How much deeper does the barge lower?

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AI Thread Summary
The discussion revolves around calculating how much deeper a rectangular barge sinks when a 400 kg block is loaded onto it. The key principle involved is Archimedes' principle, which states that the weight of the water displaced by the barge must equal the weight of the block. The barge's dimensions are 5 m long and 2 m wide, leading to a need to determine the additional volume displaced by the block. Participants highlight the importance of knowing the volume displaced and the area of the barge to find the solution more efficiently. Ultimately, the focus is on applying these concepts to find the exact depth increase of the barge.
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Homework Statement


  1. A rectangular barge floats in freshwater. When a 400 kg block is loaded on the 5 m long by 2 m wide barge, the barge sinks a few centimeters deeper. How much deeper does the barge lower?

Homework Equations


Archimedes' principle
This is where I am stuck. My textbook doesn't talk much about this at all.
barge.jpg


The Attempt at a Solution

 
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You've done all the hard work. How much deeper does the barge have to "sink" to displace the extra 0.4 m3?
 
Bystander said:
You've done all the hard work. How much deeper does the barge have to "sink" to displace the extra 0.4 m3?
barge.jpg
 
keithcuda said:
View attachment 78234
Yes, but you could have got there a bit faster from knowing the volume displaced and the area.
 
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