Density - Qualitative and Quantitative 

Bahner, Stan                         Whitney Young High School
                                     997-3739
                          

Objectives: (In the words of the student)
I will define density in words and mathematically. 

I will measure the mass and volume of three objects and calculate the 
density of the material in each. 

Apparatus Needed
1. six film containers filled with materials having a range of 
    densities. (For example: loose tissue paper. bits of styrofoam torn 
    from a styrofoam cup, saw dust, sand, small nails packed tight, 
    quarters packed tight). Label the containers a, b, c, d, e and f. 
2. six larger sized objects covering a range of densities. 
    Label the objects A, B, C, D, E and F.
    a brick
    a good sized chunk of lead or steel (tennis ball sized to baseball sized)
    a full gallon container of ditto fluid, paint thinner, or antifreeze
    a gallon milk container filled with water
    a two liter pop bottle filled with water 
    a foot long piece of 2x4 lumber
3. geometric objects having a range of densities 
    (cubes, rectangles, triangles, cylinders, trapezoids made of oak, 
    walnut, pine, maple, birch, plastic, aluminum, brass, etc.) 
    Some of the objects have holes drilled in them.
4. plastic game pieces from a Superfection game that have been filled 
    with plaster mixed with lead bb's to make a range of densities.       
    These were then sealed with polyurethane floor sealer. Thus they 
    can be immersed in water and their volumes determined using 
    Archimedes principle. 
5. telescoping pair of boxes cut from bottoms of two half-gallon  
    orange juice containers
6. rulers
7. calculators
8. balances (Cent-o-gram single pan preferred)
9. (if you wish to use Archimedes' method to have students check their 
   calculated volumes.) 
   a. 250 ml beakers
   b. thread or kite string
Recommended Strategies
Set-up:  Arrange the apparatus on lab tables.   
Pre-lab: Discuss the need for a term "density" in addition to the term 
"heavy".  Common usage lets the word "heavy" have both meanings.  For 
example when handed a brick and then a smaller but heavier piece of 
iron or lead, one typically says "Wow! That's really heavy" It would be 
more precise to say "Wow! That's really dense." Students shouldn't be 
encouraged to use this odd sounding usage but only to recognize the 
difference between the two meanings which "heavy" commonly has and to 
be able to use the term density as a synonym of one of the meanings. 
    Discuss the trick question "Which is heavier, a pound of feathers 
or a pound of steel?"  Use the various objects to discuss "density".  
Use the telescoping juice container halves to explain that when you 
push them together the same mass is in a smaller volume and thus the 
density increases. Explain that floating is best explained using the 
term density. Objects less dense than water float.  Helium is less 
dense than air and thus helium filled balloons float. 
    Define density as mass divided by volume, D = M/V. Give the   
formulas for the volume of a rectangular solid [v = l x w x h], solid 
triangle [(v = 1/2 b x h)T] (T = thickness), cylinder V = 3.14 r2l.
(pi times the radius squared times length.) Explain that when you use 
metric units the density of water comes out to be 1.0 g/cm2. Thus water 
is the standard of density against which other substances are measured. 
    Discuss strategies for obtaining the volume of a complex geometric 
object.  For example a wood trapezoid with a hole drilled in it can be 
seen as a rectangular solid plus a triangular solid minus a cylinder.  
By measuring the dimensions of the object and using the formulas, the 
volume can be calculated. 
    If you wish to have the students check their calculated volumes by 
the Archimedes' method set up a balance and 250 beaker with object 
suspended in water on a string.  The Cent-o-gram single pan balances 
have a solid platform under the weighing pan which can be raised for 
this purpose. Also there is a double hook above for the string. If you 
are using double pan balances you will have to suspend the object from 
a ring stand. Explain Archimedes' principle, EUREKA story, etc. and how 
the buoyant force is equal to the volume. (Many students already know 
the Eureka story about the king's crown. Ask a student to tell the 
story.)                                                    
Student activities: 
1. Have students rank the film containers putting the most dense first.  
   Use the form Da>Dd>Dc, etc. 
2. Have the students rank the larger objects putting the most dense 
   first. Since there are two different size containers of water, it 
   should help drive home the point to the students that density is a 
   property of the substance.  Therefore they can put an = between 
   the two water containers rather than a ">" symbol. 
   (You may wish to have students experience the density of mercury by 
   having them lift a bottle of mercury. The density of mercury is 
   VERY SURPRISING and students have a tendency to let their hand 
   drop if you hand it to them. You must have a GUARANTEED SECURE way 
   to assure that the mercury won't be spilled.  Make sure the mercury 
   is in a strong unbreakable bottle. It is usually supplied in thick 
   plastic bottles. Try tying the bottle to a lab table (to the gas 
   pipe, etc.) with a short rope. Sit next to the bottle and directly 
   supervise the students coming one by one to lift it from the 
   table.  As soon as each student has experienced the density of 
   mercury put the bottle away in a carrying case and put it away for 
   proper storage.) 
3. Have each student choose two simple geometric shapes and a complex 
   geometric shape to calculate the volume for each.  Measure 
   dimensions to the nearest 0.1 cm. Mass the object and calculate the
   density.
4. Have students check their volume calculations by comparison to the 
   volume measured by the Archimedes method.