Density and Shape
Name: Lori S.
The science teacher I teach with and I are having a
misunderstanding of the word density. We are doing a clay boat activity,
and he says that if you change the shape or volume of the boat, you are
changing the density and that is why is floats. I say that the density
of an object can't be changed, because that is a property specific to that
object and that by changing the shape, you are helping it to become more
He is using the Cartesian diver experiment to support his
thoughts. I agree in that case you are changing the density because you
are exchanging amounts of air and water, therefore changing the density.
Please help! We want to make sure we are giving our students the
The dispute is one of semantics. Your version of "density" is correct --
density (m/V) is a property of a "substance" that is independent of the
shape or volume of the "substance." In other words, the density of the clay
from which you fashion the boats is constant and a property of the clay
Start with a fixed volume of clay -- for convenience, use a block shape
whose dimensions can be easily measured. Calculate its volume and then
determine its mass. Calculate its density -- d = m/V. The value you obtain
will remain the same no matter how you change the shape of the clay. You can
prove this by making various shaped "boats" of the same piece of clay and
then SINK the boats in water so that no air is trapped inside the boat.
You will note that the volume of water displaced by any and all shapes of the
same piece of clay will remain the same.
However, if you place the boats on the water so that they float, each and
every shape will settle to a depth that represents a volume of water equal
to the weight of the shape being tested. Archimedes Principle states that a
body wholly or partially immersed in a fluid will displace a volume of fluid
equal to the weight of the object.
Thus, the boat experiment is not really measuring the density of clay.
Rather, it is measuring the buoyancy of a "shape" fashioned of clay.
The density of the clay remains the same. The average density of the clay
and the air contained within the boat can change with shape. Neither is the
true test of buoyancy. The buoyant force equals the weight of the water
displaced by the boat. If an object is solid and uniform, made of only one
material, then density can be used to test buoyancy. As soon as a second
material enters into the picture (the air inside the boat), density ceases
If the boat can displace more Newtons (or pounds) of water than the boat
weighs, then the boat can float. The water pushes upward on the boat just
as hard as gravity pulls down on the boat. The net force on the boat is
zero, so the boat is not pulled down by gravity.
If the boat cannot displace enough Newtons of water, the upward buoyant
force of the water pushing on the boat can never be as large as the force of
gravity pulling down on the boat. With the downward force always larger
than the upward force, the boat is pulled downward into the water. The boat
Dr. Ken Mellendorf
Illinois Central College
Yes, in the Cartesian diver experiment you are changing the density of
the float because you are compressing the air in the float. In this case
the material of the float is essentially the air inside it. The dropper
adds weight but does not directly control the amount of water displaced.
To test this hypothesis, perform the Cartesian diver experiment with
the dropper sealed so that the water level within the dropper cannot
change. Does it still work?
With the boat you are not changing density -- the density of the
materials the boat are made of are fixed. You are just changing the
shape so that more (or less) water is displaced when the boat is placed
in the water upright. Try filling the boat up with water & see if it
still floats. If the density had changed, it would.
Density is mass divided by displaced volume. Mass is usually determined
by weighing an object. One way to determine displaced volume is to let
water get into all possible places within the object -- i.e., hold it
underwater until it is filled with water. This includes filling all
chambers within the object. Then determine how much water has been
It is a case of object versus material. Yes, density is characteristic of a
given material at defined temperature and pressure conditions (ranges). Yes,
an object is buoyant because its overall density is lower than the medium
it displaces. This often occurs object is constructed with a large volume
with little additional mass (lots of air or vacuum space). But the
materials that make-up a floating object have not changed their density. I
hope this helps.
I think this is a case when you just have to define carefully
what you are talking about. If by density you mean, as is
common, the total mass of an object divided by its total volume,
then you are clearly changing the density when you change the
shape. Of course, with an open-topped boat, volume is not well
defined so you can have endless arguments. Perhaps most
interesting is the density of the part of the boat that displaces
water. That density must be sufficiently less than the density
of water that the water supplies a buoyant force equal to the
total weight of the boat.
Most importantly, the entire boat must have a density less than
water or it will sink!
Perhaps the concept of average density might be useful, where
average density is the average of the density of the clay and the
air inside the boat.
Best, Dick Plano, Prof. of Physics emeritus, Rutgers University
He is talking about the average density of a submerged volume, and you would
like to distinguish the material from the air it encloses. Which idea
is more useful depends on the material. Suppose you have a loaf of bread.
