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- September 10th 2007, 12:27 AM #1

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## Tugboat problem

I am desperately in need of help for this problem..Please help! A tugboat of mass m = 200,000 kg pushes a barge with a mass of 800,000 kg so that starting from rest, they reach a speed of 2.9 m/s after 10s. Assume that the effects of gravity on the tug and barge are canceled by the effects of their supporting contact interactions with the water; and assume that friction interactions are negligible and that all forces are constant during the 10-s interval. The front bumper on the tug might buckle if a force of more than 150,000 N acts on it, and its propeller might fracture if it is asked to provide more than 250,000 N of force. Is this tug operating within these limits? Answer as follows: (a) Start with the barge. How much impulse did the contact interaction with the tug give the barge during the time interval in question? Argue that your answer implies that the barge’s contact interaction with the tug must have exerted a force of magnitude 160,000 N on the barge, and explain carefully why this means that the force exerted on the tug’s bumper also has a magnitude of 160,000 N, violating the limit. (b) Argue that the tug must therefore get a backward impulse of 1,600,000 kg * m/s from the barge during this interval. Yet you can calculate the tug’s actual net change in momentum during the interval from the information given. Using an arrow diagram, find the magnitude of the impulse that it must receive from the propeller, and show that this implies a propeller force of 200,000 N, which is within the operating limits of the propeller. (c) This result assumes no friction. Carefully explain, using a momentum-transfer model, how including friction would qualitatively affect these results. (That is, will the forces involved get larger or smaller? How do you know?

- September 10th 2007, 04:38 AM #2

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