Hands-on Activity: Buoyant Boats

Contributed by: Engineering K-PhD Program, Pratt School of Engineering, Duke University

Three cartoon drawings of Archimedes in the tub, the king's crown, and an equivalent volume of gold.
Archimedes was a great mathematician and scientist who was born in 287 BC. It is said that while taking a bath one day, he got the idea for using the displacement of water to compare the densities of objects. In particular, he was able to use this method to determine that a crown made for the king did not contain the full amount of gold that it should have.
copyright
Copyright © Sandia National Laboratories http://www.sandia.gov/tp/SAFE_RAM/AP.HTM

Summary

Students conduct a simple experiment to see how the water level changes in a beaker when a lump of clay sinks in the water and when the same lump of clay is shaped into a bowl that floats in the water. They notice that the floating clay displaces more water than the sinking clay does, perhaps a surprising result. Then they determine the mass of water that is displaced when the clay floats in the water. A comparison of this mass to the mass of the clay itself reveals that they are approximately the same.
This engineering curriculum meets Next Generation Science Standards (NGSS).

Engineering Connection

When designing boats and ships, engineers must determine the total amount of water displaced when. They also apply the same concept when designing waterways in order to determine the maximum sized boat that can pass through a human-made waterway such as the Panama Canal.

Pre-Req Knowledge

Completion of the Floaters and Sinkers lesson and its associated activity, Determining Densities.

Learning Objectives

  • Students will be able to describe a means to make a material that is denser than water (modeling clay) float.
  • Students will be able to describe the parallels between the design process used to create a dense but floatable object, and the scientific method of inquiry.

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Educational Standards

Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.

  • Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
  • Solve real-world and mathematical problems involving area, surface area, and volume. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
  • Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
  • Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. (Grade 8) Details... View more aligned curriculum... Do you agree with this alignment?
  • Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
  • Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
  • The design process includes defining a problem, brainstorming, researching and generating ideas, identifying criteria and specifying constraints, exploring possibilities, selecting an approach, developing a design proposal, making a model or prototype, testing and evaluating the design using specifications, refining the design, creating or making it, and communicating processes and results. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
  • Established design principles are used to evaluate existing designs, to collect data, and to guide the design process. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
  • Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
  • Solve real-world and mathematical problems involving area, surface area, and volume. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
  • Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. (Grade 8) Details... View more aligned curriculum... Do you agree with this alignment?
  • Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
  • Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
  • Compare the physical properties of pure substances that are independent of the amount of matter present including density, melting point, boiling point, and solubility to properties that are dependent on the amount of matter present to include volume, mass and weight. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
  • Understand the structure, classifications and physical properties of matter. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
Suggest an alignment not listed above

Materials List

Each group needs

  • balance, accurate to at least 0.1 g (such as a triple beam balance)
  • 500-ml beaker
  • 50- or 100-ml graduated cylinder
  • modeling clay, one-half stick (50-60 grams)
  • pan or tray to catch water that overflows from the beaker during the displacement process
  • (optional) funnel, helps to limit the amount of spilled water
  • 1-2 sponges and/or dishrags for wiping up drips and spills
  • fine-point permanent marker or grease pencil, to write on the beaker; alternative: transparent tape that can be written on with a pencil
  • several paper towels
  • access to water and a sink

Introduction/Motivation

Remember back to the density experiments you completed earlier. What happened when you put an object, such as a lump of clay, into a full beaker of water? (Listen to student responses.) That's right, the water spilled over the top of the beaker. Why did this happen? (Listen to student responses.) That's right, in in order for the clay to enter the water, it had to push some of the water out of the way, or displace it. The only place the displaced water could go was up and over the top of the beaker. How much water spilled over? (Listen to student answers.) The amount of displaced water equaled the volume of the lump of clay.

Think back to the Clay Boats activity. You took a lump of clay and shaped it so that it floated on top of the water. Since the clay was denser than the water in both situations, why was it able to float when it was molded into a bowl-like shape? Today you will attempt to answer that question by taking a closer look at the relationship between floating objects and displaced water. By studying buoyancy, we will also learn about how forces acting on an object must be balanced when the object is at rest.

Vocabulary/Definitions

buoyancy: The ability to float in a liquid (or rise in a gas).

density: The mass per unit volume of a substance at a given pressure and temperature.

