# ACTIVITY: EXERCISING METHODS OF MEASUREMENT

In the field of science, it is very important to understand measurement methods, the units we use, and how to manipulate them to get the information we need. In this project, you will review units of length, mass, and volume, practice converting from imperial units to metric units, and then calculate the density of objects using different methods.

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Though there are three parts to this experiment, your work needs to be submitted in a single document (saved in .docx, .rtf, or .odt format). Each section of your document must be labeled clearly, and you must include a proper heading. Make sure to include all of the data tables completely filled out and to answer all of the questions.

Vocabulary:

Measurement: Finding the number value of an object’s characteristics. May include length, mass, temperature, or other physical properties

Unit: A definite magnitude of a quantity or characteristic that is used as a common standard.

Conversion: Changing the units of measurement for the same object and characteristic.

Volume: The three-dimensional space that an object occupies

Mass: The amount of matter in an object

Density: The mass per unit of volume of a substance.

Part 1:

By now, you are probably familiar with the importance of including units when you are talking about a specific physical property. We use units to help standardize our measurements and make sure that everyone is using the same reference point.

The system of units most common in the United States is called the “Imperial System of Measurements”. It includes units like feet and inches for length, lbs and ounces for mass, and cups and fluid ounces for volume. Imperial units were designed for practicality of use and often are based on common cooking utensils or even the size of body parts (like the foot or inch).

The system of units most common around the world today and in the scientific community is the “Metric System of Measurements” (sometimes called “SI” units from the French title Système international). It includes units like centimeters and meters for length, grams and kilograms for mass, and milliliters or liters for volume. Metric units are designed around the factor 10. For example, there are exactly 100 centimeters in a meter. Similarly, there are exactly 1000 milliliters in a liter. As you can see, it is very easy to convert the scale of a unit by using simple prefixes.

The metric system is preferred in many scientific fields because of how easy it is to compare units, especially between different physical properties. For example, in the imperial system 1 cup of water is about 0.52 lbs. In the metric system, 1 liter of water is 1 kilogram (and therefore 1 milliliter = 1 gram). Similarly, 1 milliliter of volume is exactly equal to 1 cubic centimeter (cm3). When we need to calculate derivative properties (calculated from many basic properties) such as density, acceleration, or energy, it is much easier to use the metric system.

Luckily, it is very easy to convert between systems of measurements. Because each unit is measuring the same property, all we need is a “conversion factor” to change from one unit to another. For example, 1 inch = 2.54 cm. This project involves taking measurements using imperial units and then converting them into metric units so that it is easier to calculate the derivative properties we want, such as the density of an object.

Part 2:

Now we will practice taking measurements and converting into the units we want. Then we will calculate the density of two different objects.

Materials:

One regular-shaped object (cube or rectangular prism)
One irregular-shaped object (such as a rock)
Kitchen balance
Ruler (inches)
Large liquid measuring cup or pitcher (units of cups and ounces)
Latex Balloon
String
Possibly a pitcher or bucket

Procedure:

Method 1: Regular shaped objects

Measure the mass of your regular-shaped object using a kitchen balance. Record the mass of your object in pounds (lbs) or ounces (oz) depending on the size of your object and record in the provided data table.
Convert your mass measurement into metric units using the conversion factors provided. Record your observations and results in the table.
Use a ruler to measure the length, depth, and height of the object. Record the length of each measurement in inches in the table.
Convert your length measurements into metric units using the conversion factors provided. Include the calculations and results in the table.
Calculate the volume of the object by using the formula: Volume = Length x Depth x Height. Show your work below the table
Calculate the density of the object using the formula: Density = mass / volume. Show your work below the table:

Volume = Length x Width x Height = _____(cm) x _____(cm) x _____(cm) = _____(cm3)

Density = mass / Volume = _____(g) / _____(cm3) = _____ (g/cm3)

