Answer Key

Name: Josiah Barnett Date: 06-17-2022 Student Exploration: Archimedes’ Principle Directions: Follow the instructions to go through the simulation. Respond to the questions andprompts in the orange boxes. 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? Because it weighs more than the water it displaces, a little stone sinks. 2. A motorboat is a lot heavier than a pebble. Why does the boat float? Because its weight is equivalent to the weight of the water it moves, a motorboat floats. Gizmo Warm-up When you place an object in liquid, the downward pull of gravitycauses it to start to sink. As the object sinks, the liquid pushes backup 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 boat submerges 2 centimeters into the water. 2. Add cubes until the boat sinks. What mass of cubes causes the boat to sink? 150 g (Note: In this Gizmo, the mass of the boat itself is insignificant.) 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 cm Length: 10 cm Height: 10 cm B. How much mass can the boat hold without sinking? 950 g or 19 cubes Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

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 graduated cylinder is occasionally overfilled with water from the water tank. 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? A heavier boat has a higher chance of sinking. 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.) 100mL 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) 4 4 6 100 100 100 6 6 4 150 150 150 2 2 6 50 50 50 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 volumein 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 mass of the displaced liquid is equal to the mass of each boat. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

Activity B: How low does itgo? Get the Gizmo ready: ● Click Reset . ● Be sure the Liquid density is set to 1.0 g/mL. ● Set the Height of the boat to 10.0 cm. Introduction: In activity A, you learned that, for floating boats, the mass of the boat is equal to the mass of displaced liquid. You can use this knowledge to predict how deep a boat will sink. Question: How far will a boat sink in water? 1. Experiment: Turn on Magnify waterline . Experiment with several different sets of boat dimensions and loads. In the table, record each boat’s width, length, and mass; the depth to which it sinks, and the volumeof displaced liquid. Leave the last column blank. Width (cm) Length (cm) Boat mass (g) Sinking depth (cm) Volume of displaced water (mL) 8 8 100 1.5625 100 100 8 4 150 4.6875 150 150 3 5 50 3.33 50 50 2. Calculate: Label the last column in your table Volume underwater . To calculate the volume of the boat that is underwater, multiply the width, length, and depth of the boat. Record the underwater volume of eachboat. The units of volume are cm 3 and mL (1 cm 3 = 1 mL). 3. Analyze: What is the relationship between a boat’s mass, the volume of displaced water, and the volume of the boat that is under water? The boat's mass, water displacement volume, and submerged volume are all equal. 4. Make a rule: If you know the width, length, and mass of a boat, how can you calculate how deep it will sink in water? The boat's base area divided by its mass 5. Practice: Based on what you have learned, calculate how deep each of the following boats will sink. Use the Gizmo to check your answers. Boat Width Length Boat mass Sinking depth (calculated) Sinking depth (actual) A 8.0 cm 5.0 cm 100 g 2.5 cm 2.5 cm B 6.0 cm 5.0 cm 150 g 5 cm 5 cm Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

7. Predict: Not all liquids have the same density as water. How do you think increasing the density of the liquid will change each of the following? A. How far the boat sinks into the liquid: lower B. The volume of displaced liquid: lower C. The mass of displaced liquid: higher 8. Observe: Set the Width , Length , and Height of the boat to 5 cm. Add one cube to the boat. Move the Liquid density slider back and forth. What do you notice? The boat floats higher in the liquid as the liquid density rises. The boat submerges deeperinto the liquid as the liquid density drops. 9. Gather data: Measure how far the boat sinks into liquids with each density listed below. Click Reset between each trial. Calculate the volume and mass of displaced liquid. (Note: The mass of the displacedliquid is equal to the volume of the liquid multiplied by its density.) Boat mass Liquid density Sinking depth (cm) Volume of displaced liquid (mL) Mass of displaced liquid (g) 50 g 0.5 g/mL 4 cm 100 mL 50 g 50 g 1.0 g/mL 2 cm 50 mL 50 g 50 g 2.0 g/mL 1 cm 25 mL 50 g 10. Analyze: In the first part of this activity, you discovered that when a boat is placed in water, the volume of displaced water is equal to the mass of the boat. What is true now? The mass of the displaced liquid and the boat are always equal. 11. Summarize: If you know the length, width, and mass of the boat as well as the density of the liquid, how would you calculate how far the boat sinks into the liquid? To get the volume of displaced liquid, first divide the boat's mass by the liquid's density. Thesinking depth is then calculated by dividing the volume of liquid that has been displaced bythe boat's base area. 12. Practice: A rectangular boat has a width of 5 cm, a length of 8 cm, and a mass of 150 g. How far will the boat sink into liquid with a density of 1.2 g/mL? Check your answer. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

