Activity 5.3 Determining Density Answer Key Introduction How full is the bag that you take to each of your classes? Can you put any more stuff into it? What happens to the size of the bag? What happens to the mass of the bag? The size of the bag likely stayed the same, though the bag itself is probably about to burst open. When the volume of something stays the same while the mass increases, then the density increases. In this activity you will measure volume and mass to determine the density of several objects. Equipment ● ● ● ● ● Engineering notebook Triple beam balance or scale Graduated cylinder Dial calipers Automoblox people and wheels ● Wooden puzzle cube blocks ● ● ● ● ● Steel spheres Delrin spheres Paper clips (Optional) Aluminum ruler Density and Uses of Common Materials Chart Procedure Part I. Determining Density of a Material 1. Measure the mass or weight of the Delrin, steel, and wood samples as directed by your instructor. For improved accuracy, measure ten samples of each material and calculate the average mass or average weight. Record values including units to the appropriate precision based on the precision of the scale. Note that you need only measure either mass in SI units or weight in US units, not both.Calculate the volume of the Delrin, steel, and wood samples. For improved accuracy, measure three samples of each material and calculate the average volume. Record and calculate values to the appropriate precision including units. When adding or multiplying measurements, record the sum or product to the precision of the least precise number involved in the calculation. Delrin (diameter) Volume formula 4/3 pi r^3 Steel (diameter) 4/3 pi r^3 Wood (wdh) Width x Height x Depth (sphere or rectangular prism, as appropriate) © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 1 Measurement #1 W D H W D H W D H Calculate volume (Show all steps including units) Measurement #2 Calculate volume (Show all steps including units) Measurement #3 Calculate volume (Show all steps including units) Calculate average of three volume measureme nts (Show all steps including units) © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 2 © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 3 2. Calculate the density of the Delrin, steel, and wood samples. Show units for each measurement or quantity. Delrin Steel Wood Average of a single sample Average of three volume measureme nts Formula for density Calculate density (Show all steps including units) Formula to convert from SI to US system or from US to SI system Convert density from SI to US system or from US to SI System (Show all steps including units) 3. Do your results correspond to published values for the density of steel, Derlin and wood? If not, why do you think your density value(s) vary from the published © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 4 values? © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 5 4. (Optional) Create an Excel Spreadsheet to perform calculations and present the data calculated in number three above. Format the information in a table similar to that shown below. Print your table and attach to this activity. Delrin Steel U Wood Un n i t s Un i t s i t s Mass of 3 samples Mass Average Volume of sample Density (SI) Density (US) 5. Consider how you might determine the material from which an object is made. If you are given a sample of a metal (which you know is either steel or aluminum), a graduated cylinder and a balance or scale, how could you determine from which metal the object is made? Delrin Mass/weight of 10 samples Mass (SI) (include units) Weigh t (U S) 13g Average mass/weight of a single sample (include units) Mass (SI) 1.3g Steel Mass (SI) Wood Weigh t (U S) 84g Weigh t (U S) Mass (SI) 8.4g Mass (SI) Weigh t (U S) 32g Weigh t (U S) Mass (SI) 3.2g © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 6 Weigh t (U S) Calculate weight density and look online for properties of aluminum or steel to see which measurement is closest. Part II. Determining the Plastic Materials used in Automoblox Vehicles Obtain an Automoblox vehicle from your teacher. Study the Automoblox people and the wheels. 1. Are the Automoblox people made of the same material as the Automoblox wheels? Why do you think so? How might you test your hypothesis? 2. You will determine the density of the plastic used to manufacture the Automoblox people and the Automoblox wheels. Measure the mass of the four Automoblox people and wheels. For improved accuracy, measure the four Automoblox people together and then measure the four wheels together. Record values including units to the appropriate number of significant digits. © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 7 Automoblox People Automoblox Wheels Total mass/ weight of all sample (s) (include units) 3. Measure the volume of the four Automoblox figures and then measure the volume of the four wheels. Because of the irregular form of each object, the volume is more easily measured using a graduated cylinder. a. Add water to the graduated cylinder until it is approximately 2/3 full. b. Record the water level. c. Carefully add samples. d. Record the new water level. Automoblox People Automoblox Wheels Water level without samples (Include units) Water level with samples (Include units) Water volume displaced = volume of sample(s) © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 8 (Show calculations) © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 9 4. Calculate the density (by hand or using Excel) of the four Automoblox figures and four wheel samples. Complete the table below or attach a print of your Excel worksheet. Be sure to include units with all measurements and quantities. Automoblox People Automoblox Wheels Total mass/weight of sample(s) Volume of sample(s) Formula for density Density (SI) Density (US) 5. Does your data support or refute you hypothesis (from number 1 above)? Explain. 6. Refer to the Common Materials Density and Uses Chart. Use your results to make an educated guess as to the material used in the manufacture of the Automoblox people and wheels. What other tests might further substantiate your guess? Extend Your Learning 1. Measure the mass of the aluminum ruler and paper clip samples. Choose the appropriate number of samples of each if an average is needed for improved accuracy. Record values including units. Aluminum Ruler Total mass of sample(s) 38.47 Paper Clips 1.14 2. Measure or calculate the volume of the aluminum ruler and paper clip samples. [Note that you can calculate the volume of the ruler without submerging it in © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 10 water.] Show all measurements if using the indirect measurement. Sketch the object if using the calculation method. 3. Calculate the density of the aluminum ruler and paper clip samples by hand or using Excel. Complete the table below or include a print of your Excel worksheet. Be sure to use the mass and volume based on the same number of objects. Show units for all measurements and calculated quantities. Aluminum Ruler Paper Clips Mass of sample(s) 38.47 1.14 Volume of sample(s) 0.489 0.001 Formula for density Density (SI units) Density (US units) 4. Do your results support the manufacturer’s claim that the ruler is made of aluminum? Justify your answer. (Refer to the Common Materials Density and Uses chart.) 5. Are the paper clips made from the same material as the ruler? How do you know? No. The densities of the two objects aren’t the same. Conclusion 1. How can you use density to identify a material? After finding the density of the object, you compare it to the known list of densities. For example, aluminum has a density of 2.70 and if your object has that density, your object © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 11 is made of aluminum. 2. What are limitations of the calculated and indirect volume measurement? Calculated measurement can only be used for simple shape like a cube or sphere since the sides are measured. Indirect volume measurement can only be used on objects small enough to fit in a graduated cylinder and would have to be able to be submerged underwater. 3. Explain the difference between weight and mass. Weight is the measurement of the pull of gravity on an object while mass is the amount of matter the object contains. © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 12