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How much deeper does the barge lower?

Thread starter keithcuda
Start date Jan 25, 2015

3 replies · 5K views · last reply Jan 25, 2015

keithcuda

Thread starter
Jan 25, 2015

#1

Homework Statement

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.

Handwritten-style worked notes under 'Knowns': Crate=400kg, Area of barge 5m*2m=10m², g=9.8m/s², Density of fresh water=1,000kg/m³, and volume of displaced water from crate = 400kg / 1000kg/m³ = .4m³; beside them, Density = mass/volume and Volume = mass/density.

The Attempt at a Solution

Discussion

Bystander

Science Advisor

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Gold Member

Jan 25, 2015

#2

You've done all the hard work. How much deeper does the barge have to "sink" to displace the extra 0.4 m³?

keithcuda

Jan 25, 2015

#3

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?

Handwritten-style worked solution on a worksheet: Knowns list crate 400kg, barge area 5m x 2m = 10m², g = 9.8m/s², fresh water density 1000kg/m³, displaced volume 400kg/1000kg/m³ = 0.4m³; red working gives buoyant force 3920kg m/s², then 3920 = 98100*h, h = 0.04m = 4cm.

haruspex

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Insights Author

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Jan 25, 2015

#4

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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