## Experiment 3-4

Density of Solids

### Background Information

We have all noticed that some objects give us the impression of being heavy while others seem light.  But this is not just a matter of mass.  a large sheet of aluminum seem light while a much smaller piece of lead seem light.  Apparently our impressions are formed by comparing the objects' mass to what we anticipate their mass should be.

It was Archimedes (of Syracuse, Sicily, 287 BC to 212 BC) who receives credit for realizing that this could be measured as a valuable characteristic property.  Archimedes may have been the greatest mathematician of ancient times.  His job entailed applied mathematics including fortifying and defending the city from invasions, tasks that history (or perhaps mythology) records he approached with "out of the box" creativity.

Archimedes was asked by Hiero, the king of Syracuse, to determine whether a crown fashioned by alchemists had been made of the pure gold provided, or diluted in both content and value as rumored of some alchemists.  The task was complicated because the king wished the content of the crown determined, but required that it not be altered or destroyed in testing.  Procedures such as melting point would destroy the craftsmanship of the crown.  Archimedes could not find an established procedure which was capable of the task.  Serendipity is a process where a mind prepared in all the relevant understanding seems to accidentally discover a solution to a perplexing problem.  As often happens, the discovery occurred to Archimedes not when he was hard at work, but when he was relaxing in the public bath.  As he descended into the bath he notice the common knowledge event of the water meniscus rose according to his volume, just as his weight was decreased by the buoyancy of that water.  This connection of volume and weight led immediately to his appreciation that this connection provided a non-destructive test providing a characteristic property useful for verifying if the crown was pure gold.  He was so excited that he ran naked through the streets of Syracuse shouting Eureka!  eureka!  (I have found it!)

As in Archimedes day, we have balances to measuring mass.  We also can measure the volume of irregular shaped solids using the displacement of a liquid such as water.  The ratio of those properties is today known as density:

Density = mass / volume

### Experiment

In this experiment we want to compare the densities of a set of diverse solid objects.

1. Select a half dozen or more solids that are or a size and mass convenient to measure with your equipment.
2. Use your balance to measure the moss of each object. (Recall that a penny is approximately 2.5 grams.
3. Measure enough water in your graduated cylinder to potentially immerse an object.
4. Submerge the object under water and measure the new meniscus.
5. Subtract the volume of the water alone from the volume of water containing the object.
6. Do this for each object, obtaining the volume in milliliters or equivalent cm3.
7. Divide the mass of each (in grams) by the volume (in mL or cm3)
8. Compare the densities.  Do any have about the same density?  Are there other properties such as appearance that indicate these objects are in fact composed of the same material?

to experiment 3-5