# Density

## Density and Measurement

#### Objectives

• To become familiar with the physics laboratory equipment.
• To learn to distinguish between measured and calculated quantities.
• To understand the concepts of significant figures.
• To become aware of the uncertainty associated with measurement.
• To learn how to use calipers.

#### Equipment

• Scale, Vernier Calipers
• Two differently shaped metal objects: rectangular solid and a cylinder

#### Theory

An important concept in experimental science is the difference between measured quantities and calculated quantities. In this experiment, you will be directly measuring lengths and mass of the four regularly-shaped solids: cube, rectangular solid, cylinder, sphere. You will be using the measured lengths to calculate the volume of each of the solids. The lengths are the measured quantities; the volume is the calculated quantity.

##### Density

You will then calculate the density ρ (from the greek letter “rho”, pronounced “row”) as equal to the mass of the object (m) divided by the volume (V). Mathematically, we write the formula as:ρ = mass / volume

##### Significant Digits

The devices you will be using to measure the lengths and the mass will each have their inherent limitation on how accurate they can be. The number of significant figures for each measured quantity is limited by the precision of the instrument. Significant figures are the digits that contribute to the precision of a number.For example, the Vernier calipers provide an accuracy of a measurement of length to the nearest hundredth of a centimeter. Any data that is recorded using this device should be recorded with a number that includes hundredths of a centimeter, but no more (i.e. 1.26 cm, but not 1.268 cm or 1.2684 cm).Is is also important to remember that a calculated quantity cannot have more significant figures than the measured quantities that went into it.

##### Volume of various geometric objects
SolidVolume
Rectangular(length) x (width) x (height)
Cylinderπ x (radius)`2` x (height)

Where π = 3.14159.

#### Experiment, Data and Results

##### Rectangular Solid

Have each student measure the length, the width, and the height of the rectangular solid using the Vernier calipers, and to calculate its volume. Record each partner’s data in the table below.

 Length   (cm) Width   (cm) Height   (cm) Volume (cm3) mass (g) ρ (g/cm3)

Calculate the average volume and write it down with the correct units.

Measure the mass of the object and record it with the correct units.

Calculate the density by dividing the mass over the volume and write it down with the correct units:

##### Cylinder

Have each student measure the radius and the height of the cylinder and record it in the table. Calculate the volume of the cylinder and record it.

 Student Name Radius   (cm) Height   (cm) Area = πr2   (cm2) Volume (cm3) mass (g) ρ (g/cm3)

Calculate the average volume and write it down with the correct units.

Measure the mass of the object and record it with the correct units.

Calculate the density by dividing the mass over the volume and write it down with the correct units:

#### Questions

Can you identify the most likely material the objects are made of?