Purpose
To experimentally investigate the concept of density using several different materials.
Preliminary Questions
1. Explain what the term "volume" means in science.
2. Explain what the term "mass" means in science.
3. You buy a box of crackers. Your friend buys two boxes of crackers. Compare the mass of the two purchases. Compare the volume of the two purchases.
4. You buy a gallon of milk. Your friend buys half a gallon of milk. Compare the mass of the two purchases. Compare the volume of the two purchases.
5. Explain what the term "density" means in science.
6. Compare the density of the crackers purchases in question 3.
7. Compare the density of the milk purchases in question 4.
8. Consider a rigid gas tank and its contents. Initially it is full. Later is it half filled with gasoline. Eventually it is empty of gasoline. Compare the mass, volume and density of the total tank contents in the three cases. Then, compare the values for the gasoline only.
9. Explain how the mass, volume, and density of a material will change as material is added and removed under constant temperature and pressure conditions.
10. Someone has 1.00 kg of water. It occupies a volume of 1.00 l (liters). The person drinks some of the water. The new volume of water is 0.25 l. What is the mass of water left?
Suggested Apparati
Wood blocks, glass spheres (marbles), metal cylinders, irregular shaped objects, meter sticks, strings, balances, cups, paper towels, and graduated cylinders (be careful about breakage)
Suggested Procedure
A. For each object you are given find the mass in grams and measure all the dimensions needed to calculate the volume and/or measure the volume by displacement. Be sure to record each measurement with appropriate significant figures and units. Use a data table to record this information.
B. Determine the volume in cm3 (cc) and the measured density for each object. Add this information to the data table.
Sample Data Table
|
Description |
Mass (g) |
Length or radius (cm) |
Height (cm) |
Width (cm) |
|
Volume (cm3) |
Density (g/cm3) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Useful Information
Volume Formulas:
Vblock = (length)(width)(height)
Vcylinder = (p)(radius)2(height)
Vsphere = (4/3)(p)(radius)3
1 cc = 1 cm3 = 1 ml = 1.0 g of water under room conditions
Accepted densities () of some common materials:
Al = 2.7 Fe = 7.9 Pb = 11.3 Alcohol = 0.8 Glass - Crown = 2.5 - 2.7 Pine Wood = 0.35 - 0.5 Brass = 8.4 Glass - Flint = 3.0 - 3.6 Sn = 7.3 Cu = 8.9 H20= 1.0 Zn = 7.1
Follow Up Questions:
1. Does the density of a material depend on the size or shape of the object of which it is made?
2. One cm3 of gold weights more than one cm3 of aluminum. Which of these will displace more water when completely submerged? Explain.
3. Explain how, if at all, density, mass, and volume measures will be different if the object is solid or hollow.
4. In ancient Greece, the king had a new crown made of solid gold. Rumors spread that the jeweler filled the inside of the crown with a cheaper metal, e. g., lead, and kept most of the gold. The king told Archimedes to determine if the jeweler had stolen the gold without damaging the crown. The story goes that Archimedes discovered how to solve the problem while getting into a full bath. The solution is related to the concept of density. Explain how he determined if the jeweler was thief. (The story says the jeweler did steal from the king.)
5. Twenty thousand (20,000) tons of water are displaced by a ship. What volume of water is displaced?
6. A particular car contains approximately 2500 kg of steel (iron). What volume would this steel occupy if solid?
7. A particular glass company uses 32.5 grams of glass which occupies a volume of 9.00 cm3 for each cup. How much glass is needed to make 50 cups? 100 cups? How many cups can be made from 1.00 m3 of glass?
8. A person measures 10 pennies getting the data shown below. The masses were measured on a triple beam balance. The thickness is the average of measurements at the head and to the left and right of the head, avoiding the rim. The diameter is the average of the diameter parallel and perpendicular to the face vertical. Is possible these pennies are solid copper?
|
Year |
Mass (g) |
Thickness (cm) |
Diameter (cm) |
Year |
Mass (g) |
Thickness (cm) |
Diameter (cm) |
|
|
1960D |
3.10 |
0.139 |
1.99 |
1993D |
2.52 |
0.128 |
2.03 |
|
|
1980 |
3.07 |
0.133 |
1.96 |
1995 |
2.53 |
0.134 |
2.03 |
|
|
1980 |
3.09 |
0.132 |
1.97 |
1996 |
2.54 |
0.134 |
2.06 |
|
|
1982 |
3.12 |
0.136 |
1.96 |
1998 |
2.51 |
0.136 |
2.03 |
|
|
1983 |
2.54 |
0.137 |
2.01 |
2000 |
2.53 |
0.132 |
2.02 |
9. During World War II some pennies were made out of zinc due to copper shortages. What would the mass of one zinc penny be (use data given in problem 8 as needed)?
10. A person is approximately 70% water. Estimate the density of a typical person giving you reasoning.
11. Density actually depends upon temperature. How would the properties of density, mass, and volume tend to change with temperature? Is ice compared to water consistent with this trend (explain)?
12. What is the difference between mass density and weight density?
13. How does a physicist define the mass of an object and the weight of an object? What factors can change the mass or weight of an object?
14. Is the weight of an object proportional to its mass? What is the proportional constant if it exists? Explain.