Physics

posted by .

Archimedes purportedly used his principle to verify that the king's crown was pure gold, by weighing the crown while it was submerged in water. Suppose the crown's actual weight was 14.0 N. The densities of gold, silver, and water are 19.3 g/cm^3, 10.5 g/cm^3, and 1.00 g/cm^3, respectively.

(a) What would be the crown's apparent weight if it were made of pure gold?

(b) What would be its apparent weight if it were made of 80% gold and 20% silver, by volume?

  • Physics -

    Gold, being denser than silver, will have less volume and less buoyant force acting upon it.

    (a) Crown mass = W/g = 14.0/9.8
    = 1.428 kg
    Crown volume = V = 1428 g/19.3 g/cm^3
    = 74.0 cm^3 = 74.0*10^-6 m^3
    Buoyant force = V*g*(water density)
    = 74*10^-6*9.8*1000 = 0.725 N
    Apparent weight = 14.0 N - 0.725 N
    = 13.3 N

    (b) density of alloy = 0.8*19.3 + 0.2*10.5 = 17.54 g/cm^3
    Volume will be 1.10 times as large to achieve the same crown weight.
    Buoyancy force will be 10% greater. or 0.798 N
    Apparent weight = 13.2 N

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics

    Take the density of the crown to be . What is the ratio of the crown's apparent weight (in water) to its actual weight ?
  2. physics

    According to legend, to determine whether the king's crown was made of pure gold, Archimedes measured the crown's volume by determining how much water it displaced. The density of gold is 19.3 g/cm^3. If the crown's mass was 6.00 * …
  3. English

    Can you please check the following sentences?
  4. physics

    The density of gold is 19 times that of water. If you take a gold crown weighing 24 N and submerge it in water, how much upward force must you exert on the submerged crown to keep it from accelerating?
  5. physics

    The density of gold is 19 times that of water. If you take a gold crown weighing 24 N and submerge it in water, how much upward force must you exert on the submerged crown to keep it from accelerating?
  6. Physics

    A king's crown is said to be solid gold but may be made of lead and covered with gold. when it is weighed in air, the scale reads 0.475 kg. when it is submerged in water the scale reads 0.437 kg.is it solid gold?
  7. Physics

    The density of gold is 19 times that of water. If you take a gold crown weighing 32 N and submerge it in water, how much upward force must you exert on the submerged crown to keep it from accelerating?
  8. Physical Science

    Suppose an all good crown has mass m=3800 grams. Gold has a density of 19 grams/ cm^3. What is the volume of water displaced by a gold crown (in cm^3)?
  9. Chemistry 101

    A crown is determine to weigh 2.65 kg. When this crown is submerged in a full basin of water, the overflow is found to be 145 mL. Is the crown pure gold or a gold-silver alloy?
  10. Chemistry 101

    A crown is determine to weigh 2.65 kg. When this crown is submerged in a full basin of water, the overflow is found to be 145 mL. Is the crown pure gold or a gold-silver alloy?

More Similar Questions