A small varge measuring 8 meters wide and 6 meters deep is siling in freshwater.

Question

A small varge measuring 8 meters wide and 6 meters deep is siling in freshwater.  The barge has a length of 10 meters.  During a storm, the cargo was not properly secured, and it shifted to one side causing the barge to tilt as shown in the sketch.  Determine the following:

a) The total buoyancy force

b) The total weight of the vessel inc;uding its contents

c) Is the barge stable? Why?

d) The magnitude of the moment causing the barge to tilt

A small varge measuring 8 meters wide and 6 meters deep is siling in freshwater. The barge has a length of 10 meters. During a storm, the cargo was not properly secured, and it shifted to one side causing the barge to tilt as shown in the sketch. Determine the following: The total buoyancy force The total weight of the vessel including its contents Is the barge stable? Why? The magnitude of the moment causing the barge to tilt

Explanation / Answer

a)

Volume of displaced fluid, V = [(1/2)*(10/2)*4.618]*8 = 92.36 m^3

Weight of displaced fluid = (rho*V)*g = 1000*92.36*9.81 = 906051.6 N

Buoyancy force = 906051.6 N

b)

Weight = Buoyancy force = 906051.6 N

c)

As O' lies to the right of G, developed moment will be counter-clockwise which will restore its original poisiton. Hence, stable.

d)

angle = atan (2.309 / 5) = 24.78 deg

Moment arm = 5.383 - (0.691*sin24.78) - 5/cos24.78 = 0.414 m

Moment = 906051.6*0.414 = 375127.8 Nm

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