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 6.1 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 750 kg/min. How much additional force must be provided by the driving engines of the faster barge and (b) the flower 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

By Newton’s 3rd law, the force in the horizontal direction experienced by the coal must be of the same magnitude of force that the fast barge experiences due to the coal

F = dp/dt

=> dp(c,b) / dt = v(c,b)*dm/dt

dm/dt = 750 kg/min = 12.5 kg/s

v(c,b) = 0

v(c,b) = (20-6.1) km/h = 3.861 m/s

F = dp(c,b) / dt = 3.861 m/s * 12.5 kg/s

= 48.3 N

So the engine of the faster barge will require additional force of 48.3 N
and the engine of the slower barge will require 0 additional force

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