Calculating the Height Difference of a Loaded Barge - Urgent

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Homework Help Overview

The discussion revolves around calculating the height difference in the water line of a barge when it is loaded with sand. The subject area includes principles of buoyancy and fluid mechanics, particularly focusing on Archimedes' principle.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the mass of the barge, the mass of the sand, and the resulting water displacement. Some question the assumptions made regarding the densities involved and the setup of the problem.

Discussion Status

There are various hints and guidance offered regarding the application of Archimedes' principle and the buoyant force. Some participants express difficulty in understanding the topic, while others emphasize the importance of allowing the original poster to engage with the problem independently.

Contextual Notes

There is a repeated emphasis on the urgency of the question due to impending exams, which may influence the nature of the responses. Additionally, some participants note the importance of clearly stating the implications of the calculations regarding the waterline's position.

matthew77ask
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Height of the loaded barge - urgent

Hi

Got a question to prepare for my exams tomorow.

A barge of mass m and area A is loaded with sand of mass M. What is the difference in water line between the empty and the loaded barge.

Many thanks for any reply...


Regards.
 
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Height of the loaded barge - urgent

Hi

Got a question to prepare for my exams tomorow.

A barge of mass m and area A is loaded with sand of mass M. What is the difference in water line between the empty and the loaded barge.

Many thanks for any reply...


Regards.
 
You're not going to get an answer faster by posting in multiple forums.
 
HINT: The buoyant force equals the weight of water displaced.
 
Sorry, this topic really is difficult for me - what would be the solution?

thanks a lot for the help
 
Look up Archimedes' principle and buoyant force. (Tide gave you the big hint.)
 
Please give the OP the opportunity to do his own work.
 
opee5230 said:
Archimedes: (density of water)*(initial height)*A*g = m*g
...

We try not to do the work wholesale for the poster.
 
Density * H1* A = m => H1 = m /(density*A)
Density * H2 *A = m+ M => H2 = (m+M)/(density*A)

hence
H2 - H1 = height difference = m / (density *A)

is this correct?
 
  • #10
matthew77ask said:
Density * H1* A = m => H1 = m /(density*A)
Density * H2 *A = m+ M => H2 = (m+M)/(density*A)

hence
H2 - H1 = height difference = m / (density *A)

is this correct?

That should be a big "M" (mass of sand) in the answer right? If so, it's correct.

BTW, remember to state that the new waterline (with sand) is higher up the barge than the old one, even if it seems obvious. Otherwise the answer isn't complete.
 
Last edited:

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