### 5.3.A DetermineDensity

```Determining Density
Introduction to Engineering Design
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/sec2)
= 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
W
m =
g
100 lb
=
= 3.1 slugs
ft
32.2
s2
– Her mass is 3.1 slugs
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
Formula Sheet
m = VDm
m
Dm =
V
W = VDw
W
Dw =
V
Mass/Weight Density
• Mass Density commonly used for SI units
– g/cm3 or kg/m3
• Weight Density commonly used for US
Customary units
– lb/in.3 or lb/ft3
Material
Mass Density Weight Density
(g/cm3)
(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
Record new level
Difference is sample volume
Volume
Change
level
here
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?
4
V = π r3
3
4
V = π 1.12 in. 3
3
V = 5.88 in3
W = VDw
W
0.82 lb
Dw =
=
V 5.88 in.3
Dw = 0.14 lb/in.3
• What volume of water (mL) would it displace?
5.88 in.3
3
1 ft
1L
1728 in.3
3
0.0353 ft
= 0.096 L or 96 mL
```