BRANDON FORREST AND HAYVON LEE
Activity 5.3 Determining Density 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. Delrin Mass/weight of 10 samples (include units)
Mass (SI)
Average mass/weight of a single sample (include units)
Mass (SI)
Weight (US)
Steel Mass (SI)
0.00232 units Weight (US)
Weight (US)
Wood Mass (SI)
0.03469 units Mass (SI)
Weight (US)
Weight (US) 0.00266 units
Mass (SI)
Weight (US)
© 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 1
2. 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
Steel (diameter)
4/3 pi r3
4/3 pi r3
.5
.5
Wood (wdh) wdh
(sphere or rectangular prism, as appropriate)
Measurement #1
Calculate volume
65.4498
65.4498
.5
.5
W
D
H
.485
.47
.5
0.113975
(Show all steps including units) Measurement #2
Calculate volume
65.4498
65.4498
.5
.5
W
D
H
.53
.48
.48
0.122112
(Show all steps including units) Measurement #3
Calculate volume
W
D
H
.53
.485
.48
65.4498
65.4498
0.123384
65.4498
65.4498
0.119824
(Show all steps including units) Calculate average of three volume measurements (Show all steps including units)
© 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 2
3. 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
0.00232
0.03496
0.00278
Average of three volume measurements
65.4498
65.4498
0.119824
Formula for density
Dw= W/V
Dw= W/V
Dw= W/V
Calculate density
0.000035447014353
0.000534149836974
0.023200694351716
Formula to convert from SI to US system or from US to SI system
1 lb = 4.44822162 N
1 lb = 4.44822162 N
1 lb = 4.44822162 N
1 N = 0.225
1 N = 0.225
1 N = 0.225
Convert density from SI to US system or from US to SI System
14.726205
14.726205
0.0269604
(Show all steps including units)
(Show all steps including units) 4. 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 values? Manufacturing errors
© 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 3
5. (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 Units
Steel
Wood Units
Units
Mass of 3 samples Mass Average Volume of sample Density (SI) Density (US) 6. 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?
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? No the wheels are rubber and the people are made of plastic 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 4
Automoblox People
Total mass/weight of all sample(s)
0.486
Automoblox Wheels
.0652
(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 Water level without samples (Include units) Water level with samples (Include units) Water volume displaced = volume of sample(s) (Show calculations)
170 192 22
Automoblox Wheels
N/A N/A N/A
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. © 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 5
Automoblox People
Automoblox Wheels
Total mass/weight of sample(s)
22.1
29.6
Volume of sample(s)
22
N /A
Formula for density
Dw= W/V
Dw= W/V
Density (SI)
2.3
N/A
Density (US)
0.00508
N/A
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
Paper Clips
Total mass of sample(s) 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 water.] Show all measurements if using the indirect measurement. Sketch the object if using the calculation method.
© 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 6
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) Volume of sample(s) 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?
Conclusion 1. How can you use density to identify a material?
2. What are limitations of the calculated and indirect volume measurement?
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3. Explain the difference between weight and mass.
© 2012 Project Lead The Way, Inc. Introduction to Engineering Design Activity 5.3 Determining Density – Page 8
