Materials that have the ability to flow Fluids Liquids Gases Density A measure of a material s compactness The amount of matter per unit volume Density mass volume m V Mass grams g kilograms kg Volume Cubic centimeters cm 3 Cubic meters m 3 Density g cm 3 or kg m 3 In general the density of a solid is greater than the density of a liquid and the density of a liquid is greater than the density of a gas Example A certain piece of metal has a mass of 125 grams and a volume of 25 cm 3 What is the mass of 1 cm 3 of this metal density m V 125 25 5 g cm 3 5 grams What is the volume of 80 grams of this metal mV 5 80 V 5V 80 V 16 cm 3 What is the mass of 40 cm 3 of this metal mV 5 m 40 m 200 grams Buoyancy in a Liquid An object submerged in a liquid experiences an upward lift force called the buoyant force The buoyant force is a result of increased pressure with depth The bottom of an object experiences a greater pressure than the top and therefore a greater force Archimedes Principle A submerged object is buoyed by a force equal to the weight of fluid it displace This force is called the buoyant force F b F b mg the object floats less dense than liquid F b mg the object sinks more dense than liquid Floatation A floating object displaces a weight of fluid equal to its own weight In other words the buoyant force on a floating object must be equal to the weight of the object Net force zero system is in equilibrium and forces must balance Large cargo ships are built to displace a great amount of water Example An object weighs 25 N in air and 18 N in water What is the buoyancy force acting on the object 7 N What is the weight of the water that is displaced when the object is totally submerged 7 N What is the mass of the displaced water 0 7 kg What must be the volume of the displaced water Density of water 1000 kg m 3 V 7 x 10 4 m 3 also equals volume of object What is the density of the object V 7 x 10 4 m 3 m 2 5 kg 3571 kg m 3 Pressure A way of describing the way in which force is distributed Pressure is defined as the force per unit area Pressure Force Area P F A F Force N A Area m 2 P Pressure Pa Pascals Atmospheric Pressure The pressure exerted by the Earth s atmosphere The force is the weight of a column of air above your head It s a very large column so it s heavy Atmospheric pressure is 101 00 Pa at sea level average value The pressure decreases with increasing altitude about 1 every 80 m But there s an equal pressure from within your body so you re not crushed Liquid Pressure Formula Liquid Pressure density of liquid x gravity x depth P fluid gd P liquid pressure Pa fluid fluid density kg m 3 g gravity 10 m s 2 d depth below the surface m Example A submarine is located 50 m below the surface What is the water pressure on the submarine P liquid fluid gd P liquid 1000 10 50 P liquid 500 000 Pa What is the total pressure at this depth Total pressure P atmospheric P liquid Total pressure 100 000 500 000 Total pressure 600 000 Pa Liquid Pressure The pressure is the same at any given depth regardless of the shape of the container Average water pressure acting against the dam depends on the average depth of the water and not on the volume of the water held back