Find the length of a roll of GI steel sheet given its weight

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To find the length of a roll of galvanized iron sheet steel given its weight, the density, width, and thickness are essential. The cross-sectional area is calculated as 0.000005 m², and using the density of 7850 kg/m³, the mass of the roll is confirmed to be 75 kg. The volume is derived from the mass and density, leading to a calculation of length based on the area. A discrepancy arises in the calculations, particularly regarding the conversion between weight and mass, which prompts clarification on the differences between force, weight, and mass. Ultimately, the corrected length of the roll is approximately 2011.39 meters.
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Homework Statement


I have a roll of galvanized iron sheet steel.
Its width is 19mm and thickness 0.25mm
Density 7850 kg/m^3
Weight of the roll is 75kg
I want to find how long would be the roll if its unwound.

Homework Equations


Density D = M / V
Length L = V / A
Area A = Width * Thickness

The Attempt at a Solution



I need to find the volume of the material first,
so I find the cross sectional area A from the length and thickness
A = 0.000005 m^2

For finding volume I know that D = 7850 kg / m^3 but I need to find mass (M)
So here is where I'm stuck up
Should I use Mass as 75kg
or Do I need to calculate Mass from the Weight which is 75 kg.
using W = m * g or m = W/g
even in this equation so m would be 75 / 9.8 = 7.65kg.
The final answer I have is Length = 200m but I don't know if that is correct.
 
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Do a quick check.

What does one metre weigh in kg? ( 1 * 0.019 * 0.00025 * 7850 ) = 0.0372875 kg
So the length is ( 75 / 0.0372875 ) = 2011.39 m

Where is the missing factor of 10 ?

What is the difference between a force a weight and a mass?
Consider units; Newton, kg force and kg mass.
 
Last edited:
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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