1. Determining Density Introduction to Engineering Design
© 2012 Project Lead The Way, Inc.

2. Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Density
Density is a measure of the amount of matter (atoms) per unit of volume
Objects more dense than water sink
Objects less dense than water float
High Density
Low Density
Think about identically sized samples of steel and Styrofoam—for instance small cubes the size of the wooden cubes used for the puzzle cube. Which is more dense? Steel or Styrofoam?

3. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
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 = weight ; m = mass ; g = acceleration of gravity
Project Lead The Way®
Copyright 2006

4. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Matter: Mass vs. Weight
Mass and Weight are often confused.
An example using SI units
A man has a mass of 100 kg
He weighs …
W = mg
W = (100 kg)(9.8 m/s2)
W= 980 Newtons
Project Lead The Way®
Copyright 2006

5. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Matter: Mass vs. Weight
Mass and Weight are often confused.
An example using US Customary units
A teen has a weight of 100 pounds
His mass is …
W = mg
m = W / g
m = 100 lb / 32.2 ft/s2
M = 3.11 slugs
But no one uses “slugs” so we just treat “pounds” as BOTH a unit of mass and a unit of weight
Project Lead The Way®
Copyright 2006

6. Mass Property Analysis
Introduction to Engineering Design
Unit 3 – Lesson 3.3 – Structural Analysis
Mass vs. Weight
How are pound-mass (lbm) and pound-force (lb) related?
On Earth (g = ft/s2)
1 pound-mass object weighs1 pound-force
In free fall (no gravity)
1 pound-mass object has no weight
On the moon (g = 5.32 ft/s2)
1 pound-mass object weighs pound-force
BUT WHO CARES? ANYONE GOING TO THE MOON WILL US KILOGRAMS AND NEWTONS.
Unfortunately, in common practice we have come to use the word “pound” to refer to a mass and a force, and the meaning of the word can be confusing.
On Earth the mass of an object in units of pound-mass can change slightly due to differences in the acceleration of gravity but is roughly equivalent to the force of gravity, or weight of the object in units of pound-force.
However, because the mass of an object does not change but the weight (force of gravity) of an object is directly related to the acceleration of gravity imposed on the object, the weight of an object will change if the acceleration of gravity changes (for instance an object is taken into outer space or to the moon).
Project Lead The Way®
Copyright 2006

7. D = M / V Density Density = Mass / Volume
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Density
Density = Mass / Volume
Unless, of course, you’re using US Customary units where pound is a weight. Then, “density” is a “weight density”. But that doesn’t matter as long as you’re on Earth.
D = M / V
The context of the situation will determine whether the density is expressed in terms of mass or weight. We will not worry too much about differentiating among the two at this point. However it is important to be able to distinguish between the two terms of mass and weight and know the difference.

8. Weight Density (lb/in.3)
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
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
Although density is often defined as the mass per unit volume, weight density is commonly used to express density when using U.S. Customary units. In the curriculum, density will refer to either mass density or weight density depending on the measurement device and the measurement system being used.

9. 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

10. Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Volume: Measurement
Volume is the amount of three dimensional space enclosed by an object.
Calculate volume using geometry of object
Measure volume indirectly using water displacement (or 3D scanner)
Ex: V = (4/3) πR3 or V = L x W x H
A 3D scanner is available to purchase as an optional item as shown in the Purchase Manual.

11. Volume: Indirect Measure
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Volume: Indirect Measure
Record water level with only water.
Add samples.
Record new level.
Difference is sample volume.
Explain to students the need to read the water level based on the bottom of the meniscus. The meniscus might be very slight depending on the attraction between the water and the graduated cylinder material.
Volume
Change
Read level here
Meniscus shape is
exaggerated for clarity

12. Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Example
What is the density of a 2.24 in. diameter sphere of titanium that weighs 0.82 lb?
V = (4/3)πR3 = (4/3)π(1.123) = 5.88 in3 ; D = M/V = 0.82 lb / 5.88 in3 = 4.83 lb/in3 = 4.8 …
V = 5.88 in3 = 5.88 (2.54 cm)3 = 96.4 cm3 = 96.4 mL
A note about precision. Notice that the volume is reported to the hundredths place, which reflects the same number of digits as the measured value (diameter) from which it is determined. However, this volume value is an intermediate calculated value since it is used in the density calculation. You should keep the unrounded value for volume in your calculator and use the unrounded value when performing the density calculation.
The density value is reported with two significant digits because the weight value includes only two significant digits (the least number of significant digits associated with the measured values used to calculate the density).
What volume of water (mL) would it displace?