as dense as the cooler water at the bottom. Object that are much denser than water will always sink to the bottom regardless of the depth of the water. Archimedes’ Principle: Archimedes’ Principle Palmer drops an ice cube into his glass of water. The ice, whose density is 917 kg/m3, has dimensions 0.030 m x 0.020 m x 0.020 m. What is the buoyant force acting on the ice? William’s wedding ring, presumed to be pure gold, has a mass of 0.1 kg. When submerged in water its apparent mass is 0.080 kg. The density of water is 1000 kg/m3 which is equivalent to 1 kg/L. What is the buoyant force in Newtons? What volume of water (in liters) is displaced? Is the ring made of pure gold (ρ = 19.3 kg/L)? Pine is 0.50 as dense as water and therefore floats in water. Weight density of water is 9800 N/m3 or 9.80 N/L. What weight of water will be displaced by 25 kg of floating pine? What additional force would be required to poke the pine beneath the surface so it is completely submerged? Sink or Float?: Sink or Float? An object more dense than the fluid in which it is immersed sinks. Fb = Fg (displaced fluid) = mfg = ρfVfg An object less dense than the fluid in which it is immersed floats. Fb = Fg (object) = mog = ρoVog An object with density equal to the density of the fluid in which it is immersed neither sinks or floats Apparent Weight: Apparent Weight Apparent weight depends on the density Apparent weight = Fg – Fb = ρfVfg – ρoVog For a submerged object: A piece of metal weighs 50.0 N in air, 36.0 N in water, and 41.0 N in an unknown liquid. Find the densities of the following: The metal The unknown liquid Flotation: Flotation How can a ship be made of iron if a solid block of iron sinks? It has to do with the shape of the ship Principle of Flotation—a floating object displaces a weight of fluid equal to its own weight The ship must be shaped to displace enough water to equal its own weight The deeper the ship is immersed, the more water it displaces—a loaded ship will ride lower in the water than an unloaded ship Flotation: Flotation What is the buoyant force on a 10 ton ship floating in fresh water? In salt water? In a lake of mercury? 10 tons in each case; the weight of the ship is constant, so the weight of the water displaced must also be constant. The volume of the liquid displaced will differ based on the density of the liquid. Pascal’s Principle: Pascal’s Principle The change in pressure on one part of a confined fluid is equal to the change in pressure on any other part of the confined fluid. A small force exerted over a small area will result in a large force exerted over a large area. Used in hydraulic lifts—a force is exerted on a smaller piston providing a pressure that is applied, undiminished, to the larger piston enabling it to lift the car Pascal’s Principle: Pascal’s Principle Every Sunday morning, Dad takes the family trash to the trash compactor in the basement. When he presses the button on the front of the compactor, a force of 350 N pushes down on the 1.3 cm2 input piston, causing a force of 22,076 N to crush the trash. What is the area of the output piston that crushes the trash?