**Key concepts**

Water

Density

Physics

Hydrodynamics

Fluid dynamics

**Introduction**

Have you ever wondered how a ship made of steel can float? If you drop a steel bolt into a bucket of water, the bolt quickly sinks to the bottom. Then how can a steel ship float? And better yet, how can a steel ship carry a heavy load without sinking? It has to do with the density of the ship (including its cargo) relative to the density of water. In this activity, you'll make little "boats" out of aluminum foil to explore how their size and shape affects the amount of weight they carry and how this relates to water density.

**Background**

What determines whether an object floats or sinks? It's the density (mass per unit of volume) of the object compared with the density of the liquid it is in. If the object is denser than the fluid, the object will sink. If the object is less dense, then it will float.

With a steel-hulled ship, it is the shape of the hull that determines how well it floats and how much of a load it can handle. On an empty ship with a steel hull enclosing a volume of air, the ship's density is equal to the sum of the mass of the steel hull and the mass of the enclosed air, all divided by the hull's volume: The ship floats because its density is less than the density of water. But when cargo or other weight is added to the ship, its density now becomes the sum of the mass of the steel hull, enclosed air *and* cargo, all divided by the hull's volume. If too much weight is added, the ship’s density becomes greater than that of the water, and it sinks. Excess cargo would need to be thrown overboard in a hurry or it's time to abandon ship!

**Materials**

• Aluminum foil

• Ruler

• Tape

• Calculator

• Scrap piece of paper and pen or pencil

• Bucket, tub, sink or dishpan

• Water

• Pennies. You may need as many as 200, depending on the size and shape of the boats you make.

• Rag or paper towels

• Dry rice and measuring cup (optional)

**Preparation**

• Cut two squares of aluminum foil, making one square with dimensions that are twice that of the other square. For example, you could make one square that is 30 by 30 centimeters (one by one foot), and make the second square 15 by 15 centimeters (six by six inches).

• Fold the two aluminum foil squares into two different boat hulls. Try to make them the same shape. For example, you could make them both have two pointed ends (like canoes) or you could make them square or rectangular with straight edges that come up on the sides (more like a barge).

• Make finishing touches to the boat hulls. Make sure they don't have any leaks. If needed, use a little tape to make them stronger. Flatten the hull bottoms. On each, try to make sure the rim is the same height going all around the hull edges. *Why do you think this is important?*

• Calculate the volume of each boat hull. If both hulls are square or rectangular, you can measure the length, width and height of each and multiply these dimensions together to get its total volume. If parts of the hull have an irregular shape, measure the volume piece-wise and then add these volumes together. Use triangles to approximate any areas of the hull that are curved or angled. *What is the volume of each hull? *Write this down.

• Alternatively, you can use dry rice to calculate the volume of each boat hull. To do this, carefully fill each hull with dry rice so that the rice is level with the top of the hull. Being careful not to damage the hull, transfer the dry rice into a measuring cup. W*hat is the volume of each hull using the rice?* Write this down.

• Fill the bucket, tub, sink, or dishpan with some water.

**Procedure**

• Take one of the boat hulls and carefully float it in the container of water deep enough to completely submerge the boat.

• Gently add one penny at a time. To prevent the hull from tipping, carefully balance the load as you add pennies (left to right, front to back—or port to starboard, fore to aft, if you're feeling nautical).

• Keep adding pennies until the hull finally sinks.

• Carefully take out the sunken hull and place it and the pennies on a rag or paper towels. Dump any excess water back into the container.

• Count how many pennies the hull could support before sinking (the penny that sank the hull does not count). *How many pennies could it support? *Write this number down.

• Repeat this process with the other hull. Be sure to only add dry pennies. *Why do you think using dry pennies (instead of wet ones) is important?*

• *Could the larger hull support a lot more pennies than the smaller one?*

• Make sure that the volume you calculated for each boat is in cubic centimeters (cm^{3}). Convert it if necessary and write it down. (Cubic centimeters are the same as milliliters, or mL.)

• Convert the number of pennies each hull could support to grams. To do this, multiply the number of pennies by 2.5 grams (the weight of a single penny). *How many grams could each hull support? *Write this number down for each hull.

• For each hull, divide the number of grams it could support by its volume in cubic centimeters. This roughly gives you the hull's density. *What was the density of each hull right before sinking? How do you think this relates to the density of water?*

• **Extra: **In this activity you compared boat hulls that had two different sizes but you could repeat this activity trying a wider range of shapes and sizes of boat hulls. *Do you get the same results if you use aluminum foil boat hulls that have a different shape? Do you see a pattern in your results?*

• **Extra:** You roughly calculated the density of water in this activity, but your calculation could be made even more accurate. Thinking about what factors affected your calculation, develop a way to more accurately determine the density of water, such as by including the weight of the boat hulls, adding something smaller than pennies to measure how much weight the hulls can carry, and more accurately determining the volume of the hulls. *How close can you get your calculations to the actual density of water?*

• **Extra:** Repeat this activity but this time use liquids (or semisolids) other than water, such as cooking oil, liquid detergent or even snow. (Check with an adult to make sure it is alright if you use household liquids for your activity.) Make sure not to use any dangerous chemicals, such as household cleaning solutions. If you do not want to use much of the liquid, you can dilute it with water or use a small container (just wide enough to fit your boat hull in) and fill it so it is just a little deeper than the height of the hull—so that the hull can sink. *What are the densities of other liquids and semisolids? How do their densities compare with that of water?*

**Observations and results**

Did the larger boat hull support a greater amount of weight? Did both hulls have a similar density right before sinking, which was roughly one gram per cubic centimeter—the density of water?

When you first put one of the boat hulls on the water, it should float because its total density is less than that of water. As you add pennies to the hull, its density increases and the hull floats lower. Eventually, when enough pennies are added, the hull's density roughly equals the water’s. This happens right before the penny that sinks the hull is added. The hull sinks because its density has finally become greater than that of water. Consequently, the hull’s density right before sinking should roughly equal the density of water, which is one gram per cubic centimeter. Even though the larger hull supports more weight, it also has a greater volume, and both hulls should roughly have a density of one gram per cubic centimeter right before sinking. (Your densities may not have been exactly this, but may have ranged between 0.7 to 1.3 grams per cubic centimeter. Sources of error that could be eliminated to give you an answer closer to the actual density of water include more accurately calculating the volume of each hull, using something smaller than pennies and including the hull's weight in your calculations.)

**Cleanup**

Be sure to recycle the aluminum foil when you are done testing your hulls.

**More to explore**

How does a boat float if it's heavy?, from the University of California, Santa Barbara, ScienceLine

Rainbows on Titan, from NASA Science News

Cartesian Diver, from PBS Kids DragonflyTV

How Much Weight Can Your Boat Float?, from Science Buddies

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