The Physics
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Mass of a Grain of Sand

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Bibliographic Entry Result
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Earth Science. Englewood Cliffs: Prentice Hall, 1987: 569. "Mineral: Quartz, Specific Gravity: 2.65" N/A
"Sand." World Book Encyclopedia. Chicago: World Book, 2000. "Scientists define sand as grains that measure from 1/400 inch (0.06 millimeter) to 1/12 inch (2.1 millimeters) in diameter." 0.30 μg–13 mg
Hess, Kunze, Leslie, Letro, Millage, Sharp, & Theodore Snow. Earth Science: Geology, the Environment, and the Universe. Columbus, OH: Glencoe McGraw Hill, 2002. "Sand may be sub-divided into five categories according to grain size: (1) Very coarse (2 mm–1 mm) (2) Coarse (1 mm–0.5 mm) (3) Medium (0.5 mm–0.25 mm) (4) Fine (0.25 mm–0.10 mm) and (5) Fine sand (0.10 mm–0.05 mm)." 0.17 μg–11 mg
Berman, Bob. "Much Ado About Nothing: Time to let go of matter — emptiness is what rules the universe." Discover. 23,7 (July 2002). "But if you extended a one-inch wide tube all the way from Earth to Vega and scooped up every bit of matter within, the contents would weigh just one-millionth of an ounce, roughly equal to a grain of sand." 28 μg
Corbett, Dan, Stafford, Kate, and Wright, Patrick. Introduction to String Theory. "Strings' minimum energies are actually whole-number multiples of the Planck energy (roughly 1000 kilowatt-hours), which, translated into mass, yields the Planck mass (ten billion billion times that of a proton; roughly 1/100 of 1/000 of a gram; about the mass of a grain of sand)." 10 μg

Sand is a type of sediment produced by the breakdown of various types of rocks. Once parted from the original source rock, the material is then eroded and transported via wind, water, or even ice. Sand often lands at the deposits of lakes or rivers as sand dunes or may ultimately reach the depths of the sea where it may harden into sedimentary rock. Sand varies in size, color, and composition.

The composition of sand depends largely on the source material. Mineral sands are old beach sands that are made up of the important minerals, rutile, ilmenite, zircon, and monazite. Since these minerals are heavy they are also known as "heavy minerals". Most beach sands, however, are composed of grains of the mineral quartz. The relative density (also known as specific gravity) of quartz is 2.65. Relative density refers to the weight of a mineral relative to an equal volume of water.

Since the grain size of sand may vary, the mass of the individual grain of sand may vary according to its size as well as its composition. Using the ranges of diameters, I obtained the volume of the sand grain by using the formula for the volume of a sphere

volume = 4/3π·radius3

Since we know the density of quartz, using the density formula

density = mass/volume

I obtained the mass of a grain of sand for both ranges of diameters.

diameter  =  0.060 mm diameter  =  2.10 mm
volume  =  1.13 × 10−13 m3 volume  =  4.85 × 10−9 m3
mass  =  3.00 × 10−10 kg → 0.30 μg mass  =  1.28 × 10−5 kg → 13 mg

Marina Theodoris -- 2003