## Density and Measurement

**Purpose: To determine the density of an unknown object. **

**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**

Solid | Volume |
---|---|

Rectangular | (length) x (width) x (height) |

Cylinder | π x (radius) x (height) |

Where π = 3.14159.

**Experiment, Data and Results**

**Questions**

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