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