Shape Change and Density
Date: Fall 2009
Why does changing the shape of an object have no effect
on the density of that object?
In a uniform, unchanging material, density is a measure of how much mass
there is per unit volume of the material. Density is an "intrinsic"
property of the material, which means it's not affected by changes in
the amount of the material. You can add, remove, or reshape the material
all you want, and its density will be unaffected. If the material is *not*
constant (like if you squished bread), then changing shape may change the
Hope this helps,
Density is a measure of the amount of mass (weight) that exists in a given volume.
Mathematically, density equals mass divided by volume. Density is commonly reported
in grams per cubic centimeter.
Volume is reported in units of cubic length (that is, cubic feet, cubic centimeters,
cubic meters…). One could easily define objects that have different shapes, yet
similar volumes. Consider, for example, a right rectangular prism that measures 5
(long) x 5 (wide) x 4 (height); this object has 100 cubic units of volume. An
object that measures 10 (long) x 10 (wide) x 1 (height) also has 100 cubic units
of volume. The two units have different shapes, yet equivalent volumes. If the same
mass (weight) of material exists in each of the two objects, then the density would
be the same in each object. Density is independent of shape.
The equation for density is a ratio, so density does not depend on the size of the
material under study, only the ratio between the objects mass and its volume.
Certainly a larger object will weigh more, but it will also have a larger volume.
Think about this: How can two objects of similar volumes have different densities?
I suppose it makes a difference how the shape of the object is changed.
Let us imagine the object is a lead brick. If the shape is changed
by cutting off a piece of the brick, the density of the pieces is the
same as the density of the original brick. However, if the lead
brick is compressed in a powerful vise in order to change its
volume, the same mass is being forced to occupy a smaller volume,
which therefore causes its density to increase.
There are two basic values that control what the density is: mass
(the amount of stuff), and volume (how much space the amount of stuff takes).
Now imagine a sample of water. Whether that water is in a tall, thin
container (such as a glass) or in a flat, wide container (such as a
bowl) - the amount of stuff (the mass) has not changed, you still
have the same quantity of water. Also, the volume has not changed,
whether the 1 cup of water is in a glass or in a bowl, does not
change the fact that there is 1 cup of water. So since the mass and
the volume has not changed, and since mass and volume are the only
two factors in determining density, then the density has not changed.
Having said that, there is a "change of shape" that does change
density. Imagine a sponge (like the kind used to wash dishes). If
the sponge is squeezed it takes up less volume, even if the mass
(the amount of sponge) has not changed. So in this case, the change
in shape did cause a change in density. BUT, it does so because the
air pockets in the sponge has been squeezed out, if you just
consider the actual plastic that makes up the sponge - without
considering the air pockets in the sponge, then the volume occupied
by just the plastic has not changed. So while the sponge object
changed in density with the squeezing, the plastic in the sponge has not.
Greg (Roberto Gregorius)
The units of "density" is "mass" per "volume". Assuming the object is
uniform, at rest,
Mass = Density x Volume. So the increase (or decrease) in the Volume of the
object results in a proportional corresponding change in the Mass of the
object. There are of course ways to "trick" the object, e.g. changing the
temperature, applied pressure and the like, but in the "simple" case the
Mass and Volume will vary in the same proportion.
Density is the amount of matter in the space an object takes up
(called its volume).
Unless a body changes volume or the amount of matter changes, its
density stays the same.
R. W. "Bob" Avakian
B.S. Earth Sciences; M.S. Geophysics
Oklahoma State Univ. Inst. of Technology
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Update: June 2012