In the figure, two long barges are moving in the same direction in still water,

Question

In the figure, two long barges are moving in the same direction in still water, one with a speed of 12 km/h and the other with a speed of 20 km/h. While they are passing each other, coal is shoveled from the slower to the faster one at a rate of 850 kg/min. How much additional force must be provided by the driving engines of (a) the faster barge and (b) the slower barge if neither is to change speed? Assume that the shoveling is always perfectly sideways and that the frictional forces between the barges and the water do not depend on the mass of the barges.

Explanation / Answer

F external = dp / dt
F external = { [ (Mf + dm) * vf + (Ms - dm) * vs ] - [ (Mf * vf) + (Ms * vs) ] } / dt
F external = ( vf - vs ) * (dm / dt)
F external = [ ( 20 - 12 ) * ( 5/18 ) ] m/s * [ 850 / 60 ] kg/s
F external = 31.484 N

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