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

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?

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

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

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

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 = 32.174 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 0.166 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

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.

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.

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

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.

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

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?