Physics, 06.10.2019 04:00 emwemily

Agold crown recently acquired is suspected to be brass covered in gold. the crown weighs 25.0 n in air and has an apparent weight of 22.5 n in fresh water. based on these results, which of the following conclusions is correct?
a. $\rho_{gold}$ = 19,300 kg/m³b. $\rho_{brass}$ = 8300-8700 kg/m³

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the weight of the crown is very close to the weight of brass, so the crown is made of brass with a very small part of gold.

Explanation:

Let's apply Archimedes' principle to this situation, in this principle he says: the thrust (B) is equal to the weight of the liquid dislodged.

Let's analyze the weight of the crown in the air has a weight of 25.0 N, when we submerge it in water the weight (F = 22.5 N) is reduced due to the thrust of the liquid, we can look for the thrust

F = W -B

B = W -F

B = 25.0 -22.5

B = 2.5 N

It is the weight of the water dislodged, using the concepts of density

d = m / v

B = (dw Vw) g

dw = 1000 kg / m3 water

Vw = B / dw g

Vw = 2.5 / 1000 9.8

Vw = 2.55 10⁻⁴ m3

As the crown is submerged this volume is also the volume of the crown, so we can calculate the weight of the crown for the two given materials

Gold

W gold = dgold V g

W gold = 19300 2.55 10⁻⁴ 9.8

W gols = 48.2 N

Brass

W brass = dbrass V g

W brass = 8700 2.55 10-4 9.8

Wbrass = 21.7 N

As we can see the weight of the crown is very close to the weight of brass, so the crown is made of brass with a very small part of gold.

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Agold crown recently acquired is suspected to be brass covered in gold. the crown weighs 25.0 n in a...

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