**Key concepts**

Hydrodynamics

Fluid dynamics

Physics

Water

**Introduction**

Have you ever wondered why when you drop a steel nail into water it sinks like a stone, but when a well-built steel ship is in the ocean it floats, even though it weighs much more than a tiny nail?

The answer has to do with the fact that when an object is placed in water, water is pushed out of the way. You may have noticed this when you take a bath in a bathtub. Known as Archimedes' principle, as water is pushed away by an object, the water exerts a force back on the object that is equal to the object's weight. This is what helps make an object float.

**Background**

More than 2,200 years ago, a scientist named Archimedes sat down in his bath and figured out that when an object is placed in water, water moves out of the way—it gets displaced. If the object is floating, the amount of water that gets displaced weighs the same as the object. There is a force, called a buoyant force, which pushes on an object when it displaces water. The strength of this upward acting force exerted by water is equal to the weight of the water that is displaced. So, if an object displaces just a little bit of water, the weight of that small amount of water is small, and so the buoyant force is small, too. If, on the other hand, the object displaces a lot of water, then there will be a large buoyant force pushing upward. Whether an object sinks or floats depends on its density and the amount of water it displaces to create a strong enough buoyant force. How dense can an aluminum "boat" be before it sinks?

**Materials**

• Cloth towel (or paper towels)

• Large, clear bowl or container

• Water

• Aluminum foil

• Metric ruler

• Pen

• Scissors

• Permanent marker

• Hammer or mallet

**Preparation**

• Spread out the towel or paper towels on a hard work surface. Fill the bowl or container about two thirds full of tap water and set it on the towel(s).

• Measure out a square of aluminum foil that is about 25 centimeters (cm) square. Cut out the square. This will become the metal "boat" you test.

• Mark the four corners of the aluminum foil square with permanent marker.

• Be careful: later in the experiment you will use the hammer. Be sure to pound on a surface that can safely withstand the force and is resistant to damage.

**Procedure**

• Pull the corners of the aluminum foil square together and crumple the square into a loose ball that is approximately six cm in diameter. Rumple the aluminum such that the marked corners stay together and are visible in one spot.

• Set the ball gently in the bowl of water, placing it so that the marked corners are at the top of the ball, as this will help prevent the ball from filling up with water. Immediately observe the ball. *Does it sink or float?*

• Get down low so that you are at eye level with the aluminum foil ball and quickly observe how much of the ball is below the surface of the water. *Is about 10 percent, 25 percent, 33 percent, 50 percent, 67 percent, 75 percent, 90 percent or 100 percent of the ball underwater?*

• Remove the ball from the bowl, shake out any water and dry it on the towel.

• Now crumple the ball a little more tightly, into one that is approximately five cm in diameter. If you crumple it too much, just carefully pull apart some of the aluminum foil to get the desired size.

• Again, set the ball gently in the water, placing the marked corners at the top. *Does it sink or float? What percentage of the ball is below the top of the water?* Remove it, shake out any water and dry it.

• Continue to crumple the ball to be smaller and tighter, and test whether it floats or not (as you have been doing) as it gets smaller. Keep testing smaller diameters until the ball completely sinks. Try testing these diameters (or ones roughly similar): 4.0 cm, 3.0 cm, 2.5 cm, 2.2 cm, 2.0 cm, 1.8 cm, 1.6 cm. If it is too hard to squeeze the ball smaller by hand strength alone, then carefully use the hammer or mallet to gently pound the foil into a smaller ball (or as close to a ball-shape as you can make it). *For each diameter you test, what percentage of the ball is submerged?*

• *At which diameter did the ball sink to the bottom? Do you think that the ball that sank had the lowest or highest density? At which diameter did the ball have a density that was approximately equal to that of water? (When was the ball almost completely submerged or fully submerged but not quite sinking to the bottom?)*

• **Extra**: Cut out at least two additional aluminum foil sheets that are 25 cm square and repeat this activity. *Do you get the same results with all the aluminum squares you test, or is there a lot of variation?*

• **Extra**: You can do this activity again, but this time weigh the aluminum sheet on a scale and calculate its mass in grams. Calculate the volume of the spheres for each diameter, using the fact that the volume of a sphere is equal to four thirds times pi (3.14) times the radius cubed. Using the mass and the volumes, compute the average density of the aluminum sheet for each diameter by dividing mass by volume. *At what density did the aluminum ball sink? At what density was the aluminum ball approximately equal to that of water? For each diameter of the sphere, what is the mass of the water that was displaced?* For more accurate results, continue testing additional 25-cm aluminum squares.

**Observations and results**

Did more and more of the ball end up below the top of the water as the ball's diameter decreased? Was about half of the ball below the water when the ball had a diameter of about 2.5 cm, and did the entire ball sink when its diameter was about 1.6 cm or smaller?

If an object is floating in water, the amount of water that gets displaced weighs the same as the object. Consequently, while it was floating, the ball should have displaced the same amount of water as it decreased in diameter, and so the buoyant force should have remained the same. However, the density of the ball was changing—it increased as the ball's diameter decreased.

Density is the mass per unit volume—it describes how much "stuff" is packed into a volume of space. When the aluminum ball had a diameter of 6.0 cm, the ball should have floated well because it had a density lower than that of water due to the air inside of the ball, just like steel ships that can float because their density has been lowered by encasing air inside the hull. And as long as the ship displaces enough water to create a strong buoyant force, it can stay afloat—even if it is loaded with cargo. As the diameter decreased and density increased, the ball should have sank more and more. When its diameter was about 1.8 cm or 1.6 cm, you may have seen it become 90 percent (just barely) submerged. This is when the ball had a density approximately equal to that of water. With a diameter of about 1.6 cm or smaller, the ball should have completely sank, indicating that its density was greater than that of water, thereby overcoming the buoyant force.

**Cleanup**

Pour the water down a drain and recycle the aluminum foil.

**More to explore**

Archimedes' Principle from Hila Science Videos

*How Stuff Works*

Archimedes' Principle by *ORACLE ThinkQuest*: Education Foundation

*Science Buddies*

*This activity brought to you in partnership with *Science Buddies