Introduction to Engineering Design

Determining Density

© 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/sec

2

) = 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

m = W g – Her

mass

is 3.1 slugs = 100 lb 32.2

ft s2 = 3.1 slugs

Mass vs. Weight

•

Pound-mass

(lb m ) is a unit of mass  1 lb m = 0.45359237 kg (by definition)  1 kg = 2.205 lb m (formula sheet)  1 slug = 32.2 lb m (formula sheet) Formula Sheet

Mass vs. Weight

•

Pound-force

(lb) is a unit of force    The gravitational force exerted on a mass of one lb m 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/s 2 ) •

1 pound-mass

object weighs

1 pound-force

– In outer space (no gravity) •

1 pound-mass

object has

no weight

– On the moon (g = 5.32 ft/s 2 ) •

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 = VD m Dm = m V W = VD w Dw = W V

Mass/Weight Density • Mass Density commonly used for SI units – g/cm 3 or kg/m 3 • Weight Density commonly used for US Customary units – lb/in.

3 or lb/ft 3

Material

Apples Water (Pure) Water (Sea) Ice Concrete Aluminum Steel (1018) Gold

Mass Density (g/cm 3 ) Weight Density (lb/in.

3 )

0.64

1.00

1.03

0.92

2.40

2.71

7.8

19.32

0.023

0.036

0.037

0.034

0.087

0.098

0.282

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 Read level here Volume Change Meniscus shape is exaggerated for clarity

Example

• What is the density of a 1.12 in. diameter sphere of titanium that weighs 0.82 lb?

V = V = 4 3 4 π 3 π r3 1.12 in. 3 V = 5.88 in 3 W = VD w Dw = W V = 0.82 lb 5.88 in.3

Dw = 0.14 lb/in.

3 • What volume of water (mL) would it displace?

5.88 in.3

1 ft3 1728 in.3

1L 0.0353 ft3 = 0.096 L or 96 mL