Density, Hookes Law & ScalingChapter 18Sections 2, 3, 4, & 5

DensityDensitya measure of how much matter is squeezed into a given spaceThe amount of mass per unit volume

Density is NOT the same as massTwo objects can have the same mass, but not the same density1 kg of iron and 1 kg of feathers have the same mass, but very different densitiesTwo objects can have the same density, but not the same massA cup of water and a gallon of water have the same density, but the gallon of water has more mass than the cup

DensityDensity depends onAtom massSpacing between atomsOsmium is the densest substance on Earth (22.6 g/cm3)Density varies with temperature and pressure (table on p 261 densities are given at 0C and atmospheric pressure)Water is the densest at 4 C

DensityThe planet Saturn has a mass of 5.69 x 1026 kg and a volume of 8.01 x 1023 m3. What is the density of Saturn? Would Saturn sink or float if you could place it in a gigantic bathtub filled with water (water has a density of 1000. kg/m3)?

Diamond has a density of 3520 kg/m3. During a physics lab a diamond drops out of Virginias necklace and falls into her graduated cylinder filled with 5.00 x 10-5 m3 of water. This causes the water level to rise to the 5.05 x 10-5 m3 mark. What is the mass of Virginias diamond?

DensityWeight densitythe amount of weight a body has per unit volumeWeight density is used in liquid pressureSpecific gravity is a standard measure of densitythe ratio of the mass (or weight) of a substance to the mass (or weight) of an equal volume of waterthe ratio of the density of the material to the density of waterHas no unitsIf a substances weighs 3 times as much as an equal volume of water, its specific gravity is 3

DensityWhat happens to the density of each piece of an object when it is cut into pieces?Each piece has the same density as the original object hadWhich has a greater density, a kilogram of lead or a kilogram of feathers?Any amount of lead is more dense than any amount of feathers.

Elasticity & Hookes LawElasticitythe property of a body by which it experiences a change in shape when a deforming force acts on it, and by which it returns to its original shape when the deforming force is removedMaterials that do not return to their original shape are call inelasticElastic limitthe distance at which permanent distortion occurs in an elastic materialHanging a weight on a spring causes it to stretchThe amount the spring stretches is dependent upon the amount of mass on the spring

Hookes LawHookes Law: the amount of stretch/compression of a spring is directly proportional to the applied forceFelastic = kxk = spring constant (units N/m)x = displacement (units m)Hookes law holds as long as the spring is not compressed beyond its elastic limit

Hookes LawA 76 N crate is hung from a spring (k = 450 N/m). How much displacement is caused by the weight of this crate?

A spring of k = 1962 N/m loses its elasticity if stretched more than 50.0 cm. What is the mass of the heaviest object that the spring can support without being damaged?

ScalingTrue or False: When a structure is scaled up or down in size, its properties go up or down in direct proportion.Falsesome properties such as weight, strength, surface area, and volume do not increase in direct proportion to an increase in linear dimensions.Scalingthe study of how size affects the relationship between weight strength, and surface areaAs the size of something increases it grows heavier much faster than it grows stronger

ScalingWeight depends on volumeStrength depends on cross sectional areaVolume and weight increases much faster than corresponding increase in cross sectional areaVolume (and weight) grows as the cube of linear enlargementSurface area grows as the square of linear enlargementCompareelephant and a deer, tarantula and daddy long legs These larger animals have disproportionately thick legs compared to their smaller counterparts as a result of scalingSmaller objects also have more surface area per kilogramGreater surface areagreater cooling abilityCrushed ice cools a drink faster than a cube of iceAn elephant has large ears to cool itself