How Much Weight Can Your Boat Float?

Introduction

You know from experience that if you drop a steel bolt in a bucket of water that it will sink like a rock to the bottom. On the other hand, you know that ships made of steel can float. How does it work?

What determines whether an object floats or sinks? It is the density (mass per unit volume) of the object compared to the density of the liquid. If the object is more dense than the fluid, it will sink. If the object is less dense than the fluid, it will float. If the object has the same density as the fluid it will neither sink nor float.

With a steel-hulled ship, it is the shape of the ship's hull that matters. On an empty ship the hull encloses a volume of air so that the total density is defined by Equation 1 below.

Equation 1:

Densityofanemptyship=massofsteelhull+massofenclosedairvolume

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 is now defined by Equation 2 below.

Equation 2:

Densityofashipwithcargo=massofsteelhull+massofenclosedair+massofcargovolume

If too much cargo or weight is added to the ship, the density of the ship becomes greater than the density of water, and the ship sinks. Extra cargo would need to be thrown overboard in a hurry or it is time to abandon ship!

Archimedes discovered that an object placed in water displaces a volume of water. If the object is floating, the amount of water that gets displaced weighs at least as much as the object. The displaced water creates an upward force on the object, called buoyancy. The strength of this upward acting force exerted by water is equal to the weight of the water that is displaced. Whether an object sinks or floats depends on its density and the amount of water it displaces to create a strong enough buoyant force.

In this hydrodynamics science project you will make boat hulls of various shapes and sizes using simple materials (aluminum foil and tape) and determine how much weight can be supported by these hulls and how this relates to the density of water. Can you predict how many pennies each of your boats will support without sinking?

Terms and Concepts

• Density
• Mass
• Volume
• Density of water
• Displacement
• Buoyancy

Questions

• What is density?
• How can the density of something, like a boat, be changed?
• If a boat is sinking because it has too much cargo, how does its density compare to the density of water? What about its density right before it became too heavy?

Bibliography

Here are some good background resources on buoyancy and how heavy objects float in water:

• Wikipedia contributors. (2013, January 16). Buoyancy. Wikipedia, The Free Encyclopedia. Retrieved January 22, 2013, from http://en.wikipedia.org/w/index.php?title=Buoyancy&oldid=533387673
• ScienceLine. (n.d.). How does a boat float if it's heavy? University of California, Santa Barbara. Retrieved January 22, 2013, from http://scienceline.ucsb.edu/getkey.php?key=2673

Here is an article to get you thinking about what happens if the fluid in which the object is immersed has a density lower or higher than that of water:

• Phillips, T. (2005). Rainbows on Titan, National Aeronautics and Space Administration (NASA), Science News. Retrieved January 22, 2013, from http://science.nasa.gov/headlines/y2005/25feb_titan2.htm

The following link shows you how to make a Cartesian Diver, which will make an interesting demonstration of buoyancy you can use along with your display board:

• PBS Kids. (2006). Do It: Cartesian Diver. DragonflyTV, Twin Cities Public Television. Retrieved January 22, 2013, from http://pbskids.org/dragonflytv/superdoit/cartesian_diver.html

Materials and Equipment

• Aluminum foil
• Cellophane tape, such as the common Scotch® tape brand
• Optional: Permanent marker
• Metric ruler or dry rice kernels and either a metric measuring cup or graduated cylinder
• A sink, tub, bucket, or dishpan
• Water
• Pennies (at least 200, depending on the size of your boat hulls)
• Optional: Paper towels or rag
• Calculator
• Lab notebook

Experimental Procedure

1. Use the aluminum foil and tape to construct at least five boat hulls with different sizes and shapes.
   1. Try building some different boats using the same amount of aluminum foil for each.
   2. Also try building some different boats using different amounts of aluminum foil.
   3. Some different shapes you could try include making the hulls have two pointed ends (like canoes), like the ones on the left in Figure 1, or be square or rectangular (like a rectangular prism), like the ones on the right in Figure 1.
   4. You can fold or even cut the aluminum foil if you wish to obtain the desired shape.
   5. Make sure the hulls are not too large to fit in the sink, tub, bucket, or dishpan you will be using.
   6. Make finishing touches to the boat hulls so that they are ready to test.
      1. Make sure there are no leaks!
      2. Make sure the hulls seem to hold their shape. If they do not, try adding a little tape to make them stronger.
      3. Flatten the bottoms of the hulls.
      4. Try to make sure each hull's rim is the same height going all around the edge of the hull. In other words, make sure there is not a low point in the rim of any of the hulls.
   7. Assign a number (1 to 5) to each boat hull. You could do this by using a permanent marker to label each hull with a number or by describing and/or drawing each hull in your lab notebook. However you do it, just be sure you have a way to identify each hull by a number.