Procedure

  1. Gather materials and make copies of the Instructions for Students Handout.
  2. Divide the class into teams of three to four students each.
  3. Provide groups with materials and handouts.
  4. Oversee the groups as they conduct the activity, guided by the handout instructions.
  • Determine and record the clay lump's mass.
  • Find and record the clay lump's volume.
  • Fill a 500-ml beaker about three-quarters full of water. Mark on the outside of the beaker the water level.
  • Without splashing any water, lower your lump of clay into the beaker. Make a new mark to show the new water level.
  • Without overflowing the water in the beaker, remove the clay and pat it dry with a paper towel. Shape the clay into a boat shape that your team thinks will float inside the beaker. Before putting the clay in the water, predict where you think the new water level will be by drawing a short, dashed line on the outside of the beaker.
  • Carefully place the clay boat on the water surface. Mark the new water level. What happened? How close was your prediction to the actual water level?
  • Find and record the volume of the water displaced by the clay boat.
  • Find and record the mass of the water displaced by the clay boat.
  • Compare the volumes and masses of the displaced water to the volumes and masses of the original clay lump.
  • Squash your clay boat back into a lump and remove about one-quarter of the clay. Set it aside. Using the remaining clay (the larger portion), repeats the procedure again.
  • When you repeated the steps with a smaller lump of clay, did you get similar results?
  • Draw a diagram of the sum of the forces on the clay. Just think about forces in the up and down directions. If gravity is pulling the boat down, what is pushing it up? If these forces are equal, will the boat float? What if these forces are not equal?
  1. Conclude by leading a class discussion and giving a quiz, as described in the Assessment section.

Attachments

Investigating Questions

  • All scientific experiments start with a question. What was the question being asked in this experiment? (Answer: Which displaces more water—a sinking object or a floating object— when both are made of the same material and have the same mass?)
  • What was the answer to the question? (Answer: The floating object displaced more water.)
  • How did the mass of the water that was displaced compare to the mass of the floating clay? (Answer: They are approximately equal.)
  • Did you get similar results when you repeated the experiment using a smaller lump of clay? (Answer: Yes. Expect the results to be very similar. The floating clay displaces more water, and that displaced water has the same mass as the smaller lump of clay.)
  • Why do you think you were asked to repeat the experiment, using a smaller lump of clay the second time? (Answer: To make sure the results of the first experiment were not just some sort of coincidence having to do with the size of the clay used. In other words, to generalize the results about the relative quantities and masses of displaced water to other floating [or sinking] objects.)
  • How many pounds of water does a fishing boat that weighs 80 tons displace (assuming it is afloat!)? (Answer: 80 tons = 80 x 2000, or 160,000 pounds of water.)
  • How many gallons of water does it displace? (The answer depends on whether the fishing boat is floating in fresh water or sea water. A gallon of fresh water weighs 8 pounds, so 160,000 divided by 8 = 20,000 gallons of water. Sea water, however, is more dense; a gallon of sea water weighs 8.2 pounds, so the sea water displaced by an 80-ton boat is 19,512 gallons.)
  • We learned that the upward force on the boat must be equal to the force of gravity if the boat is floating. This upward force is called the buoyant force. From your observations, what does the buoyant force depend on? (Students should observe from their experiments that the buoyant force depends on the volume of water displaced).
  • Knowing that the buoyant force depends on the volume of water displaced, how does this connect to what we learned about a floating boat displacing its mass in water? (Weight is mass times gravity. The force of gravity pulling down on the boat is given by the mass of the boat multiplied by gravity. The buoyant force is equal to the volume of water displaced multiplied by the density of water and then multiplied by gravity. When volume and density are multiplied together, the product is mass. Then, the buoyant force pushing up the boat is just (mass of water displaced) x gravity. So, when the boat is floating, the force of gravity pulling down, (mass of boat) x gravity, is equal to the buoyant force pushing up, which we said reduced to (mass of water displaced) x gravity. Gravity doesn't change in this example... so the mass of the boat must be equal to the mass of water displaced!)
  • Would the boat need to displace more or less water in order to float if it was in the ocean instead of a freshwater lake? (Less. Sea water is denser than freshwater, so the buoyant force is larger).

Assessment

Concluding Discussion: Lead a class discussion in which students share and compare their results, observations, conclusions and questions. Ask the Investigating Questions. Use this opportunity to assess students' understanding of the experiment and concepts.

Quiz: In the form of a quiz or written assignment, ask students to predict the weight of water that would be displaced by an empty canoe weighing 120 pounds. Assume the canoe is afloat. Also, ask if the amount of water displaced by the same canoe would increase or decrease if the canoe tipped over, filled with water and sank. Have students draw diagrams of the sum of the forces acting on the canoe in both the floating and sinking examples. Review students' answers to gauge their comprehension.

Activity Extensions

See the Extension Activities section provided in the associated lesson for similar experiments students can conduct to explore the differences between buoyancy in fresh and salt water, and warm and cold water.

Contributors

Mary R. Hebrank , project writer and consultant

Copyright

© 2013 by Regents of the University of Colorado; original © 2004 Duke University

Supporting Program

Engineering K-PhD Program, Pratt School of Engineering, Duke University

Acknowledgements

This content was developed by the MUSIC (Math Understanding through Science Integrated with Curriculum) Program in the Pratt School of Engineering at Duke University under National Science Foundation GK-12 grant no. DGE 0338262. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.

This activity was originally published, in slightly modified form, by Duke University's Center for Inquiry Based Learning (CIBL). Please visit http://www.biology.duke.edu/cibl for information about CIBL and other resources for K-12 science and math teachers.

Last modified: August 10, 2017

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