Archimedes' Block - Janica Henzie
Author
Janica Henzie - John Muir Middle School, Burbank, CA
Principles
Density, Displacement, Buoyancy
Standards
Grade 8: Density and Buoyancy
8a. Students know density is mass per unit volume.
8c. Students know the buoyant force on an object in a fluid is an upward force equal to the weight of the fluid the object has displaced.
Materials needed
Archimedes' Block, spring scale, 5g and 10g masses, container to hold Archimedes' Block, water, string, optional solutions of other densities (i.e., salt water, alcohol, etc)
Procedure
Density:
Determine the mass of the block. (m = 25 g)
Determine the volume of the block: count the number of centimeter squares along one edge of a length, width and height of the block and then multiply these three numbers together. (V = 100 cm3)
Determine the density of the block. (D = 0.25 g/cm3)
Tell students the density of water is 1 g/cm3. Have students predict how far the block will sink when it is placed in a container of water.
Prove/disprove the guesses by placing the block in water and observing how much of the grid design is submerged. (one fourth of its volume should submerge under water)
Place two 10 g masses and one 5 g mass inside the block so that the total mass of the block is 50 g.
Determine the density of the block. (D = 0.5 g/cm3)
Have students predict how far the block will sink when placed in water. Place the block in water and now one-half of it will submerge in water.
Continue with other masses.
(by adding 75 g of masses to the block, the block's mass will = 100 g which will give it a density of 1 g/cm3 which is equal to the density of water. The block will float in water below the surface)
Displacement and Buoyancy
Archimedes' principle states that when an object is submerged under water, it loses weight equal to the weight of water it displaces. To demonstrate this:
Add 85 g of masses to the empty block so that the block has a total mass of 110 g.
Thread a piece of string through the loop at the top of the block and suspend the block from a spring scale. It should read 110 g.
Next, completely submerge the block in a container of water. The block displaces 100 mL of water (100 cm3), which is equal to its entire volume. Since 100 mL of water has a mass of 100 g, the block has an apparent weight of only 10 g. The reading on the spring scale should be 10 g.
Additional masses can be added to the block to demonstrate that the apparent weight of the block under water is always the total mass of the block minus the buoyant force. Since the block displaces its own volume of 100 mL of water every time it is submerged, its apparent weight under water is always 100 g less the total mass of the block.
This demonstration can be extended by using different liquids like alcohol (D = 0.8 g/cm3), Epsom salt solution (D = 1.2 g/mL), etc.
Explanation
Density is defined as mass per unit volume. The density of water is 1 gram/cm3 (an early standard for mass was water which defined one gram as the mass of 1 cm3 of water).
Buoyancy is caused by fluid pressure - fluid pressure increases with depth, creating an unbalanced upward force on the bottom of the submerged object. Archimedes' Principle states that the buoyant force on a submerged object is equal to the weight of the fluid displaced. Therefore, objects of equal volume experience equal buoyant forces. The volume of the Archimedes' Block does not change so the buoyant force acting on it will remain the same as well, regardless of the mass added to the block.
Questions
How is density calculated? D = m / V
What causes the Block to float or sink? Changing the mass of the block will change the density of the block. When the block has a density less than water (less than 1 g/mL) the block will float. When the block has a density greater than water (more than 1 g/mL) the block will sink. When the block has a density equal to water (1 g/mL) the block will not float at the top nor sink to the bottom but will be neutrally buoyant.
An object has a mass of 150 g. When placed on a spring scale and then submerged in a liquid, the object has an apparent mass of 80 g. Why did the mass of the object change? The object is experiencing an upward buoyant force from the liquid. The object displaced 70 g of liquid therefore its apparent mass is 80 g (150 g - 70 g = 80 g).
Everyday examples of the principles illustrated
Boats float in water because they are designed to displace a large amount of water to increase the buoyant force. (otenmaritime)
Salt water has a greater density than fresh water, producing a greater buoyant force - objects will float higher in salt water than in fresh water. (rescuediver)
The buoyant force also explains hot air balloons are able to float. (howstuffworks)
Photos
Density:
1)
The mass of the empty Archimedes' Block is 25 g.
The volume of the block is 100 cm3 (4 cm x 5 cm x 5 cm)
The density of the empty block is 0.25 g/cm3.
2)
The density of water is 1 g/cm3.
Since the block's density (0.25 g/cm3) is one fourth of water's density, when placed in water the block floats with one fourth of its height (1 cm) submerged under water and three fourths of its height (3 cm) above water.
See picture:
3)
Mass has been added to the block. Its mass is now 50 g.
The volume of the block is 100 cm3 (4 cm x 5 cm x 5 cm)
The density of the block is now 0.5 g/cm3.
4)
Students can now observe that since the block has one-half the density of water, it sinks half way in water. That is, one half of the block's total height (2 cm) is under water and the other half (2 cm) is above water.
5)
Mass has been added to the block. Its mass is now 75 g.
The volume of the block is 100 cm3 (4 cm x 5 cm x 5 cm)
The density of the block is now 0.75 g/cm3.
6)
Students can now observe that since the block is three-fourths the density of water, three-fourths of its volume (75 cm3) is submerged under water and one-fourth of it (25 cm3) above water.
7)
Mass has been added to the block. Its mass is now 100 g.
The volume of the block is 100 cm3 (4 cm x 5 cm x 5 cm)
The density of the block is now 1 g/cm3.
8)
The new density of the block is equal to the density of water. Since the block has the same density of the liquid that surrounds it, the block will now float in water below the surface. The entire weight of the object is equal to the upward buoyant force of water.
9)
Mass has been added to the block. Its mass is now 125 g.
The volume of the block is 100 cm3 (4 cm x 5 cm x 5 cm)
The density of the block is now 1.25 g/cm3.
10)
The new density of the block is greater than the density of water. Since the block has a greater density than the water that surrounds it, the block will now sink in water.
Buoyancy:
1)
The mass of the block is 110 g.
The volume of the block is 100 cm3.
2)
Submerge the block in water. The block displaces 100 cm3 of water, which is equal to its entire volume. Since 100 cm3 of water has a mass of 100 g, the block has an apparent weight of only 10 g. The reading on the spring scale should be 10 g.
3)
The mass of the block is now 125 g.
The volume of the block is 100 cm3.
4)
Submerge the block in water. The block displaces 100 cm3 of water, which is equal to its entire volume. Since 100 cm3 of water has a mass of 100 g, the block has an apparent weight of only 25 g. The reading on the spring scale should be 25 g.
Movies
Density
Buoyancy