Transcript Density of an Irregular Solid Object

Density of an Irregular Solid
Object
Water Displacement
Let’s Review
• We already know how to calculate
the density of any system.
• We simply use the density
equation or refer to the density
pyramid.
mass
mass
Density =
volume
Density
volume
To Practice:
A solid object has a mass
of 180 grams and a volume
of 45 cubic centimeters.
What is the density of this
object?
Mass = 180 grams
Volume = 45 cubic centimeters
Using the “Pyramid”:
mass
Density =
volume
mass
=
180 grams
45 cm3
Density
volume
=
4.0 grams/cm3
But what if the object does not
have a nice geometric shape?
height
?
length
Easy to calculate
the volume here !!
How do you find the
volume of a solid object
that does not have
convenient length, width,
and height ??
The answer is:
Water Displacement !!!
Fact of Life: A solid object will displace (means pushes out of
the way) a volume of water exactly equal to the volume of
the object itself. (This will be true for any liquid – not just
water…)
• Mass of the object has nothing to do with this.
• Shape of the object has nothing to do with this.
• Only the volume of the object determines how much water
is displaced.
This is why the water rises when you get into the bath tub…
How does this work?
We fill a graduated
cylinder half full of water.
This original volume of
the water is called the
initial volume = Vi
Remember that we read the bottom
of the “meniscus” in a graduated
cylinder to know the volume of the
liquid.
Next:
We add the solid object to
the graduated cylinder. As
expected, the water level
rises. The volume of the
water after the object has
been added is called the final
volume = Vf
Remember – this
first volume was the
initial volume.
Now to calculate:
The difference between the
initial volume and the final
volume is called “delta V”.
You can easily determine
its value by subtraction.
We write “delta V” like this:
Vf
ΔV
Vi
So…
If an irregular solid object is placed into a graduated
cylinder that contains 50.0 ml of water and the water level
rises to a final reading of 75.0 ml, we can calculate the Δ V
is 75.0 – 50.0 = 25.0 ml.
Vf = 75.0 ml
ΔV = 75.0mL – 50.0mL
Vi = 50.0 ml
= 25.0 ml
Here’s the cool part:
It is a “fact of life” in nature that a liquid volume of 1.0 ml is
exactly equal to (and therefore interchangeable with) a
solid volume of 1.0 cubic centimeter.
So… if the object causes a change in the water volume
equal to 25.0 ml, the volume of the object must be exactly
25.0 cm3.
Remember, we describe the volumes of solids in cubic centimeters…
Now to connect to density
problems:
Remember that density is
still equal to mass divided by
volume. That equation does
not care how you get the
volume of the object – it will
work for both regular and
irregular solid objects.
mass
Density
Δ V is the volume of the object !!
volume