Students generally find it difficult to distinguish between
mass/weight and density. That should not surprise us since the
same terms are commonly used to describe both the property of
mass/weight and the property of density, "heavy" and
"light". As in the frequently statement, "Water is heavier
than air." I use this inquiry demonstration to help students
develop a conceptual understanding of the difference to go along with
memorized definitions. I do this after we have some lessons on
density.
Theory:
When comparing the masses/weights of two objects we use the relative
terms "heavier" and "lighter". When comparing the densities of
two objects we use the relative terms "heavier" and "lighter".
While all students have experiential knowledge of the different uses,
they have not consciously distinguished between them. This
activity should draw out, from at least one student, a verbal
explanation of different uses of "lighter".
Preparation:
Equipment: A triple beam balance (or other
devise for measuring mass or weight), a large beaker (or other
transparent container) containing water, and three balls as described
below.
Get three balls, wherever you can find them which have the
correct relative properties. The three I used were as follows
(though I don't remember the exact masses, it is relative mass that
counts).
A. golf ball, painted gray, mass = 76g
B. cork ball (softball size), painted black, mass =
115g
C. density sphere (designed to have a density of
1g/cm3, it floats in cold water,
sinks in warm), painted white, mass = 140g
Line the balls up where they can easily be seen by each student, and
label them A, B, and C.
Performance:
Teacher: Class! Please observe these three objects
carefully (pointing) A, B, C. I will give you a few seconds to
think about it.
(pause)
Now I'm going to ask you a fairly simple question. Which of these
objects is the lightest? (Call on any student.)
Student: A! (Or another it doesn't matter.)
T: How many think A is lighter? Hands please.
How many think B is lighter?
How many think C is lighter?
How many don't know? I know this is unusual for this class, but
I'm going to ask you to guess, even if you have no idea which is
correct. So, of those who haven't already indicated, how many
guess C? B? A?
A most amazing thing has just happened! For the first time in
history, every student in this class has given a correct answer to the
same
question! Congratulations!
(After order is restored.)
I say it is a fact, (writing on the overhead) A is lighter than B and B
is lighter than C. It is a fact, B is lighter than C and C is
lighter than A. It is a fact, C is lighter than A and A is
lighter than B. So, every answer is correct!
What! You still don't believe me?
Who said A was lightest? Ok, John, explain why you think object A
is lighter than the others.
S: Because it's smallest.
T: Why would being smaller make it lighter?
S: Because it weighs less.
T: Are you saying that, "A weighs less than B and B weighs less
than C?"
S: Yes.
T: How can we find out if that is true?
S: Weigh them.
T: All right, I have a triple beam balance here. So, I will
measure their masses. Since weight is proportional to mass, the
result will be the same.
(If I used a spring balance, I would make it clear
that I was measuring weight, not mass.)
(measure and record the mass of each object on the overhead.)
T: So, is A lighter than B and B lighter than C?
S: Yes.
T: True. But! here it says (pointing) that C is lighter
than A
and A is lighter than B. How can that be true?
(It may take a few minutes.)
S: C is white. And white is lighter than gray, and gray is
lighter than black.
T: Very good Sue. Does everyone see that even though we
were using the same words, we were comparing different
properties? First we were comparing the objects by their masses,
now we are comparing the objects by their brightness, the amount of
light they reflect. White reflects the most light, and so is
lightest.
Any questions about that?
One problem remains, it says here (pointing) that B is lighter than C
and C is
lighter than A. What property are we comparing here?
(After some time to think, some classes may require hints.)
Hint: What property of matter have just studied in the book?
S: Density.
T: all right, so how can we compare their densities?
S: (If your lucky.) We would have to measure the volume of each object,
and then divide it by the mass.
T: Very good. But I'm going to use a quick and dirty method that
wouldn't work with just any set of objects. I'm going to compare
the density of each object with the density of water. (Placing
the beaker with water front and center.) How do you suppose I'm
going to do that?
S: (maybe) Put it in the water and see if it floats.
T: How very perceptive of you. (Place B in the
beaker.) How does the density of B compare to the density
of water?
S: It's lighter, it floats.
T: (Place C gently in the beaker.) And how does the density of C
compare to the density of water?
S: It sort'o floats.
T: Yes, the density of this object is very close to the density
of water, so if I place it near the top, it should stay at the top, if
I place it at the bottom, it should stay there. So, is B lighter
than C?
S: Yes.
T: Now for A. (Place object A in the beaker.) How does the
density of object A compare to the density of water?
S: It's heavier than water, it sinks.
T: So now, was I right? Is B lighter than C and C lighter
than A?
S: Yes.
T: Then we have proved that each of these three statements
(Pointing to the on the overhead.) is true. But each statement is
true only in relation to one of the properties of the objects.
Let's take a minute or two to think. Are there any questions or
confusions about what we've done? Could you explain it to your
parents?
...
T: In conclusion. We often use the same words with
different meanings. In this example it is necessary to know which
property of matter we are discussing, Earlier it was said that
object A is heavier than water. A has a mass of 76g, and the
water in this beaker has a mass of 800g. So how can 76g be
heavier than 800g? To avoid confusion it would have been better
to say, "Object A is more dense the water, so it sinks. Object B
is less dense than water so it floats."
