New Problem: Archimedes Reloaded

The king asks Archimedes (did they actually have kings in ancient Greece?) to test whether his crown is pure gold or a gold-silver alloy. Archimedes uses the following procedure.

  1. get a balance, which can tell whether two samples have the same or different mass
  2. put the crown in one pan of the balance, and add pure gold to the other end until the masses are even
  3. get a thing of water
  4. put the crown in the water and mark how high the water level is
  5. take the crown out of the water, put the pure gold in, and see if the water rises to the same level. if it does, the crown is pure gold. if not, the crown is part silver

Unfortunately, Archimedes’ test is not very sensitive. Even if he did not lose or add a single drop of water when switching the crown for the known pure gold, he would still have a hard time telling whether the water level was exactly the same, or a tiny bit different.

Using the same physical ideas, and without any fancy new material, Archimedes can design a far more sensitive test. How?

2 Responses to “New Problem: Archimedes Reloaded”

  1. Nik Says:

    Archimedes can weigh both the crown and the pure gold underwater. Once he does that it’s easy to figure out the buoyant forces acting on each one. Then he can more accurately calculate the volume of each and so find their densities. If the densities differ, the crown is made of an alloy. Though, he needn’t go further than find the buoyant forces, if they are unequal then the crown is a fake.

    I really should check your blog more often.

  2. Answer: Archimedes Reloaded « Arcsecond Says:

    […] Arcsecond Playing on the Sea-Shore, Rough Pebbles Welcome « New Problem: Archimedes Reloaded […]

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