What Would Be the Mass of an Iron-Dense Empire State Building?

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Homework Help Overview

The discussion revolves around calculating the mass of an object with the dimensions of the Empire State Building, assuming it has the density of iron. The original poster provides the estimated volume and density values to facilitate the calculation.

Discussion Character

  • Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the method of calculating mass by multiplying density by volume. There is a question regarding the conversion of units from cubic feet to cubic meters and whether the calculations were performed correctly.

Discussion Status

Some participants have provided calculations and are exploring the implications of their results, such as the mass exceeding 8 billion kilograms. A follow-up question regarding the energy required to propel the object at high speeds has also been introduced, indicating a shift in focus.

Contextual Notes

There is a mention of the assumption of 100% efficiency in propulsion and the neglect of air resistance in the follow-up question, which may affect the discussion on energy calculations.

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If an object the size of the empire statbuilding had iron density,what would be ...

the mass of it?

The estimated volume of the empire state building is 37 million cubic feet,how could I calculate the mass of this solid object if it had a density of Iron(which would be 7870 kg/m³)?
 
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Multiply the density by the volume.
 


So I converted the ft^3 to m^3 and I have 1.04 million m^3* 7870kg/m^3=8184800000 kg/m^3.Did I do this right or do I have to remove the kg/m^3?
 


Wow if I am correct is that over 8 billion kilograms of mass?
 


So here is a follow up question,how much energy would be required to propel this object at Mach 7 speeds?
 


1/2 mv2

m=mass in kg
v=speed in meters / second

That would be if the propulsion device was 100% efficient and there was no air resistance.
 

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