Student Exploration: Archimedes’ Principle Vocabulary: Archimedes’ principle, buoyant force, density, displace, mass, volume, weight Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1. Why does a small pebble sink in water? It sinks because its weight is greater than the weight of the small amount of water it displaces. 2. A motorboat is a lot heavier than a pebble. Why does the boat float? When we submerge a ship in water, it floats with a force equal to the weight of the liquid it displaces. Gizmo Warm-up When you place an object in liquid, the downward pull of gravity causes it to start to sink. As the object sinks, the liquid pushes back up on the object with a force that opposes gravity. In the Archimedes’ Principle Gizmo, you will see how these forces cause objects to either sink or float. 1. Check that the Width, Length, and Height of the boat are set to 5.0 cm. Drag one of the green 50-g cubes into the rectangular “boat.” What happens? The rectangular boat is still floating but is now a bit underwater. 2. Add cubes until the boat sinks. What mass of cubes causes the boat to sink? (Note: In this Gizmo, the mass of the boat itself is insignificant.) 150 g 3. Click Reset. Experiment with different boat dimensions until you create a boat that holds the most cubes without sinking. A. What are the boat’s dimensions? Width: 10 Length: 10 Height: 10 B. How much mass can the boat hold without sinking? 950 g 2018 Activity A: Displaced liquid Get the Gizmo ready: • Click Reset. • Set the Width, Length, and Height to 5.0 cm. • Be sure the Liquid density is set to 1.0 g/mL. Question: How does the mass of the boat relate to the amount of displaced liquid? 1. Observe: Place several of the 50-g cubes into the boat. What happens to some of the liquid in the tank? The boat is displaced water. The liquid that is pushed into the graduated cylinder is called displaced liquid. 2. Predict: How do you think the mass of the boat will relate to the amount of displaced liquid? The mass of the displaced liquid is the same volume of the liquid multiplied by its density. 3. Observe: Click Reset. Drag two cubes into the boat, yielding a total mass of 100 grams. How much water is displaced into the graduated cylinder? (Units are mL.) 100 ml 4. Experiment: Click Reset. Choose a new set of boat dimensions. Add cubes to the boat and record the volume of displaced liquid. (If the boat sinks, try a larger set of dimensions.) Record your findings for three boats in the table (include units). Leave the last column blank. Width (cm) Length (cm) Height (cm) Boat mass (g) Volume of displaced liquid (mL) Mass of displaced liquid (g) 6.5 cm 4.5 cm 7.5 cm 200 g 200 ml 6.0 cm 5.5 cm 9.5 cm 300 g 300 ml 4.5 3.5 cm 9.5 cm 100 g 100 ml 5. Calculate: Density is equal to mass per unit volume. To calculate density, divide an object’s mass by its volume. If the liquid’s density is 1 gram per milliliter (the density of water), the mass in grams is equal to the volume in milliliters. Use this information to fill in the last column of your data table. 6. Draw conclusions: What is the relationship between the mass of the boat and the mass of the displaced liquid? The difference in mass is equal to the mass of the volume of 2018 liquid released, therefore. Ships float because their submerged part displaced a volume of water whose weight is greater than the weight of the ship.