Determining Density
© 2012 Project Lead The Way, Inc.Introduction to Engineering Design
Density
• Density is a measure of the amount of matter per unit of volume
– Objects more dense than water sink– Objects less dense than water float
High Density Low Density
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 = weightm = massg = acceleration of gravity
W = mg
• Many materials are purchased by weight
Matter: Mass vs. WeightMass and Weight are often confused.• An example using SI units
– A man has a mass of 100 kg
– He weighs 980 N
W = (100 kg)(9.8 m/sec2) = 980 Newton
Matter: Mass vs. WeightMass and Weight are often confused.• US Customary units example
– A woman weighs 100 pounds
– Her mass is 3.1 slugs
¿100 lb
32.2 fts2= 3.1 slugs
W = mgm = Wg
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
m = VDm
Dm =mV
Formula Sheet
W = VDw
Dw =WV
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 (g/cm3)
Weight Density (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.
VolumeChange
Meniscus shape isexaggerated for clarity
Read level here
Example• What is the density of a 2.24 in. diameter
sphere of titanium that weighs 0.82 lb?
5.88 in .3 (1 ft3 1728 in .3 )(1L 0.0353 ft3 ) = 0.096 L or 96 mL
0.14 lb/in.3
Dw = WV =
0. 82 lb5.88 in .3
• What volume of water (mL) would it displace?
W = VDw