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 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 W = mg Many materials are purchased by weight 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 980 N W = mg W = (100 kg)(9.8 m/sec2) = 980 Newton 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 US Customary units example A woman weighs 100 pounds Her mass is 3.1 slugs W = mg m = W g Slugs are not commonly used because the pound is a more practical unit for commerce. As a result, pounds are often used to indicate mass instead of slugs. But since “pound” is used as a unit of force as well, there is often confusion about what the unit “pound” represents. = 100 lb 32.2 ft s 2 = 3.1 slugs Project Lead The Way® Copyright 2006

Density Density can be indicated in multiple ways m = VDm W = VDw Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Density Density can be indicated in multiple ways Mass Density = mass per unit volume Weight Density = weight per unit volume Formula Sheet m = VDm D m = 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. W = VDw D w = W V

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 US 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 US 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 Two methods to determine volume Calculate using geometry of object Measure indirectly using water displacement (or 3D scanner) A 3D scanner is available to purchase as an optional item as shown in the Purchase Manual.

Volume: Calculation Some object volumes can be calculated Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Volume: Calculation Some object volumes can be calculated What is the volume formula for each object? Students should refer to the Engineering Formula Sheet.

Volume: Indirect Measure Volume of an irregular object can be determined indirectly with fluid displacement Level Elevates

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 1.12 in. radius sphere of titanium that weighs 0.82 lb? V = 4 3 π r 3 V = 4 3 π 1.12 in. 3 V = 5.88 in3 W = VDw D w = W V = 0.82 lb 5.88 in. 3 D w = 0.14 lb/in.3 The formula for the volume of a sphere is on the formula sheet. McMaster-Carr published value for Titanium Grade 2: http://www.mcmaster.com/#=i6dpgt What volume of water (mL) would it displace? 5.88 in. 3 1 ft 3 1728 in. 3 1L 0.0353 ft 3 = 0.096 L or 96 mL