U5 Determining Density

Presentation Name Course Name Unit # – Lesson #.# – Lesson Name

Density

• Density is a measure of the amount of matter per unit of volume

Determining Density High Density Low Density

– Objects more dense than water sink – Objects less dense than water float

Matter: Mass vs. Weight Matter: Mass vs. Weight Mass and Weight are often confused • Mass is the amount of matter in an object or the • An example using SI units quantity of the inertia of the object – A man has a mass of 100 kg • Weight is the force of gravity on mass

W = mg W = mg 2 W = (100 kg)(9.8 m/sec ) W = weight = 980 Newton m = mass

g = acceleration of gravity – He weighs 980 N

• Many materials are purchased by weight

Matter: Mass vs. Weight Mass vs. Weight

Mass and Weight are often confused • Pound-mass (lbm) is a unit of mass • US Customary units example . 1 lbm = 0.45359237 kg (by definition) – A woman weighs 100 pounds . 1 kg = 2.205 lbm (formula sheet)

. 1 slug = 32.2 lb (formula sheet) W = mg m

W Formula Sheet m = g

100 lb = = 3.1 slugs ft 32.2 s2 – Her mass is 3.1 slugs

Mass vs. Weight Mass vs. Weight • Pound-force (lb) is a unit of force • How are pound-mass and pound-force . The gravitational force exerted on a mass of related? 2 one lbm on the surface of the Earth – On Earth (g = 32.174 ft/s ) . 1 lb = 4.44822162 N • 1 pound-mass object weighs1 pound-force . 1 N = 0.225 lb – In outer space (no gravity) • 1 pound-mass object has no weight Formula Sheet – On the moon (g = 5.32 ft/s2) • 1 pound-mass object weighs 0.166 pound-force

Density Mass/Weight Density • Density can be indicated in multiple ways • Mass Density commonly used for SI units – Mass Density = mass per unit volume – g/cm3 or kg/m3 – Weight Density = weight per unit volume • Weight Density commonly used for US Formula Sheet Customary units – lb/in.3 or lb/ft3 m = VDm Material Mass Density Weight Density m 3 3 Dm = (g/cm ) (lb/in. ) V Apples 0.64 0.023 Water (Pure) 1.00 0.036 Water (Sea) 1.03 0.037 Ice 0.92 0.034 W = VDw Concrete 2.40 0.087 W Aluminum 2.71 0.098 D = w V Steel (1018) 7.8 0.282 Gold 19.32 0.698

Mass and Weight: Measurement Volume: Measurement

• Balance – measures mass • Volume is the amount of three – Uses objects of known mass to find the dimensional space enclosed by unknown mass of an object an object – Measurement is unaffected by difference in gravity – Two methods to determine volume • Calculate using geometry of object • Scale – measures weight – Measures force caused by gravity – Measurement is affected by difference in the • Measure indirectly using water acceleration of gravity displacement (or 3D scanner) – May display a “mass” measurement reading by using an assumed acceleration of gravity to convert from weight to mass

Volume: Calculation Volume: Indirect Measure

• Some object volumes can be calculated • Volume of an irregular object can be • What is the volume formula for each object? determined indirectly with fluid displacement Level Elevates

Volume: Indirect Measure Example • What is the density of a 1.12 in. diameter • Record water level with only water sphere of titanium that weighs 0.82 lb? • Add samples 4 V = π r3 • Record new level 3 W = VDw 4 • Difference is sample volume V = π 1.12 in. 3 W 0.82 lb 3 Dw = = V 5.88 in.3 V = 5.88 in3 Dw = 0.14 lb/in.3 Volume Read Change level • What volume of water (mL) would it displace? here 3 1 ft 1L 5.88 in.3 = 0.096 L or 96 mL 3 3 Meniscus shape is 1728 in. 0.0353 ft exaggerated for clarity