# Equal Mass

## Student Laboratory Kit

### Materials Included In Kit

Aluminum cylinder, 15 g, ½" diameter, 15*
Brass cylinder, 15 g, ½" diameter, 15*
Polyethylene cylinder, 15 g, ½" diameter, 15*
PVC cylinder, 15 g, ½" diameter, 15*
Nylon cylinder, 15 g, ½" diameter, 15*
*Cylinders are 15.0 g ±0.40 g. See Tips section.

(for each lab group)
Water, 2550 mL
Beaker (optional)
Graduated cylinder, plastic, 50- or 100-mL
Toothpick (or similar tool)

### Safety Precautions

Although the materials in this activity are considered nonhazardous, please use all normal laboratory safety precautions. Remind student to wash hands thoroughly with soap and water before leaving the laboratory.

### Disposal

The materials in this lab kit should be saved for future use.

### Teacher Tips

• Enough materials are provided in this kit for 30 students working in pairs or for 15 groups of students. This laboratory activity can reasonably be completed in one 50-minute class period.
• For a more accurate volume reading, a toothpick or similar tool should be used to totally submerge the polyethylene cylinder.
• For more accurate results have students measure the actual mass of each cylinder using a balance.
• As an extension to the given procedure, further demonstrate or explain buoyancy. Have each student group place one of the metal cylinders in a graduated cylinder of water to show that the metal cylinder is heavier than the upward force (buoyancy) exerted upon it from the water. Now have the students choose the longest cylinder and place it in a graduated cylinder of water. The floating plastic cylinder demonstrates that the upward force of the water is great enough to support the weight of the cylinder. It also shows that the displaced water actually weighs the same as the cylinder (it floats fully submerged). The total weight of the displaced water equals the weight of the cylinder.
• If time allows, the calculated volumes of the cylinders (v = πr2h) may also be compared to the measured volumes.
• You may also wish to compare the buoyancy of the cylinders using other liquids than water (e.g., salt water, vegetable oil, mineral oil).
• If glass graduated cylinders or beakers are used, be careful adding the metal objects in order to avoid breaking the glass vessel.

### Science & Engineering Practices

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

### Disciplinary Core Ideas

MS-PS1.A: Structure and Properties of Matter
HS-PS1.A: Structure and Properties of Matter

### Crosscutting Concepts

Patterns
Scale, proportion, and quantity

### Sample Data

{11962_Data_Table_1}

1. Was the same amount of water displaced for each sample cylinder? Why?
The amount of water displaced for each cylinder was different. The amount of water displaced is equal to the volume of the cylinder.
2. If all of the sample cylinders were of equal volume, would the same amount of water be displaced for each sample?
Yes, if each of the cylinders were of the same volume, the amount of water displaced would be equal.
3. What was the relationship between the volume and density of the sample cylinders? (Remember, they all have the same mass.)
It was an inverse relationship. As the volume of a cylinder increased, the density of the cylinder decreased.
4. Did any of the sample cylinders float in the water? If so, why?
The longest cylinder floated in the water. The density of this cylinder was less than the density of water.

# Equal Mass

### Introduction

What is the relationship between volume and density? Do objects of equal mass have the same density? Let’s experiment and find out.

### Concepts

• Density
• Length
• Specific gravity
• Mass

### Background

In this activity, the volume and density of five different cylinders of the same mass and diameter will be determined by water displacement. Using Equation 1, the volume of each cylinder may be determined.

{11962_Background_Equation_1}
{11962_Background_Figure_1}
If the mass and the volume of an object have been measured, then the density may be found using the following equation.
{11962_Background_Equation_2}

Density, which is defined as an object’s mass divided by its volume, is a characteristic property of a material. The density of a solid is commonly expressed as g/cm3. Remember that 1 mL = 1 cm3.

Specific gravity is a similar term to density. Specific gravity is a comparison of the density of a substance to the density of a reference substance (water for liquids). Since the density of pure water is approximately 1.00 g/cm3 at 20° C, the specific gravity of a substance is equivalent to the density. Specific gravity, however, is unitless.

### Materials

Water, 25 to 50 mL
Aluminum cylinder, 15 g, ½" diameter*
Brass cylinder, 15 g, ½" diameter*
Graduated cylinder, plastic, 50- or 100-mL
Nylon cylinder, 15 g, ½" diameter*
Polyethylene cylinder, 15 g, ½" diameter*
PVC cylinder, 15 g, ½" diameter*
Toothpick (or similar tool)
*Cylinders are 15.0 g ±0.4 g. For best results, mass each cylinder.

### Safety Precautions

Although the materials in this activity are considered nonhazardous, please use all normal laboratory safety precautions. Wash hands thoroughly with soap and water before leaving the laboratory.

### Procedure

1. Obtain a sample cylinder. Measure its length (in cm) and record its color in the data table.
2. Fill a 50- or 100-mL graduated cylinder about half way with water. Record the initial volume of water (in mL) in the data table.
3. Carefully place the sample cylinder into the graduated cylinder. It works best to tip the graduated cylinder and slide the sample cylinder down the side.
4. Record the new volume of water in the graduated cylinder in data table. This is the volume of the sample cylinder and the water. If the sample cylinder is not totally submerged in the water, use a toothpick (or similar tool) to gently push the cylinder into the water. Record the volume.
5. Does the sample cylinder float or sink in the water? Record your observation in the data table.
6. Calculate the volume of the sample cylinder using Equation 1 (see the Background section).
7. Record the volume of the sample cylinder in the data table.
8. Calculate the density of the sample cylinder using Equation 2. Remember that each sample cylinder weighs 15 g. Record the density of the sample cylinder in the data table.
9. Repeat steps 1–8 for the remaining four sample cylinders. Record all information in the data table.

### Student Worksheet PDF

11962_Student1.pdf

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