Materials Included In Kit

Additional Materials Required

Prelab Preparation

1. Place a small piece of tape in the center of the underside of eight vial caps.
2. Bend a paper clip into a hook shape (see Figure 4).
   {12196_Preparation_Figure_4}
3. Carefully push the larger hook end of the paper clip through the tape and the center of a cap from the underside (see Figure 5).
   {12196_Preparation_Figure_5}
4. Repeat steps 2 and 3 for each cap. (Optional: Place a drop of hot glue around the paper clip to completely seal the hole in the cap.) Note: Two of the caps will not have a paper clip hook.
5. Fill two vials about half way with BBs.
6. Place the bottom portion of a paper clip hook in the center of each vial and fill the rest of the vials completely with BBs.
7. Securely fit the cap with the paper clip hook on each vial.
8. Repeat steps 5–7 with each of the remaining materials: gravel, iron filings, and sand.
9. Securely cap the two empty vials.
10. Use a permanent marker and write numbers 1–5 on the caps according to the list below.

    1—Empty (no paper clip hanger needed)
    2—BBs
    3—Gravel
    4—Iron filings
    5—Sand

Safety Precautions

Wear chemical splash goggles or safety glasses. Instruct students to wipe up any spills immediately. Please follow all laboratory safety guidelines. Please review current Safety Data Sheets for additional safety, handling and disposal information.

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. All materials may be stored for future use. If any water leaked into the vials, spread materials out on paper towels to dry completely before storing.

Lab Hints

• Enough materials are provided in this kit for 30 students working in groups of three or for 10 groups of students. This laboratory activity can reasonably be completed in one 45- to 50-minute class period. The prelaboratory assignment may be completed before coming to lab, and the data compilation and calculations may be completed the day after the lab.
• This lab may be set up as five activity stations, with two vials of each type at each station. Students may complete each station in any order, rotating from one station to the next, making sure they are recording data in the correct place on the worksheet. Station 1 with the empty vial requires no water or spring scale, just a metric ruler. Alternatively, all the vials may be placed at a central location where students can take one at a time and return each vial as they finish collecting data.

Teacher Tips

• This guided-inquiry investigation fits in well with the concepts of forces, properties of fluids, and liquid pressure.
• Students should have some knowledge of Newton’s second law, F = ma, acceleration due to gravity, and weight as a measure of the force of gravity to understand the calculation in Question 4. A quick review may be helpful.
• Instruction in the use of a spring scale may be necessary. With no weight on the scale, students should align the flat top portion of the disk with the zero mark and check this before each use. A 5-N spring scale has a precision of 0.1 N, and students may estimate ±0.05 N.
• Some accounts describe Archimedes as having placed the crown in a full container of water and measuring the overflow, then comparing the overflow from the same mass of pure gold. This method has met with some criticism, as the difference in the displaced water would have been too small to measure accurately, especially with the surface tension of the water creating a source of error. This method also does not employ the law of buoyancy. Since Archimedes also worked with levers, he may have suspended the crown on one side of a balance and a nugget of gold of equal weight on the opposite side. Both could be submerged in water at the same time. If the two objects remained balanced, that would mean the buoyant force on each was the same, and their volumes would be equal. If the crown had a greater volume than the mass of pure gold, then the buoyant force on the crown would be greater, and the balance would tip down on the gold nugget side.
• As an extension, measure the weight of the empty vial out of water and when placed in water. Help students discover why the buoyant force on the empty vial is less when the vial is not completely submerged in the water. This can lead to a discussion of why objects sink or float.
• Discuss possible sources of error in this investigation such as the effect of the cap on the total volume, the limitations of the accuracy of the spring scale, etc.
• Explore the relationship between density and buoyancy with Flinn Scientific’s Archimedes’ Principle—Student Laboratory Kit (Catalog No. AP6380).

Answers to Prelab Questions

1. The volume of a cylinder can be calculated using Equation 2.
   {12196_PreLab_Equation_2}
   1. What is the volume in cubic centimeters (cm³) of a cylinder that has a radius, r, of 3 cm and a height, h, of 9 cm?

