Density. Chapters 12-14: Phases of Matter. Example: Density. Conceptual Check. Springs 2/27/12. Mass Density vs. Weight Density
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1 Chapters 12-14: Phases of Matter Density Sequence of increasing molecule motion (and kinetic energy) Solid Liquid Gas The densities of most liquids and solids vary slightly with changes in temperature and pressure Densities of gases vary greatly with changes in temperature and pressure Example: Density Compute density of a gold brick. Dimensions: (20.5 cm)x(10 cm)x(5 cm) Mass: 19.8 kg Mass Density vs. Weight Density Mass density = mass/volume (kg/m 3 ) Weight density = weight/volume (N/m 3 ) What is the weight density of the gold brick from the previous example? Water expands when it freezes into ice. Which has more volume, 1 kg of ice or 1 kg of water? Which has more mass, 1 kg of ice or 1 kg of water? Which has a higher density, water or ice? Which has more mass, a liter of ice or a liter of water? Springs Solid materials are not all brittle! They have a certain degree to which they can bend: Elasticity We can harness this elasticity to exert forces. Hooke s Law: Force ~ Δx 1
2 Hooke s Law The more you stretch or compress a spring, the more force it can exert when released. This works up until the elastic limit of the material Pressure Pressure is force per unit area 1 N/m 2 = 1 Pascal (Pa) Other common pressure units: Pounds per Square inch (PSI) - tires, etc. mm Hg - blood pressure inches Hg - weather barometer Pressure changes with Contact Area The same force applied over a smaller area results in greater pressure think of poking a balloon with your finger and then with a needle. Example: Shoes What is pressure exerted by an 80-kg person s shoe on floor if shoe is 0.3 m by 0.1 m and each shoe supports half of total weight? What if half of weight rests on m by m stiletto heel? In which case is the pressure greatest? In which case is the pressure greatest? 2
3 Pressure in Liquids/Fluids Water seeks its own level A fluid is any substance that can flow (liquids & gasses) Liquid pressure = weight density x depth Total pressure = liquid pressure + atmospheric pressure Atmospheric pressure = kpa Pressure is the same at the bottom of each container Pressure depends on DEPTH, not volume Pressure in Liquids Pressure depends on depth: weight of what s above determines pressure. Buoyancy Pressure depends on depth. Consider a large rock: The bottom of the rock is at a lower depth, so it feels more pressure than the top of the rock. This net upward force is called buoyancy. Displacement of Liquid Objects displace a volume of liquid equal to their volume This is useful for determining irregular or odd volumes Archimedes Principle The buoyant force on an immersed object is equal to the weight of the fluid it displaces. Immersed: partially OR completely submerged Buoyant force does NOT depend on depth! 3
4 Example Helpful to know: Properties of water: 1 kg of liquid water takes up 1 L of volume 1 kg of water weighs 10 N. Water has a mass density of 1 g/cm 3, or 1000 kg/m 3 What would it take for the buoyant force to be greater than the weight of the object displacing some volume of water? Will it float? Any object immersed in a liquid will feel a buoyant force, but that doesn t mean it will 1. An object more dense than the fluid in which it is immersed will sink. 2. An object less dense than the fluid in which it is immersed will 3. Same density? Neither sink nor Why does a lifejacket help if you re out at sea? Student 1: I think the life jacket is making my size larger, so I displace more water, which makes it easier to Student 2: I think the life jacket is decreasing my mass, so the buoyant force can be more effective at balancing out my weight. Student 3: I think the life jacket is increasing my volume by a lot without adding a lot of mass, so my density is going down, making it easier for me to More Floating Remember Archimedes Principle: An immersed object feels a buoyant force equal to the weight of the fluid it displaces. Objects with density less than the fluid will How do modern ships float??? Imagine a solid block of iron, and a sheet of iron bent into a boat-like shape. We have increased the effective volume of the sheet of iron This lowers its average density, allowing it to float A floating object displaces a weight of fluid equal to its own weight Floating Depends on Average Density 4
5 Example: Tip of the Iceberg Ice has a lower density than liquid water. As the iceberg melts, what will happen to the level of the ocean? A. The level will rise B. The level will lower C. The level will remain the same. Main Points Density Spring force Pressure Pressure in liquids Buoyancy Archimedes Principle 5
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