Method 2: Irregular-shaped objects

Measure the mass of your irregular-shaped object using a kitchen balance. Record the mass of your object in pounds (lbs) or ounces (oz) depending on the size of your object and record in your data table.
Convert your mass measurement into metric units using the conversion factors provided. Record your calculation and results in the table.
Pour water into the liquid measuring cup, stopping at one of the marked levels. Record this volume of liquid in your data table (cups or fluid ounces).
Place your irregular shaped object into the water until it is completely submerged. Record the new water volume level in your data table (cups or fluid ounces).
Convert your volume measurement into metric units using the conversion factors provided. Record the calculations and results in your table.
Find the volume of your irregular-shaped object by subtracting the water+object volume by the original water volume. Show your work below the table
Calculate the density of the object using the formula: Density = mass / volume. Show your work below the table:

Object Volume = (Water Volume + Object) – (Water Volume) = _____ (mL) – _____(mL) = _____ (mL)

Density = mass / Volume = _____(g) / _____(mL) = _____ (g/mL)

Part 3:

Now we will use our knowledge of volume, density and conversion factors to determine something that would be very difficult to measure using everyday tools: the mass of air inside a balloon. We will be using both of the previous methods to determine the volume of our balloon.

Procedure:

1. Fill your balloon up with air using your breath, a pump, or an air compressor. Try to get the balloon into as close to a spherical shape as you can. Try letting some air out of the balloon, pushing the remaining air to the top, and twisting the bottom of the balloon before tying your knot. A smaller balloon will be easier to handle and perform calculations on.

2. (Method 1)

a. Calculate the circumference of your spherical balloon by wrapping a string around the center of the balloon. Measure the length of the string in inches and record it in your data table.

b. Convert your length measurements into metric units using the conversion factors provided. Include the calculations and results in the table.

Circumference = _____ (in) x 2.52cm = Circumference ____ (cm)

c. Calculate the radius of the balloon using the formula below:

Radius = Circumference / 2·pi ____ (cm) = _____ (cm) / 2·pi

d. Calculate the volume of the balloon using the radius you calculated and the formula provided beneath the table (make sure to cube your radius).

3. (Method 2)

a. Prepare a container of water to submerge your balloon into. If the balloon is too big for your liquid measuring cup, you might need to use a bigger container of water like a pitcher or a bucket. You can use your liquid measuring cup and a marker to measure and mark some volumes on the side of your container.

b. Record the volume of water in your container (in cups).

c. Convert your volume measurement into metric units using the conversion factors provided. Record the calculations and results in your table.

d. Submerge your balloon in the water and record the new water volume level (in cups) in your data table.

e. Convert your volume measurement into metric units using the conversion factors provided. Record the calculations and results in your table.

f. Find the volume of your balloon by subtracting the water+balloon volume by the water volume. Show your work below the table.

Method 1 Volume:

Volume of a sphere = 4 / 3·pi = 4/3 x pi x (____ cm)3 = _____ (cm3)

Method 2 Volume:

Balloon Volume = (Water Volume + balloon) – (Water Volume) = _____ (mL) – _____(mL) = _____ (mL)

*Don’t forget that 1 mL = 1 cm3*

Your calculated volumes for the balloon should be close to each other, but they probably aren’t exactly the same. For the future calculations, you can pick the volume you think is most accurate, or take an average of the two values.

Wikipedia lists the average density of air at room temperature to be 0.001204 g/cm3. Now that we know the density of the air in the balloon and the volume of the balloon, we can solve for the mass of the air in the balloon. Use the formulas below to calculate the mass of the air in the balloon.

Density(g/mL) = mass(g) / volume(mL) Therefore: Mass(g) = Density(g/mL) x Volume(mL)

_____ (grams) = _____(g/mL) x _____(mL)

Questions:

What is the mass of air inside your balloon? Does this answer make sense to you?
Why does Method 1 only work with regularly-shaped objects?
Will Method 2 work for any objects? What limitations might it have?
Why did we convert all of our units into metric units before calculating the density of our objects?
Why do you think the measurements for you balloon volumes were slightly different?
Is one method more accurate at determining volume than the other? What makes a method accurate or inaccurate?
Why can’t we just measure the weight of the balloon to determine the mass of the air inside it? [hint: think about doing the project with a helium balloon instead]

Summary of Submission Requirements:

Section titles
All calculations are complete and thorough
All work is typed
Completed work submitted through TurnItIn
Ignitia assignment submitted with TurnItIn Submission ID

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