Download Volume Displacement Introduction - RIT

Volume Displacement
Introduction:
Archimedes was a Greek mathematician, inventor and physicist who
lived from 287 - 212 B.C. A king once gave him a difficult task. The
king had a crown. He had paid for pure gold. He was afraid that the
crown-maker had mixed silver with the gold. He wanted Archimedes to
find out if the crown was pure gold, or gold mixed with silver.
Archimedes knew that all he had to do was to figure out the density of
the metal. Silver's specific gravity is 10.5 and the specific gravity of
gold is 19.3. It should be easy to detect the
difference. There was a serious problem,
though. Archimedes needed the mass of the
crown and the volume of the crown. The mass
was easy to measure. The problem was to
determine the volume of the crown. The king did
not want Archimedes to harm the crown in any
way. How could Archimedes calculate the
volume of a crown?
Archimedes went home to think about the
problem. He filled his bathtub with water and
stepped in. He watched the water rise and
overflow onto the floor when he sat. Suddenly,
his problem was solved! The story tells that he
ran out into the street, naked and dripping, shouting "Eureka!", which
means "I have found it!"
What did he find?
When an object is submerged in water, the
level of the water rises. This is because the
object has moved some of the water out of
the way, to make room for itself. (This is
called displacement. The object displaces
water. When Archimedes sat down in his
bathtub, his body took up so much room that
the water overflowed onto the floor. He
realized that the water that he pushed out of
the tub was the same volume as his body.
If he submerged the crown in water, he could
measure the volume of the crown. It was easy to measure the mass of
the crown. He could compare the volume of the crown to the volume
of an equal mass of pure gold. If the volume of the crown was greater
than the volume of the pure gold, then the crown was a fake.
We will test to see if Archimedes' idea was correct.
Purpose: This experiment will test
1. to see if an object displaces its own volume when submerged.
2. to determine the volume of a small number of marble chips and
find the density of marble. We will compare the density that we
calculate with the known density.
Equipment: two graduated cylinders (one 100 ml and one 10 ml),
water, vernier calipers, three regularly-shaped objects, a small
quantity of marble chips, a scale.
Method:
Part I.
1. Calculate the volumes of the three regularly-shaped
objects.
o You will have to measure the objects
with the vernier calipers. Write the
measurements in a table
2. Choose a graduated cylinder.
o Remember that a graduated cylinder
shows you the volume of the liquid in it.
o Make sure that the objects will fit into
it.
o Partially fill it with water.
o Write down the level of the water in the cylinder. (Measure
at the bottom of the meniscus. The meniscus is the bottom
of the curved surface of the water.)
3. Lower the object into the water slowly.
4. Write down the new level of the water in the cylinder.
5. Subtract the first level of water (from step 2) from the second
level (from step 4)
6. Write down the difference in the water levels.
o This difference is called the change of volume of the water.
3
o Remember that a ml is a cm . The markings on the
graduated cylinder tell you the volume of the water.
7. Compare the change in volume of the water to the volume
of the object.
8. Record your results in a table:
Object
Volume Of
Object
Volume Of
Water In
Graduated
Cylinder
New
Volume Of
Water In
Graduated
Cylinder
Amount Of
Change In
Volume Of
Water
Answer these questions:
Question 1: Compare the change in the volume of the water to the
volume of the object. Are they the same?
Question 2: Suppose you drop an irregular object (an object with no
simple shape, like a rock) into the graduated cylinder. The water rises
25.3 ml. What is the volume of the irregular object?
Part II.
1.
2.
3.
4.
5.
6.
Measure the mass of your marble chips.
Partially fill the smallest graduated cylinder.
Write down the volume of water in the cylinder.
Drop the chips into the cylinder.
Write down the new volume of the water in the cylinder.
Subtract the beginning volume from the second volume.
o This is the change of the water's volume.
o in Part I, you learned that the change of the water's
volume is equal to the volume of the object.
7. Write down the volume of the marble chips.
8. Calculate the density of marble.
9. Calculate the specific gravity of marble.
10.
The accepted specific gravity of marble is 2.6.
Compare the specific gravity of your marble chips to the
accepted specific gravity of marble. Is it the same or
different?
Volume
Of
Water
In
Cylinder
Volume Difference Volume
Of
In
Of
Water
Volume
Marble
+
Chips
Marble
Chips
Mass
Of
Marble
Chips
Density
Of
Marble
Chips
Specific
Gravity
Of
Marble
Chips
Answer these questions:
Question 3: The marble chips displaced water. We assumed that the
amount of displaced water was equal to the volume of the chips. If this
assumption had been incorrect, would you have gotten the correct
specific gravity for marble? Why or why not?
Question 4: What can you conclude about the displacement method for
determining the volume of an irregular object?