3.125 cm Activity C: Weight andbuoyancy Get the Gizmo ready: ● Click Reset , and turn off Magnify waterline . ● Set the Width , Length , and Height to 10.0 cm. Introduction: When a boat is placed in liquid, two forces act on the boat. Gravity pulls the boat down with a force equal to the weight of the boat. Weight is measured in newtons (N). To calculate the weight of a boat, multiply its mass in grams by 0.00982. As the boat sinks into the liquid, the liquid pushes back. The force of the liquid pushing up on the boat is calledthe buoyant force . Question: How do gravity and the buoyant force affect a boat? 1. Observe: Turn on Show data . Place four cubes in the boat. A. What is the Boat weight ? 1.96 N B. What is the Buoyant force ? 1.96 N C. What is the Net force on the boat? 0 N 2. Analyze: Try dragging the boat up or down. Pay attention to the Buoyant force . A. What happens to the buoyant force when the boat is pulled down? increase B. Why do you think this happens? The boat is sinking faster because of the force acting on it. C. What happens to the buoyant force when the boat is lifted up? decreases D. Why do you think this happens? It is the exact reverse of the previous circumstance. 3. Explore: Answer the following questions by dragging the boat up or down in the liquid. A. What happens to the boat when its weight is greater than the buoyant force? The boat begins to sag. B. What happens to the boat when its weight is less than the buoyant force? The boat floats up. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

C. What happens to the boat when its weight is equal to the buoyant force? The boat floats on the water motionless. 4. Observe: Click Reset . Set the Liquid density to 1.0 g/mL. Add a 50-g cube to the boat. A. What is the weight of the boat? .49 N B. What is the mass of the displaced liquid in the graduated cylinder? 50 g C. What is the weight of the displaced liquid? .49 N (Hint: If the mass is measured in grams, w = m • 0.00982.) D. What is the Buoyant force on the boat? .49 N 5. Predict: What do you think is the relationship between the buoyant force and the weight of displaced liquid? weight of displaced liquid = buoyant force 6. Collect data: As you add cubes to the boat, record the boat’s weight, the mass of displaced liquid in the graduated cylinder, the weight of displaced liquid, and the buoyant force. Number of cubes Boat weight (N) Mass of displaced liquid (g) Weight of displaced liquid (N) Buoyant force (N) 2 0.98 100 0.98 0.98 3 1.47 150 1.47 1.47 4 1.96 200 1.96 1.96 7. Analyze: What do you notice? buoyant force = boat weight + weight of displaced liquid 8. Make a rule: Archimedes’ principle states that an object is pushed up by a buoyant force that is equal to the weight of the displaced liquid. 9. Apply: A hollow ball weighs 40 newtons. In a water tank, it displaces 15 newtons of water. A. What is the buoyant force on the ball? 15 N B. Will the ball float or sink? Explain your reasoning. Because the ball weighs more than the water that has been displaced, it will sink. Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

Extension: Sinking boats Get the Gizmo ready: ● Click Reset . Check that Show data is turned off. ● Set the Width , Length , and Height to 5.0 cm. ● Be sure the Liquid density is set to 1.0 g/mL. Question: What are the forces on a sinking boat? 1. Observe: Place three 50-g cubes into the boat. What happens? The boat sinks to the bottom of the tank as it fills with water. 2. Calculate: Notice that the boat has filled up with water and sunk to the bottom. In this model, the walls of the boat are very thin. Therefore, the volume of water displaced by the boat is equal to the volume of waterdisplaced by the cubes. A. Each cube is 2 cm × 2 cm × 2 cm. What is the volume of each cube? B. What is the total volume of cubes in the boat? C. If the water density is 1.0 g/mL, what is the mass of displaced water? 24 g D. What is the weight of displaced water? (Recall w = m • 0.00982) .236 N E. What is the buoyant force on the boat? .236 N F. What is the mass and weight of the boat? Mass: 150 g Weight: 1.473 N G. What is the net force on the boat? (Hint: Downward force is negative.) -1.237 N Turn on Show data to check your answers to parts E, F, and G. Recheck your calculations if necessary. 3. Apply: A valuable statuette from a Greek shipwreck lies at the bottom of the Mediterranean Sea. The statuette has a mass of 10,566 g and a volume of 4,064 cm 3 . The density of seawater is 1.03 g/mL. A. What is the weight of the statuette? 103.76 N B. What is the mass of displaced water? 4,185.92 g C. What is the weight of displaced water? 41.11 N Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

D. What is the buoyant force on the statuette? 41.11 N E. What is the net force on the statuette? -62.65 N F. How much force would be required to lift the statuette? >62.65 N Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

Gizmo Answer Key: Archimedes’ Principle

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