In this lesson, students used the M/V ratio to discover that objects will float in water if their densities are less than the density of water (1 g/cc) and sink if their densities are greater than the density of water.
Direct students' attention back to the opening vignette on the Sink and Float pages in the Student Guide. Review each of the students' claims.
- Nicholas thinks an object's mass is the reason things sink or float. Do you agree or disagree? (Possible response: Nicholas is partly correct.)
- Jackie thinks volume is the reason things sink or float. Do you agree or disagree? Why? (Possible response: Jackie is also partly correct. Sinking or floating has something to do with both mass and volume. If an object is heavy for its size, it will sink. If it is light for its size, it will float. We measure heaviness by mass and size by volume. Density is the ratio of Mass / Volume. If the density of an object is greater than the density of water, 1 g/cc, it will sink. Otherwise, it floats.)
- The steel balls in this experiment sunk. Luis wonders why big, heavy, steel ships float. Can you explain why? (Possible response: You have to think about the ratio of mass to volume for the ship and you have to think about the air that is inside the ship. If the ship's volume is greater than its mass, it will float.)
Explain to students that the air inside a ship must be taken into consideration. Most of the inside of a ship is air, unlike the solid steel sphere. The boat will float as long as there is a large amount of air inside.
If water leaks in and takes the place of the air, the ship will sink. The density of a ship including its air is very light compared to the density of water so the ship displaces its weight in water before it is completely underwater, and the rest of it floats. See Content Note.
Why Do Boats Float? This lesson began with the question of why boats float. An ocean liner is made mostly of steel,
so why doesn't it sink? When considering the ratio of mass to volume for a boat in the water, we have to take into account not just the hull of the boat, but also the space inside—which is filled with air. In symbols:
Density of Boat = Mass (Hull) + Mass (Air)/Volume (Hull) + Volume (Air)
Since the mass of the air is very small, the boat will float as long as the volume of the space inside is sufficiently large. If you take the same boat and let water into the hull (for example, by springing a leak), the ratio of mass to volume changes.
Density of Water-Filled Boat = Mass (Hull) + Mass (Water Inside)/Volume (Hull) + Volume (Water Inside)
In this case, the density of the water-filled boat is larger than the density of the surrounding water, so it sinks.
Compare the boat in Check-In: Question 20 to the boat in Homework Question 3.
Ask the students these or similar questions:
- Which boat can hold more mass? (Possible response: The aluminum boat in Homework Question 3 can hold more mass.)
- Why can one boat hold more mass than the other? (Possible responses: Since both boats have the same volume, whichever boat is lighter or has less mass can hold more. The boat in Check-In: Question 20 has a greater mass than the aluminum boat. One boat has a mass of 150 g and the other has a mass of 10 g.)
- How much more mass can the aluminum boat hold than the other? (Possible response: Just subtract 10 g from 150 g. The aluminum boat can hold 140 g more mass than the other boat.)
- How are submarines different from ships? (Possible responses: A ship floats on the water and a submarine can go underwater and on top of the water; ships are designed to move on the surface of the water and submarines are designed to be able to submerge and travel under the water's surface, as well as on the surface; when ships go down, they stay down, but submarines are able to come back up after they go down.)
Students should save their data for use in the next lesson.
