Answered: A rectangular barge, 5.4 mm long and…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A rectangular barge, 5.4 mm long and 1.2 mm wide, floats in fresh water. Suppose that a 360-kgkg crate of auto parts is loaded onto the barge. How much deeper does the barge float?

Expert Solution

Step 1: Weight and buoyancy force

When the crate is loaded onto the barge, the weight of the crate will be equal to the buoyancy force.

$table row cell W subscript b equals F subscript B end cell row cell m subscript b g equals rho subscript text fluid end text end subscript V subscript text displaced end text end subscript g end cell row cell m subscript b equals rho subscript text fluid end text end subscript V subscript text displaced end text end subscript end cell row cell m subscript b equals rho subscript text fluid end text end subscript left parenthesis l cross times b cross times h right parenthesis end cell row cell h equals fraction numerator m subscript b over denominator rho subscript text fluid end text end subscript left parenthesis l cross times b right parenthesis end fraction end cell end table$

Here, m_b is the mass of the crate, $rho subscript text fluid end text end subscript$ is the density of the water, l is the length of the barge, h is the depth of the barge, and b is the width of the barge.

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