Capacity of a Barge: 10.56 Million kg Coal

[Mitchell Powell]

Homework Statement

An open barge has the dimensions shown in the figure.
https://physicsforums-bernhardtmediall.netdna-ssl.com/data/attachments/59/59574-46462a33e8dd3e05fa12094d99749d9c.jpg
If the barge is made out of 5.2-cm-thick steel plate on each of its four sides and its bottom, what mass of coal can the barge carry in freshwater without sinking?

Homework Equations

p = m/V

The Attempt at a Solution

V = 22 * 40 * 12 m³ = 10,560 m³

p_water = 1,000 kg/m³

1,000 kg/m³ = m/10,560

m = 1,000*10,560 = 10,560,000 kg

 

[SteamKing]

What about the steel plate from which the barge is constructed? Is this a new, weightless steel?

 

[Mitchell Powell]

I wasn't sure what to make of that. The density of steel is not given, and answers online range from 7,750 kg/m³ to 8,050 kg/m³. Is it significant if I go with one vs. the other?

 

[SteamKing]

When in doubt, you can take an average density of steel, or use the heaviest steel to cover your bases.

As to whether the weight of steel is significant, you have enough information to determine the weight of steel in the barge.

 

[Mitchell Powell]

I see that I can determine the volume of steel used,

H = 12 m
W = 22 m
L = 40 m
T = .052 m

V = 2(H * W * T) + 2(H * L * T) + (L * W * T) = 123.136 m³

I can't see how you would determine the weight of steel with the information given, without using the density (7,900 kg/m³ average).

 

[Mitchell Powell]

I was actually able to work it out. Seems the steel density is insignificant.

m_barge = p_steel * V = 7,900 * 123.136 = 972774.4 kg

Since we are adding weight to the barge by adding coal, the weight of the barge should be m_barge + m_coal

As long as the density of the barge is less than the density of water (1000 kg/³), the barge floats. So, setting the density of water equal to the changing density of the barge gives:

p_water = (m_barge + m_coal)/V

Solving for m_coal = (p_water * m_barge) - m_barge

The mass of the coal comes out to roughly 9.6 * 10⁶

Thank you for your help! I greatly appreciate it!