# Density

### Introduction

*Density* is something that affects many of our everyday decisions. Conciously or not, we make mental calculations of density every time we interract with the physical world around us. Can we slide that box? Can we lift that rock? This lab examines some of the ways density effects our everyday lives.

People are often confused about the difference between weight and density. There is an old riddle which highlights this confusion: “What weighs more – a pound of feathers or a pound of lead?” The answer, of course, is that both weight same – one pound. However, feathers are much less dense than lead, and therefore take up much more space. Density is the ratio of an object’s mass to its volume. This means that to find density, you must measure an object’s mass and divide it by the amount of space it takes up. The standard units of density are [kg/m^{3}], although other units are commonly used such as [g/ml], [g/cm^{3}], or [kg/l]. 1 ml has the same volume as 1 cm^{3}.

### Preliminary questions

- What two things do you need to know about a sample if you are to determine its density?
- What does density indicate?
- If you measured the density of a nail on the earth and then on the moon, would the densities vary? Why?
- If you measured the density of a gallon of water and then a teaspoon of water, would the densities vary? Why?
- Consider the concrete blocks below. Explain your answers.
- Which has the greatest volume?
- The greatest density?
- the greatest mass?

- Consider the balloons above. These balloons were the same size, but the second one has gotten smaller due to a change in temperature. Explain your answers.
- Which has the greatest volume?
- The greatest density?
- the greatest mass?

### Materials

- Copper sample
- Graduated cylinder
- Plastic ruler
- Triple beam balance with platform
- Stack of post-1982 pennies

### Activity 1: Finding density using volume

- Measure and record the mass of the copper sample.
- Determine the volume of the aluminum sample geometrically using a plastic ruler. Calculate the density. Show your measured values and all your calculations.
- Determine the volume of the copper again, this time using the tall, graduated cylinder. Calculate the density. Show your measured values and all your calculations.
- Which method to you think is more accurate? Why?
- Using the table below, compare the value of each density you just calculated to the accepted value using percent error.

Substance |
Density (g/cm^{3}) |

Aluminum | 2.70 |

Zinc | 7.08 |

Tin | 7.31 |

Iron | 7.87 |

Copper | 8.92 |

Silver | 10.50 |

Lead | 11.34 |

Gold | 19.32 |

### Activity 2: What are pennies really made of?

Before the middle of 1982, pennies were made of solid copper. Beginning about halfway into the year 1982, pennies started being made of a less dense metal core with very thin copper plating. You will determine what post-1982 pennies are made of.

- Is it better to use a single penny and determine its density, or it is better to combine multiple pennies together to determine their density as a unit? Why?
- What is your method for determining the density of a penny? Describe in detail.
- Calculate the density of a post-1982. Show all your work, and all your measured values.
- How will the small coating of copper on the outside of the mystery metal affect your measured density? How did you determine this?
- Compare your density calculation to the densities of the metals in the table above. What is your best estimate of the metal of the post-1982 pennies?