      V = 3.14(32) (9) = 254 cm³

   2. If the cylinder is completely submerged in water, what volume of water will the cylinder displace?

      The cylinder will displace the same amount of water as its volume, 254 cm³.

   3. One cm³ of water has a mass of 1 g. What is the mass of the displaced water?

      254 cm³ x 1 g/cm³ = 254 g

2. An object weighs 9.2 newtons (N). When submerged in water, it weighs 7.8 N. Use Equation 1 from the Background section to calculate the buoyant force acting on the object.

   Net force (N) = F_g + (– F_B)
   F_B = F_g – Net force
   F_B = 9.2 N – 7.8 N = 1.4 N

Sample Data

Part A.

Data Table 1. Empty Vial

Part B.

Observations
What happens to the reading on the spring scale as the vial is lowered into the water?

The reading on the spring scale decreases as the vial is lowered into the water. Once the vial was completely submerged, the reading on the scale stabilized.

Data Table 2. Vials 2–5  Data Table 3. Water Displacement

Answers to Questions

1. Calculate the buoyant force, F_B, for each vial numbered 2–5. Record these values in Data Table 2.

   See Data Table 2. Sample calculation: 2.10 N – 1.50 N = 0.60 N

2. Examine the buoyant force for each vial.
   1. How does the buoyant force compare from one vial to the next?

      The buoyant force is the same or nearly the same for each vial.

   2. Does there seem to be a correlation between the weight of the vial out of water and the buoyant force?

      No, the buoyant force does not seem to be affected by the weight of the vial.

   3. Does there seem to be a correlation between the volume of the vial and the buoyant force?

      Yes, the buoyant force depends on the volume of the vial. Since the volume of each vial is the same, the buoyant force is also the same for each vial.

3. Consider the volume of the vial as recorded in Data Table 1.
   1. When the vial is completely submerged, what is the volume of the displaced water? Record this value in Data Table 3.

      See Data Table 3. The volume of the displaced water is the same as the volume of the vial.

   2. What is the mass of the displaced water in grams? Hint: See Prelab Question 1c. Record the mass in Data Table 3.

      57.9 cm³ x 1 g/cm³ = 57.9 g

   3. Remember that 1 g = 0.001 kg. Calculate and record the mass of the displaced water in kg.

      57.9 g (0.001 kg/gm) = 0.58 kg

4. Since force = mass x acceleration (F = ma), by multiplying the mass of the displaced water in kg by the acceleration due to gravity (9.8 m/s²), one can find the weight (F_g) of the displaced water in newtons.
   1. Calculate and record the weight of the displaced water.

      F_g = 0.058 kg (9.8 m/s²) = 0.57 N

   2. How does the weight of the displaced water compare to the buoyant force acting on the vial?

      The weight of the displaced water is the same as the buoyant force acting on the vial.

5. Archimedes described the relationship between the weight of water displaced by an object and the buoyant force acting on the object. Write Archimedes’ Principle in your own words.

   The buoyant force acting on a submerged object is equal to the weight of the fluid the object displaces.

References

Special thanks to Michael Riley, Bidwell Jr. High School, Chico, CA, for providing the idea and the instructions for this activity to Flinn Scientific.

Archimedes. The Golden Crown. http://www.math.nyu.edu/~crorres/Archimedes/contents.html (accessed July 2018).

Introduction

Why do people and objects seem lighter in water than on land? Certainly no one actually “loses weight” when in water. This apparent weight loss of an object when it is immersed in a fluid is known as buoyancy. The Greek mathematician and scientist Archimedes (287 B.C.–212/211 B.C.) discovered some interesting facts about buoyancy. By making careful observations and measurements of objects submerged in water, you too can discover the law of buoyancy.

