Archimedes' Principle: Buoyancy and Displacement Exercises, Study Guides, Projects, Research of Physics

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Archimedes Principle SE

Physics (Arbor View High School)

Archimedes Principle SE

Physics (Arbor View High School)

Name: Date:

Student Exploration: Archimedes’ Principle

Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts 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 its density is greater than water.

2. A motorboat is a lot heavier than a pebble. Why does the boat float?

Because it has buoyancy.

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 boat sinks 2 cm below the surface.

2. Add cubes until the boat sinks. What mass of cubes causes the boat to sink? 150 grams

(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 Length: 5 Height: 5

B. How much mass can the boat hold without sinking? 250 grams

Activity B:

How low does it go?

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 volume of displaced liquid. Leave the last column blank.

Width (cm)

Length (cm)

Boat mass (g)

Sinking depth (cm)

Volume of displaced water (mL)

Volume underwater (cm^3) 10 10 100 g 1 cm 100 mL 100 cm^ 7 7 200 g 4 cm 200 mL 196 cm^ 6 8 300 g 6 cm 300 mL 288 cm^

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 each boat. 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, volume of displaced water, and volume of boat under the water are all the same.

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 base area of the boat 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 2.5 cm 2.5 cm

B 6.0 cm 5.0 cm 150 g 5 cm 5 cm

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 greater the density of the liquid, the higher the boat floats in the water. Conversely, as the density of the liquid lowers, the deeper the boat sinks into the water.

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 displaced liquid 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 mass of the displaced boat are now 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?

In order to get the volume of the displaced liquid, first divide the boat’s mass by the liquid’s density. To then calculate the sinking depth, divide the volume of liquid that has been displaced by the boat’s base area.

B. What happens to the boat when its weight is less than the buoyant force?

The boat will begin to float up.

C. What happens to the boat when its weight is equal to the buoyant force?

The boat will start to float upwards.

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? 0.49 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? 0.49 N

(Hint: If the mass is measured in grams, w = m • 0.00982.)

D. What is the Buoyant force on the boat? 0.49 N

5. Predict: What do you think is the relationship between the buoyant force and the weight of displaced liquid?

The weight of the displaced liquid is equal to the 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. 3 1.47 150 1.47 1. 4 1.96 200 1.96 1.

7. Analyze: What do you notice?

I noticed that the buoyant force is equal to boat weight plus the weight of the 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. The ball will sink, because it weighs more than the water.

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 water displaced by the cubes.

A. Each cube is 2 cm × 2 cm × 2 cm. What is the volume of each cube? 8cm^

B. What is the total volume of cubes in the boat? 24cm^

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) 0.236 N

E. What is the buoyant force on the boat? 0.236 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.