# Archimedes’ Principle

## Student Laboratory Kit

### Materials Included In Kit

Marbles, 100
Modeling clay, 5 sticks
Plastic cups, 1-oz, 15
Plastic cups, 9-oz, 15
Weighing trays, 15

Paper towels
Scissors
Spring scale, 100 × 1 g

### Prelab Preparation

Divide the modeling clay into 30- to 35-g pieces.

### Safety Precautions

Although this activity is considered nonhazardous, please follow all normal laboratory safety guidelines.

### Disposal

Please consult your current Flinn Scientific Catalog/Reference Manual for general guidelines and specific procedures, and review all federal, state and local regulations that may apply, before proceeding. Materials from this lab can be reused many times or disposed of according to Flinn Suggested Disposal Methods 26a and 26b.

### Teacher Tips

• Enough materials are provided in this kit for 30 students working in pairs or for 15 groups of students. The activity can be completed in two 50-minute class periods.
• A class discussion after the submerged objects part of the lab should help to crystallize Archimedes’ Principle before considering floating objects.
• For the floating objects, it is important to fill the cup to the almost overflowing point. The water edge will be nearly to the edge of the cup rim. It may take several practice fills for students to see this level. The initial water level needs to be consistent for each experiment for more accurate results. Be sure to do this experiment on a level surface.
• When placing the clay ball or boat into the water, be sure to let it down gently so there is no splash or waves, and also, do not put fingers into the water, which will add to the water displacement and skew the results. The thread harness prevents this.
• Before removing the cup from the plastic weighing tray, carefully remove some of the bulging water in the cup using a pipet. This will help to prevent excess water from spilling out of the cup and into the tray when removing the cup from the tray.

### Science & Engineering Practices

Analyzing and interpreting data
Planning and carrying out investigations
Using mathematics and computational thinking

### Disciplinary Core Ideas

MS-PS2.B: Types of Interactions
HS-PS2.B: Types of Interactions

### Crosscutting Concepts

Scale, proportion, and quantity
Cause and effect

### Performance Expectations

MS-PS3-1: Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object.
HS-PS3-3: Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy.

### Sample Data

Submerged Objects—Archimedes’ Principle

1. Weight of clay in air                                                               ___47.1___ g
2. Weight of clay submerged in water                                       ___24.5___ g
3. Difference in weight (1–2)                                                    ___22.6___ g
4. Volume of clay by water displacement                                  ___22.0___ mL

(Starting volume ____ mL Ending volume ____ mL)

Floating Objects

1. Water displaced by submerged clay                                        ____22.0___ mL
2. Water displaced by floating clay boat                                     ____48.7___ mL
3. Calculate the density of clay:                                                  ____2.14___ g/mL

Should the boat sink or float? Explain.

{13876_Data_Equation_1}
Since its density is greater than 1.00 g/mL, the clay should sink.
4. Calculate the density of the clay boat                                      ___22.0___ g/mL

Should the boat sink or float? Explain

{13876_Data_Equation_2}

Since its density is less than 1.00 g/mL, the clay boat should float.

The Challenge

Since the marbles are denser than water, they will sink and displace water equal to their volume. When the marbles are floating in the boat, the amount of water displaced is equivalent to their weight. Since the marbles are denser than water, their mass is greater than their volume, and therefore, more water volume is needed to float the cup with the marbles inside. The water rises as more water is displaced. When the marbles are thrown out, less volume is displaced, by the cup and by the volume of the marbles, so the water level lowers!

Submerged Objects—Archimedes’ Principle

1. Assume water weights 1 g/mL. Explain the similarity between 3 and 4. (If your numbers are not similar, repeat steps 2–10 again.) The similarity of 3 and 4 represents Archimedes’ Principle. Write the principle based on your results.

The buoyant force on a submerged object is equal to the weight of the fluid that is displaced by the object. 22 mL of water displaced is equal to 22 grams of water. The clay weighed 22.6 grams less underwater, which is similar to the amount of water that was displaced.

Students are likely to say—An object will displace an amount of water equal to its own volume and a submerged object will weight less under water where the difference in weight is equal to the weight of the displaced water.

Floating Objects

1. What amount of water should equal the volume of that displaced by that floating clay boat? (Hint: What does the water line on a floating object indicate?)

The amount of water necessary to fill the boat up to the water line marked on the boat when it is floating (48.7 mL).

# Archimedes’ Principle

### Introduction

Legend has it that Archimedes ran through the streets of ancient Greece shouting “Eureka!” when he realized how he could utilize his density and water displacement experiments to demonstrate that the king’s crown was made of pure gold and not some imitation. This relationship between density and water displacement is known as Archimedes’ Principle.

### Concepts

• Archimedes’ principle
• Water displacement
• Density
• Buoyancy

### Background

Archimedes was born about 287 B.C. in Sicily and was killed by a Roman soldier about 211 B.C. He is generally regarded as the greatest mathematician and scientist of antiquity and one of the three greatest mathematicians of all time along with Isaac Newton (1643–1727) and Carl Friedrich Gauss (1777–1855). Archimedes was very involved in a wide range of scientific and mathematical studies.

The famous gold crown story stemmed from the fact that the king was suspicious about the purity of the gold in his crown and asked Archimedes to find a way to determine if it was the real thing. Solving the problem seemed to be nearly impossible because little was known about chemical analysis in Archimedes’ day. The story goes that one day Archimedes was thinking about the problem while he was taking a bath. As he lay floating in a pool, he thought about how his body felt “weightless.” Suddenly he realized that all bodies “lose” a little weight when placed in water, and the bigger their volume, the more weight they lose. He realized that the density of a metal could be found from its weight and its weight loss in water. The weight of the king’s crown and its apparent loss of weight in water could tell him if the crown was made of pure gold. When he realized this experimental design, the story claims that Archimedes ran into the street yelling “Eureka! I have found it.”

