In Fig. 9-72, two long barges are moving in the same direction instill water, on

Question

In Fig. 9-72, two long barges are moving in the same direction instill water, one with a speed of 7.0 km/h and the other with aspeed of 18 km/h. While they are passing each other, coal isshoveled from the slower to the faster one at a rate of 850 kg/min.How much additional force must be provided by the driving enginesof (a) the faster bargeand (b) the slower barge if neither isto change speed? Assume that the shoveling is always perfectlysideways and that the frictional forces between the barges and thewater do not depend on the mass of the barges.

Fig. 9-72
Problem 79.

Explanation / Answer

The speed of one barge is u = 7.0 km/h and the speed of theother barge is v = 18 km/h. The coal is shoveled from the slower to the faster one at arate of 850 kg/min. The additional force that must be provided by the drivingengines of the faster barge is F1= (dm/dt) * (v - u) -----------------(1) Here,(dm/dt) = 850 kg/min = (850/60) kg/s = 14.1 kg/s and (v -u) = (18 - 7.0) km/h = 11 km/h = 11 * (1000/3600) m/s or (v - u) = 3.06 m/s Substituting the values in equation (1),we get F1= 14.1 * 3.06 = 43.1 N The additional force that must be provided by the drivingengines of the slower barge is F2= (dm/dt) * u Here,u = 7.0 km/h = 7.0 * (1000/3600) = 1.9 m/s or F2= 14.1 * 1.9 = 26.8 N

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