Properties of Matter and Fluids at Rest

What you need to know

• The kinetic theory holds that matter is made of tiny particles in constant motion. In solids the particles vibrate about fixed positions with strong intermolecular forces; in liquids they slide past one another; in gases they move freely at high speed with negligible forces between them.
• Density is mass per unit volume, measured in kg/m^3. Relative density (specific gravity) is the ratio of the density of a substance to the density of water, so it has no unit, and the density of water is 1000 kg/m^3 or 1 g/cm^3.
• Pressure is force per unit area, P = F/A, measured in pascals where 1 Pa = 1 N/m^2. A woman in stiletto heels exerts far greater pressure on the floor than an elephant, because the contact area is tiny even though the force is small.
• Pressure in a liquid at depth h is P = rho g h. It increases with depth, acts equally in all directions at a given depth, depends on the density of the liquid, and does not depend at all on the shape or cross-sectional area of the vessel.
• Atmospheric pressure is about 1.0 x 10^5 Pa, equivalent to 760 mm of mercury or about 10 m of water, and it is measured with a barometer. Total pressure at a depth in an open liquid is atmospheric pressure plus rho g h.
• Pascal's principle states that pressure applied to an enclosed fluid is transmitted equally to every part of the fluid and to the walls of the container. This is the basis of the hydraulic press, the hydraulic brake and the car jack.
• Archimedes' principle states that a body wholly or partially immersed in a fluid experiences an upthrust equal to the weight of the fluid displaced. Upthrust equals apparent loss in weight, so upthrust = weight in air - weight in fluid.
• The law of flotation states that a floating body displaces its own weight of the fluid in which it floats. A body floats when its density is less than that of the fluid; a ship made of steel floats because its hollow shape makes its average density less than that of water.
• Relative density of a solid can be found as weight in air divided by apparent loss of weight in water. For a liquid it is the apparent loss of weight of a body in the liquid divided by the apparent loss of weight of the same body in water.
• Surface tension is the force per unit length acting along the surface of a liquid, caused by the unbalanced inward cohesive pull on surface molecules. It makes a liquid surface behave like a stretched elastic skin, lets a needle float and makes raindrops spherical.
• Surface tension is reduced by raising the temperature, by adding detergent or soap, and by impurities such as camphor. This is exactly why hot soapy water cleans better than cold plain water: lowering surface tension lets the water wet and penetrate the cloth.
• Cohesion is the attraction between molecules of the same substance; adhesion is the attraction between molecules of different substances. Water wets glass and rises in a capillary tube because adhesion exceeds cohesion; mercury does not wet glass and is depressed in a capillary because cohesion exceeds adhesion.
• Hooke's law states that within the elastic limit, the extension of a spring or wire is directly proportional to the applied force, F = k e, where k is the elastic constant in N/m. Beyond the elastic limit the material no longer returns to its original length.
• Young's modulus is the ratio of tensile stress to tensile strain within the elastic limit, where stress = force/area in N/m^2 and strain = extension/original length, a pure number. The energy stored in a stretched spring is (1/2)Fe or (1/2)ke^2.