Measurement of density

• Physical meaning of density of a body
• Use of the caliper in measuring lengths

The density of a material is defined as its mass per unit volume. Different materials usually have different densities, so density is an important concept regarding buoyancy. In a well-known common story, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a wreath dedicated to the gods and replacing it with another, cheaper alloy.

Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the weight; but the king did not approve of this.

So, Archimedes took a relaxing immersion bath and observed from the rise of the warm water upon entering that he could calculate the volume of the gold crown through the displacement of the water. Allegedly, upon this discovery, he went running naked through the streets shouting, "Eureka!"

Mathematically speaking, for a homogeneous object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. Hydrostatic weighing is a method that combines these two, and we will use this method to measure the volumes of the cylinders supplied with the mobile lab.

• Vernier caliper, scale 0 – 160 mm, accuracy 0.05 mm (plastic) — 2213.10
• Electronic balance 300 g, readability 0.01 g — 2219.30
• Beaker low form 500 ml, borosilicate glass — 1118.20
• Beaker low form 100 ml, borosilicate glass — 1118.50
• Food colouring — 4207.56
• Specific heat cylinders — 4230.96
• Cylinder graduated, tall form with spout. Capacity 100 x 1 ml, borosilicate glass — 1226.15

• What is the physical principle that allowed us both a static measurement of volumes and a dynamical one in this experience?
• How would you describe the proportionality between the density and the volume of a body? In this experiment you used cylinders of different volumes with equal masses. What did you observe? Plot a graph with these data to check your answer.