Density
Density is mass divided by volume: .
Example 1: Find the density of an object with a mass of 250 g and a volume of 50 cm³.
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Pressure in fluids
Pressure at a depth in a fluid of density is -- it depends only on depth and density, not on the shape or size of the container.
Example 2: Find the pressure at a depth of 5 m in water (density 1000 kg/m³, ).
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Archimedes' principle and floating
Any object in a fluid experiences an upward force (upthrust) equal to the weight of fluid it displaces. An object floats when this upthrust equals its own weight; it sinks when its weight exceeds the maximum possible upthrust.
Example 3: A block of wood with a submerged volume of 150 cm³ floats in water (density of water = 1000 kg/m³, ). Find the upthrust acting on it.
Upthrust = weight of water displaced = .
Elasticity and Hooke's law
Within a spring's elastic limit, extension is proportional to the applied force: , where is the spring constant. Beyond the elastic limit, the spring is permanently deformed and no longer returns to its original length.
Example 4: A spring stretches 4 cm under a force of 8 N. Find the spring constant.
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