Eureka! Volume and the Displacement of Water

Research Questions:

• What happens when you drop an object into a glass of water?
• What happens when you drop a larger object into a glass of water?
• How many of each object can you drop into the glass of water before it overflows?
• Can you predict how many of each object it will take to make a different glass of water overflow?

Archimedes, upon stepping naked into his bath, famously cried out “Eureka!” when he suddenly understood the correspondence between the volume of water displaced by a submerged object and the volume of the object displacing it. This project demonstrates this displacement of water and the correspondence of volumes, and exercises prediction skills.

Materials:

• Two glasses of the same size and shape
• Glasses of other sizes and shapes
• Water
• A wax pencil to mark the glasses
• A bunch of pennies
• A bunch of small rocks, approximately the same size as each other but bigger than a penny
• Other sinking objects
• A tray to control spills

Experimental Procedure:

1. Fill two glasses partway, each with the same amount of water.
2. Mark the water level on the glasses.
3. Drop a penny into the first glass. What happens to the water?
4. Drop a rock into the second glass. What happens to the water?
5. Drop 10 pennies into the first glass. What happens to the water?
6. Drop 10 rocks into the second glass. What happens to the water?
7. Keep dropping pennies and rocks into their respective glasses until the water overflows. How many pennies does it take to make the water overflow? How many rocks?
8. Fill a different glass partway with water.
9. Predict how many pennies it will take to make that glass overflow. Predict how many rocks it will take. Test your predictions.
10. Try this with many different sizes and shapes of glasses and many different (sinking) objects.
11. Predict how many Object A’s it will take to make the water level rise the same amount as Object B. How do the volumes of Object A and Object B compare to each other?

Terms/Concepts: displacement, volume, compare, predict