Archimedes' Principle-Gold Crown problem

[mchesypoof]

Homework Statement

You, Archimedes, suspect that the king’s crown is not solid gold but is instead gold-plated lead. To test your theory, you weigh the crown, and find it to weigh 60.0 N, and to have an apparent weight of 55.3 N when it is completely submerged in water. Take the density of gold to be 19300 kg/m3, the density of lead to be 11340 kg/m3, and the density of water to be 1000 kg/m3. Also, use g = 9.8 m/s2

(a) What is the average density of the crown?

(b) What percentage (by weight) of this crown is made of gold? The rest, we assume, is lead.

Homework Equations

The Attempt at a Solution

I found the answer to part a to be 12765kg/m^3, but haven't the slightest idea how to get the mass percent. I found the density percent, but don't know how to get mass percent from this.

 

[tiny-tim]

Take the density of gold to be 19300 kg/m3, the density of lead to be 11340 kg/m3, and the density of water to be 1000 kg/m3. Also, use g = 9.8 m/s2
…
(b) What percentage (by weight) of this crown is made of gold? The rest, we assume, is lead.
…
I found the density percent, but don't know how to get mass percent from this.

Hi mchesypoof!

Hint: what would the density be if it was half lead and half gold?

if it was 25% lead and 75% gold?

can you see a pattern and a formula?

 

[mchesypoof]

Yes! Thank you! It sounds so trivial now, thanks again.

 

[jimbo14]

How did you do find the average density? Anyone?

 

[tiny-tim]

welcome to pf!

hi jimbo14! welcome to pf!

How did you do find the average density? Anyone?

Show us what you've tried, and where you're stuck, and then we'll know how to help!