Title

Activity: Boat Floatation

NGSS Science and Engineering Practices

NGSS Crosscutting Concepts

NGSS Disciplinary Core Ideas

Table of Contents

## Materials

- Table 8.2
- Table 8.3
- 100 g oil-based modeling clay
- 100 g chunk of metal
- 100 g piece of wood
- Scale or balance
- Graduate cylinder or beaker with graduated markings
- Overflow container or drink pitcher with spout
- Liquid detergent
- Large tray
- Calculator
- Additional 100 g samples of materials (optional)
- Water
- Towels

**Additional Materials for Part B**

- Small, wide plastic or metal containers (e.g., food containers, wide cups)
- Small weights of uniform size (e.g., pennies, washers, pellets)
- Tape
- Bucket
- Ruler

## Procedures

**A. Determine the net buoyancy force.**

- Obtain approximately 100 g of clay. Shape the clay into a sphere. Weigh the clay on the balance and record in Table 8.2.

- Calculate the Gravitational Force exerted on the object in Newtons (N) using the formula:

**Gravitational force = (mass of the object) x (0.01 N / g)**Record the Gravitational Force in Table 8.2.

- Predict whether the clay sphere will sink or float in a container of water. Record your prediction in Table 8.2.

- Test your prediction.
- Place the overflow container in a large tray.
- Fill the container with water until it just starts to overflow. Add a drop of liquid detergent to decrease the surface tension of the water.
- Place the empty beaker near the spout of the overflow container.
- Place the clay sphere into the overflow container.
- Measure the volume of water displaced by the object.

- Calculate the weight of the water displaced by the object using the conversion 1 ml of water weighs 1 gram. Record your answer in Table 8.2.

- Calculate the Buoyancy Force of the displaced water in Newtons using the following formula:
**Buoyancy Force = (mass of displaced water) x (0.01 N/ g)**Record the Buoyancy Force in Table 8.2.

- Calculate the Net Buoyancy Force and record in Table 8.2. Note a positive Net Buoyancy Force indicates a sinking object. A negative Net Buoyancy Force indicates a floating object. Use the following formula.
**Net Buoyancy Force = Gravitational Force – Buoyancy Force** - Repeat steps 1–7 for the metal, wood, and a hollow clay boat. Record your predictions, observations, and calculations in Table 8.2. Add additional rows to Table 8.2 if you would like to test additional materials.

**B. Carrying capacity of ships.**

- Tape a small weight on the bottom center of a small, wide container to help balance the container. This container will be your ship.

- Record the weight of your ship.

- Calculate the Gravitational Force, Buoyancy Force, and Net Buoyancy Force for your zero cargo load ship, following procedure A. Record your results in Table 8.3.

- Predict the carrying capacity of your ship under full cargo load. The carrying capacity is the total mass the ship will carry without sinking.

- Determine the volume of water that your ship displaces when it is just about to sink in milliliters. Use one of the following methods.
- Measure the dimensions of your ship in centimeters and use the equation (1 cm3 = 1 ml) to determine volume.
- Place your ship in the overflow container and measure the volume of water that is displaced when you push the ship down until it is nearly submerged.

- Use the volume of your submerged ship to calculate the full cargo load Buoyancy Force as outlined in procedure A. Record your calculations Table 8.3.

- Using the equations below, determine the cargo carrying capacity of your ship. Under a full cargo load, the Net Buoyancy Force is equal to zero (i.e. neither sinking or floating). Note that you are solving for ‘mass of cargo’ (in bold) in the following equations.
**Net Buoyancy Force = Gravitational Force – Buoyancy Force****Net Buoyancy Force = [(Mass of the object) * (0.01 N / g)] – [(mass of displaced water) * (0.01 N / g)]****Net Buoyancy Force = [(mass of boat + mass of cargo) * (0.01 Newtons / g)] – [(mass of displaced water) * (0.01 N / g)]** - Record the full cargo Gravitational Force in Table 8.3.

- Test your predictions.
- Place your ship in the bucket.
- Slowly add weight evenly to the ship. Record the maximum amount of mass your ship holds before sinking.

Activity Questions

- Explain Archimedes Principle (or the principle of floatation) using your own words. Refer to the text before the activity if necessary.

- What is the direction of the
- buoyancy force?
- gravitational force?

- How do the buoyancy force and gravitational force relate to net buoyancy force?

- In a calm harbor, gravitational force and buoyancy force are the only two forces acting on a ship. These forces act in opposite directions. If the ship floats, are the opposing forces equal or unequal? If unequal, which force is greater? Explain your answer in terms of net buoyant force.

- Describe clay, metal, and wood materials in terms of their buoyancy.

- Did your sinking and floating predications for the clay (sphere and boat), metal, and wood match your observations? Explain why you think they were similar, or why you think your predictions did not match your observations.

- Compare and contrast the clay sphere and clay boat in terms of their buoyancy.

- This activity models ship design. What are the limitations of the model?

- For the carrying capacity of your ship, were your predicted, calculated, and observed values similar? Explain why you think they were similar, or why you think your predictions, calculations, and observed values were different.

- What relationship, if any, do you think there is between the shape of a hull and its carrying capacity? How is hull shape related to net buoyant force?

- Why do you think the net buoyancy force of an empty ship is different than the net buoyancy force of a ship with a full cargo?

- Using the terminology in this activity, explain how ships weighing several tons, made of materials that do not float in their raw form, float when built.

- In addition to carrying capacity, what other considerations do you think boat designers have to keep in mind when planning and constructing a ship?