Concepts

• Net force
• Archimedes’ Principle
• Buoyancy and buoyant force

Background

Consider an object immersed in a container of water. The object is pulled downward by the force of gravity, F_g. In addition, the water is exerting pressure on the surface of the object in all directions. The pressure of a fluid increases with the depth of the fluid. Since the bottom of the object is deeper in the water than the top, the upward force of the water on the object is greater than the downward force of water and the object experiences a net upward force from the water (see Figure 1).

The net upward force of a fluid is called the buoyant force, F_B. The combination of the downward force of gravity on an object submerged in water and the upward buoyant force is the total net force on the object, and the apparent weight of the object in water (Equation 1). Note: Since the forces are acting on the object in opposite directions, the sign for the buoyant force is negative. When an object is immersed in water, the water level rises. Since the object and the water cannot occupy the same space at the same time, the water is pushed aside, or displaced. The volume of water that is displaced is equal to the volume of the completely submerged object (see Figure 2). Archimedes used this fact to help solve a problem he was given by King Hiero II of Syracuse. The king wanted to know if his newly made crown was pure gold, or if some of the gold that he had given the goldsmith had been replaced by silver. As Archimedes stepped into a bath, he noticed how the water level rose as his body displaced some of the water. He knew that a crown made of a certain weight of pure gold would have less volume than a crown of equal weight made of gold and silver; therefore, a pure gold crown would displace less water. Legend has it that Archimedes ran through the streets shouting “Eureka!” (I have found it!) when he realized how he could solve the problem. Archimedes’ Principle, also called the law of buoyancy, describes the relationship between the amount of fluid displaced by an object and the buoyant force of the water on the object. Have your own “Eureka moment” as you discover the law of buoyancy for yourself.

Experiment Overview

The purpose of this laboratory activity is to discover the relationship between the buoyant force of water on an object and the amount of water displaced by the object. Vials of identical volume filled with various materials will be weighed with a spring scale and then submerged in water and weighed again.

Materials

Prelab Questions

1. The volume of a cylinder can be calculated using Equation 2.
   {12196_PreLab_Equation_2}
   1. What is the volume in cubic centimeters (cm³) of a cylinder that has a radius, r, of 3 cm and a height, h, of 9 cm?
   2. If the cylinder is completely submerged in water, what volume of water will the cylinder displace?
   3. One cm³ of water has a mass of 1 g. What is the mass of the displaced water?
2. An object weighs 9.2 newtons (N). When submerged in water, it weighs 7.8 N. Use Equation 1 from the Background section to calculate the buoyant force acting on the object.

Safety Precautions

Wear chemical splash goggles or safety glasses. Wipe up any spills immediately. Please follow all laboratory safety guidelines.

Procedure

Part A. Calculating Volume of Vial

1. Obtain an empty vial and a metric ruler.
2. Measure the diameter of the bottom of the vial in cm.
3. Divide the diameter by 2 to find the radius. Record the radius of the vial in Data Table 1 on the Discovering Buoyancy Worksheet.
4. Measure the height of the vial, including the cap, in cm. Record this value in Data Table 1.
5. Calculate and record the volume of the vial in cm³.

Part B. Measuring Weight of Filled Vials

1. Obtain one of the filled vials, numbered 2–5, a spring scale, and a beaker ¾ filled with water.
2. Zero the spring scale.
3. Attach the spring scale to the paper clip hook of the vial and measure the weight of the vial in newtons (N). Record this value in the appropriate space in Data Table 2 on the Discovering Buoyancy worksheet.
4. Lower the vial into the water so the vial is completely submerged but not touching the bottom of the beaker. The top of the cap should be just below the surface of the water (see Figure 3).
   {12196_Procedure_Figure_3}
5. As the vial is being lowered into the water, observe what happens to the reading on the spring scale. Record your observations in Part B. on the worksheet.
6. Once the vial is completely submerged, observe and record the reading on the spring scale under Weight in Water in Data Table 2.
7. Remove the vial from the water, detach it from the spring scale, and dry the vial completely with a paper towel.
8. Repeat steps 1–7 with the remaining three vials, making sure to record the data in the appropriate spaces in Data Table 2.

Student Worksheet PDF

12196_Student1.pdf