Physical Science Name:
In the first century BC, the Roman architect Vitruvius related a story of how Archimedes uncovered a
fraud in the manufacture of a golden crown commissioned by Hiero II, the king of Syracuse. The king ordered a
gold crown and gave the goldsmith the exact amount of metal to make it. When the monarch received it, the
crown had the correct weight but the monarch suspected that some silver had been used instead of gold. Hiero
asked Archimedes to determine whether the crown was pure gold. Archimedes knew that gold had a higher
density than silver, but did not know of a way to measure the density of anything but a solid cubic object. Because
the crown was a holy object dedicated to the gods, he could not disturb it in any way. He came up with a way to
determine if the density of the crown was lower than pure gold without destroying it.
Part 2: Measuring Buoyant Force
Substances of different densities will displace different amounts of water depending on their volumes. Even
though the crown had been made to have the same mass as the king’s gold, gold is denser and would have had a
lesser volume. A crown made with silver would be less dense and would have a greater volume. It would displace
more water per gram than a pure gold crown would. The weight of the water displaced by an object is equal to
the buoyant force on the object. By calculating the buoyant force, we can determine if the crown is of a pure
Find the weight of the crown:
Using a spring scale, measure and record the downward force of gravity on the crown.
Using a spring scale, measure and record the force of gravity on pure clay.
Using a spring scale, hold the crown suspended in a beaker of water. The force on the spring scale is the
force of gravity on the crown plus the upward buoyant force. Record the reading in your data table.
Using a spring scale, hold the “pure clay” suspended in a beaker of water. The force on the spring scale is
the force of gravity on the crown plus the upward buoyant force. Record the reading in your data table.
Calculate the buoyant force by subtracting the two forces. Remember that the buoyant force points up.
Repeat the calculation for the pure clay.
Force of Gravity Gravity + Buoyant force Buoyant force
1. Was the crown made of pure clay?
2. Would a crown of pure gold or pure silver weigh more in water if they had the same mass?
3. What would happen if a crown of pure gold and a crown of pure silver of the same mass were put on
opposite sides of a balance in a tub of water?