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Determining Density Introduction to Engineering Design © 2012 Project Lead The Way, Inc. Density • Density is a measure of the amount of matter per unit of volume High Density Low Density – Objects more dense than water sink – Objects less dense than water float Matter: Mass vs. Weight • Mass is the amount of matter in an object or the quantity of the inertia of the object. • Weight is the force of gravity on mass. W = mg W = weight m = mass g = acceleration of gravity • Many materials are purchased by weight Matter: Mass vs. Weight Mass and Weight are often confused. • An example using SI units – A man has a mass of 100 kg W = mg W = (100 kg)(9.8 m/sec2) = 980 Newton – He weighs 980 N Matter: Mass vs. Weight Mass and Weight are often confused. • US Customary units example – A woman weighs 100 pounds W = mg W m = g 100 lb = = 3.1 slugs ft 32.2 s2 – Her mass is 3.1 slugs Mass vs. Weight • Pound-mass (lbm) is a unit of mass 1 lbm = 0.45359237 kg (by definition) 1 kg = 2.205 lbm (formula sheet) 1 slug = 32.2 lbm (formula sheet) Formula Sheet Mass vs. Weight • Pound-force (lb) is a unit of force The gravitational force exerted on a mass of one lbm on the surface of the Earth 1 lb = 4.44822162 N 1 N = 0.225 lb Formula Sheet Mass vs. Weight • How are pound-mass and pound-force related? – On Earth (g = 32.174 ft/s2) • 1 pound-mass object weighs1 pound-force – In outer space (no gravity) • 1 pound-mass object has no weight – On the moon (g = 5.32 ft/s2) • 1 pound-mass object weighs 0.166 pound-force Density • Density can be indicated in multiple ways – Mass Density = mass per unit volume – Weight Density = weight per unit volume Formula Sheet m = VDm m Dm = V W = VDw W Dw = V Mass/Weight Density • Mass Density commonly used for SI units – g/cm3 or kg/m3 • Weight Density commonly used for U.S. Customary units – lb/in.3 or lb/ft3 Material Mass Density Weight Density (g/cm3) (lb/in.3) Apples 0.64 0.023 Water (Pure) 1.00 0.036 Water (Sea) 1.03 0.037 Ice 0.92 0.034 Concrete 2.40 0.087 Aluminum 2.71 0.098 Steel (1018) 7.8 0.282 Gold 19.32 0.698 Mass and Weight: Measurement • Balance—measures mass – Uses objects of known mass to find the unknown mass of an object – Measurement is unaffected by difference in gravity • Scale—measures weight – Measures force caused by gravity – Measurement is affected by difference in the acceleration of gravity – May display a “mass” measurement reading by using an assumed acceleration of gravity to convert from weight to mass Volume: Measurement • Volume is the amount of three dimensional space enclosed by an object. – Two methods to determine volume • Calculate using geometry of object • Measure indirectly using water displacement (or 3D scanner) Volume: Calculation • Some object volumes can be calculated. • What is the volume formula for each object? Volume: Indirect Measure • Volume of an irregular object can be determined indirectly with fluid displacement. Level Elevates Volume: Indirect Measure • • • • Record water level with only water. Add samples. Record new level. Difference is sample volume. Volume Change Read level here Meniscus shape is exaggerated for clarity Example • What is the density of a 2.24 in. diameter sphere of titanium that weighs 0.82 lb? 4 V = π r3 3 3 4 2.24 in. V= π 3 2 W = VDw 4 V = π 1.12 in. 3 3 V = 5.88 in3 Dw = 0.14 lb/in.3 W 0.82 lb Dw = = V 5.88 in.3 • What volume of water (mL) would it displace? 5.88 in.3 3 1 ft 1L 1728 in.3 3 0.0353 ft = 0.096 L or 96 mL