Weight of Gold & Lead Crown: Calculate & Solve

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SUMMARY

The discussion focuses on calculating the weight of a crown made of pure gold and a combination of gold and lead based on its volume of 26 in³ (0.015 ft³). The density of gold is established at 19,300 kg/m³ (1200 lb/ft³), while lead's density is noted as 709 lb/ft³. The weight of the crown can be calculated using the formula m = V × D, followed by W = mg, where g is the acceleration due to gravity (9.8 m/s²). The calculations for both scenarios yield definitive weights based on the provided densities.

PREREQUISITES
  • Understanding of density and its units (e.g., kg/m³, lb/ft³)
  • Familiarity with basic physics formulas for mass and weight (m = V × D, W = mg)
  • Knowledge of the properties of gold and lead, including their respective densities
  • Basic understanding of volume measurement conversions (in³ to ft³)
NEXT STEPS
  • Calculate the weight of the crown if made entirely of gold using the formula W = V × D.
  • Determine the combined weight of a crown made of half gold and half lead.
  • Explore the concept of buoyancy and how it relates to the weight of objects in water.
  • Research the implications of density in material selection for engineering applications.
USEFUL FOR

Students in physics or engineering, jewelers calculating material weights, and anyone interested in the practical applications of density and buoyancy principles.

Sabres151
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Here's the question:

It is determined by immersing a crown in water that its volume is 26in^3 = 0.015ft^3.

What would its weight be if it were made of pure gold?
What would its weight be if it half of its volume were gold and half lead?

I'm not sure how to solve. I know this for gold:

D = 19,300kg/m^3
Dw = 1200lb/ft^3

I thougt the two equations needed would be the following:

m = V X D (since we know volume)
followed by...
W = mg, where m is solved for above and g = 9.8... My answer of 2837 didn't make much sense...
 
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Well figure out what you do know, e.g. what is the weight of the crown out of water if gold? What would the combo weight be? What is the weight of an equivilant amount of water?

Dw is the density of gold?.?

The density of lead is 709 lb/cubic foot, and the density of water is 62.4 lb/cubic foot in case you didn't know.
 
Last edited:

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