Weight of Gold & Lead Crown: Calculate & Solve

[Sabres151]

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...

 

[civil_dude]

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.

 

[kyle8921]

I would approach this problem by first converting the given volume of the crown from cubic inches to cubic feet. This can be done by dividing 26in^3 by 1728in^3/ft^3, which gives a volume of 0.015ft^3.

Next, I would use the density values provided for gold and lead to calculate the mass of each material. The equation for mass is mass = density x volume. For pure gold, the mass would be (19,300kg/m^3)(0.015ft^3) = 289.5kg. For a mixture of half gold and half lead, the mass would be ((19,300kg/m^3)(0.0075ft^3)) + ((11,340kg/m^3)(0.0075ft^3)) = 144.8kg + 85.1kg = 229.9kg.

Finally, to calculate the weight of each crown, I would use the equation weight = mass x gravity. Since the question does not specify a specific location, I will assume a standard gravity of 9.8m/s^2. For the pure gold crown, the weight would be (289.5kg)(9.8m/s^2) = 2841.1N. For the half gold and half lead crown, the weight would be (229.9kg)(9.8m/s^2) = 2252.2N.

In summary, the weight of the crown if it were made of pure gold would be approximately 2841.1N, and the weight of the crown if half of its volume were gold and half lead would be approximately 2252.2N. It is important to note that these values may vary slightly depending on the actual density values used for gold and lead and the location where the weight is being calculated.