Do you consider the air spaces in your notion of density, or do you say
that the dough has one density, the air has another, and it is the way the
dough is arranged that makes it float? In this case, I would say it makes
sense to talk about average density. In the case of a boat, or a hollow
sphere, I'd say average density is not as useful an idea, because the
average density of the submerged volume will change as you push the object
down into the water. The idea may still be valid, but it does not simplify
this problem, so I would just chuck it.
This is the usual case in science: you want to look at things from the
viewpoint in which they are as simple as they can be. You do not want to
hang onto a viewpoint simply because it made the last problem simple, or
because it's esthetically pleasing, or because it's the only one you
already know how to apply. The choice of viewpoint is important, but
it's not fundamental.
Anyway, it does not matter in explaining why things float. The total
downward force is the weight of the object, and the total upward force is
the weight of the water displaced.
The law of bouncy, Archimedes' Principle, states that an object (in a
gravitational field) is subject to a force in the opposite direction that is
equal to the weight of the volume of the surrounding medium displaced by the
object. You are correct that density is a property of the material, provided
you don't do any "tricks" like turning styrene polymer into Polystyrene foam by
foaming it up. So you can make an aluminum foil "boat" by making a dish that
will float, but crumple it up in a ball and it sinks. What happens to the
"diver" is that you increase the volume of displaced water by forming a
bubble -- a very efficient way to do that and yes the "average" density of
the diver + bubble is smaller, but the real operative factor is the increase
in the amount of water displaced by the diver + bubble compared to the diver
Well, in some ways you are both correct, but I would say you are "more
correct" (if such a term exists). Density IS a function of
temperature. But in this case with your boat experiment, you are not
changing the density. You are changing the buoyancy of the clay in order
for it to float. Anything can float (see an aircraft carrier for example)
in water if the forces of the water pushing "up" the item are greater than
the weight of the item and the atmospheric pressure pushing down on it.
Hope this helps,
Strictly speaking, you are both correct. It is just a matter of what you
mean by "density." Your students will get the correct idea if they
understand what is going on instead of just worrying about how words are
An object floats or sinks in water because of the difference between the
weight of the water it displaces and the weight of the object itself. If
the water weighs more, the object floats in water; if the object weighs
more, it sinks in water.
A Cartesian diver and a boat float in exactly the same way: they trap air
below the surface of the water, so that the water they displace weighs more
than they do. The only difference is that the air in a boat is "in
communication" with the atmosphere, while in a Cartesian diver it is held
separate. Either way, the AVERAGE density of (object + air) is less than
the density of water. The density of the object by itself, not counting the
air, is greater than the density of water.
So, when you re-shape an object so that it can hold air underwater, does
that change its density? Yes, if you count the volume of the object plus
the air. No, if you disregard the volume. But what matters to the water is
the (object + air) volume and weight. THAT determines whether it sinks or
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
Sorry Lori, I am on the side of your science teacher compatriot. One of the
tricks of science is to take a variable to the extreme and see what effect
that has. Make a boat of the clay and float it. That means the density
must me less than 1 g/cm3. So far so good?
Then smash the clay into a ball and place it in the water. I will bet it
sinks... meaning a density of greater than 1 g/cm3. Why? Has the density
of the clay changed? No. But the density of the boat has because the
boat's density is affected by the air inside the boat.
Steel sinks. Steel battle ships float... because they have air inside.
Hope that helps.
Density is a characteristic physical property of a substance and can not be
changed. Because this is so, we can use density to identify one substance
from another. When you a build a boat from a wad of clay you are not
changing the density of the clay. The clay if pushed under the surface
would sink to the bottom of the container, just like the original wad. What
you are doing, is changing the surface area that is in contact with the
water. An object is buoyed up by a force equal to the to the weight of the
volume of fluid it displaces. If you make the boat with thin walls of clay
that cover a large surface, you are increasing the volume of water displaced
and therefore the buoyant force that holds the boat up. That is why you can
get a big iron ore carrier to float. The amount of water it is pushing out
of the way is still greater than its total weight, so the boat floats. But
get water in the hold and that is another matter.
Now if you look at something like a submarine, you are using a "net"
density, if you will, to make the sub rise and fall. As the boat takes on
ballast water the total or "net' density is changed. In other words, you are
adding more stuff, (water), inside the hull of the sub. The sub overall
volume does not change but the mass increases with the addition of water to
the ballast tanks. So this effectively changes the density. Please, please.
be very careful when you teach this. Density DOES NOT CHANGE, the sub thing
is caused by the addition of water which increases the mass. Do not let the
kids think the steel has a density change.
You did not say what grade level you taught, so I guess I am just being a
little over careful.
Changing the shape of the clay boat changes the amount of water that is
displaced making it buoyant. The density remains the same.
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Update: June 2012