Density is a characteristic property of a material and pure elements or compounds may be identified by their density. Density is defined as the mass of a substance per unit of volume.

{13876_Background_Equation_1}
Density is commonly expressed as g/cm3 or g/mL. The density of pure water is 1.00 g/cm3 at 20 °C. Objects with a density greater than 1.00 g/cm3 will sink in pure water. Objects with a density less than 1.00 g/cm3 will float in pure water.

### Materials

Marbles, 6
Modeling clay, 30- to 35-g piece
Paper towels
Plastic cup, 1-oz
Plastic cup, 9-oz
Pipet, Beral-type
Scissors
Spring scale, 100 x 1 g
Weighing tray

### Safety Precautions

Although this activity is considered nonhazardous, please follow all normal laboratory safety guidelines.

### Procedure

Submerged Objects

1. Get a piece of modeling clay approximately 30–35 g (1" x 1" x 2").
2. Use thread to make a harness for hanging the clay piece (see Figure 1).
{13876_Procedure_Figure_1_Harness to hang piece of clay}
3. Loop the clay/harness onto the hook of a spring scale and determine the weight of the clay piece. Record the weight on the Archimedes’ Principle Worksheet on line 1.
4. Fill a 9-oz plastic cup about ¾ full with water. With the clay piece still hanging from the spring balance, lower the clay into the water until it is submerged. Do not let the clay touch the sides or bottom of the cup. Read and record the weight of the clay while it is submerged in the water. Hold the apparatus steady while taking the reading. Record the weight on line 2 of the Archimedes’ Principle Worksheet.
5. Calculate the difference between the weight of the clay piece in air and its weight in water on the worksheet on line 3.
6. Untie the harness from the clay piece. Dry the clay and roll it into a cylinder shape so that it can be lowered into a 100-mL graduated cylinder.
7. Reuse the thread and tie a harness around the cylinder-shaped clay piece.
8. Fill a 100-mL graduated cylinder about ½ full of water. Read the precise volume of the water in the cylinder. Record this as the starting volume.
9. Lower the clay cylinder into the graduated cylinder until it is completely submerged.
10. Carefully read the new volume of water in the graduated cylinder and record it as the ending volume. Subtract the starting volume (step 8) from the ending volume (step 10) and record the difference as the volume of the clay as determined by water displacement on the Archimedes’ Principle Worksheet on line 4.
11. Answer Question 5 on the Archimedes’ Worksheet.
12. Participate in the class discussion of Archimedes’ Principle before studying Floating Objects.
Floating Objects

Archimedes’ Principle applies to objects submerged in liquids. What about objects floating on the top of liquids?
1. Use a plastic tray as a catch basin and place a 9-oz plastic cup in the middle of the catch basin. Use a beaker or graduated cylinder to slowly fill the cup with water. When water gets to the very brim, add water very slowly using a Beral-type pipet. Fill the cup so that the water actually appears to be “bulging” up over the top plane of the cup, as shown in Figure 2.
{13876_Procedure_Figure_2_Cup nearly overflowing}
2. Make a string harness for the clay piece.
3. Slowly, and without splashing, lower the clay into the full cup of water until the clay is completely submerged. (Water will spill out of the cup and into the catch basin.
4. Carefully lift the clay out of the water and set it aside. Lift the cup out of the catch basin without spilling any water from the cup. It will take a steady hand(s)!
5. Set the cup aside. Pour the water from the catch basin into an empty graduated cylinder. Measure the volume of water carefully and record it on the Archimedes’ Principle Worksheet on line 6.
6. Dry the clay completely and flatten or roll the clay into a thin piece. Use your hands to shape the clay into a clay boat. Keep shaping the boat and testing it in a cup of water to be sure it floats. The clay boat needs to fit inside the top of the plastic cup without touching the sides.
7. Completely dry the completed boat with paper towels.
8. Use a plastic tray as a catch basin and place the plastic cup in the middle of the catch basin. Use a beaker or graduated cylinder to slowly fill the cup with water. When the water gets to the very brim, add water very slowly with a Beral-type pipet. Fill the cup so that the water actually appears to be “bulging” up over the top plane of the cup (see Figure 2).
9. Make a string harness for your boat, as shown in Figure 3.
{13876_Procedure_Figure_3_Harness for clay boat}
10. Slowly, without splashing, lower the boat into the full cup of water until the boat is floating completely. (Water will spill out of the cup and into the catch basin.)
11. Note the spot on the side of the boat where the water level is when the boat is floating. Use a pencil to lightly mark the level (see Figure 4).
{13876_Procedure_Figure_4_Boat in cup}
12. Using the harness, slowly and carefully lift the boat out of the water being careful to not splash any extra water out of the cup.
13. Set the boat aside and carefully lift the cup out of the catch basin. It will take a steady hand to not spill any water from the cup into the catch basin!
14. Set the cup aside. Pour the water from the catch basin into an empty graduated cylinder. Measure the volume of water carefully and record it on the Archimedes’ Principle Worksheet on line 7.
15. Answer questions 8, 9 and 10 on the worksheet.
16. Consult your instructor for appropriate disposal procedures.
Challenges