Figure 1. Some different boat hull shapes you could make include boat hulls that have two pointed ends, like the ones on the left in this image, or boat hulls that are square or rectangular, like the ones on the right in this image.

2. Calculate the volume of each boat hull. Below are two alternative methods you could use. (Or, you could use both methods, and compare your results. Which method is more accurate?)
   1. Ruler Method
      1. If the hull is a rectangular prism, use the ruler to measure the length, width, and height of the hull in centimeters (cm). Calculate the volume by using Equation 3 below.Equation 3:
         
         Volumeofarectangularprism=length×width×height
      2. If parts of the hull are rectangular prisms but other parts are curved or angled, measure the (imagined) parts of the hull piece-wise (in centimeters), calculate the volume of each part, and add up the volumes to get the total volume for each hull.
         1. Use triangular prisms to approximate any areas of the hull that are curved or angled. Calculate the volume by using Equation 4 below.
         2. Calculate the volume of any rectangular prism parts by using Equation 3 above.
      3. If the entire hull is a triangular prism, calculate the volume by using Equation 4.
      4. In your lab notebook, record the volume for each hull in a data table like Table 1 below.Equation 4:
         
         Volumeofatriangularprism=½×length×width×height
   2. Dry Rice Method
      1. Carefully fill the boat hull with dry rice. The rice should be level with the top of the hull.
      2. Being careful not to damage the hull, move the dry rice into the measuring cup (or graduated cylinder).
      3. Gently shake the cup to level the rice.
      4. Read the volume of the dry rice, in milliliters (mL).
         1. If this is all of the rice that was in the boat hull, then this is the volume of your boat hull.
         2. If there is still rice left in the hull, empty the rice from the measuring cup and fill it with rice from the hull until the hull is empty. In your lab notebook, keep track of the amount of rice that you have filled the measuring cup with. The total amount of rice that was in the hull is the volume of the hull.
      5. In your lab notebook, record the volume for each hull in a data table like Table 1 below.
         1. Record the volume in cubic centimeters (cm³). Cubic centimeters are the same as milliliters.

Boat hull	Volume (in cm³)	Number of Pennies it Supported	Weight it Supported (in grams)	Density Before Sinking (in grams per cm³)
1
2
3
4
5

Table 1. In your lab notebook, create a data table like this one to record your measurements.

3. Measure the buoyancy of each boat hull.
   1. Fill the sink, tub, bucket, or dishpan with some water.
      1. The water level should be deeper than the height of the boat hulls so that they are able to sink.
   2. Carefully float one of the hulls in the container of water.
   3. 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 and back— or port to starboard, fore and aft, if you are feeling nautical).
   4. Keep adding pennies until the boat finally sinks.
   5. Count how many pennies the boat could support before sinking (i.e., the penny that sank the boat does not count).
   6. In the data table in your lab notebook, record how many pennies the boat could support.
   7. Repeat steps 3b to 3f until you have tested each hull.
      1. Only use dry pennies. If you run out of dry pennies, you may need to use paper towels or a rag to dry some, or wait until they have dried.
   8. For each hull, convert the number of pennies it could support to grams. Do this by multiplying the number of pennies by 2.5 grams (which is the weight of a single penny in grams). Record this in the data table in your lab notebook.
4. Calculate the density of each hull right before sinking.
   1. For each hull, divide the number of grams it could support by its volume. This will give you the hull's density in grams per cm³.
   2. Record your results in the data table in your lab notebook.
5. Make a line graph of buoyancy. To do this put the weight supported by the boat (in grams) on the y-axis and the boat hull volume (in cm³) on the x-axis. Include each boat on your graph.
   1. You can make a graph by hand or use a website like Create a Graph to make a graph on the computer and print it.
6. Make a bar graph of the density of each hull before sinking. To do this put the density before sinking (in grams per cm³) on the y-axis and make a bar for each of the boats (on the x-axis).
7. Analyze your graphs.
   1. What do your results tell you about the relationship between buoyancy (amount of weight a boat can support) and volume of the boat hull?
   2. The density of the hulls right before sinking should roughly be the same as the density of water. (Tip: Reread the Introduction in the Background tab if you are unsure of why this is.) Based on the results in your bar graph, what do you think is the density of water?