Calculating the Height Difference of a Loaded Barge - Urgent

[matthew77ask]

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.

 

[matthew77ask]

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.

 

[eep]

You're not going to get an answer faster by posting in multiple forums.

 

[Tide]

HINT: The buoyant force equals the weight of water displaced.

 

[matthew77ask]

Sorry, this topic really is difficult for me - what would be the solution?

thanks a lot for the help

 

[Doc Al]

Look up Archimedes' principle and buoyant force. (Tide gave you the big hint.)

 

[Doc Al]

Please give the OP the opportunity to do his own work.

 

[Curious3141]

Archimedes: (density of water)*(initial hight)*A*g = m*g
...

We try not to do the work wholesale for the poster.

 

[matthew77ask]

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?

 

[Curious3141]

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.