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hello physics forums,

this is lengthy but pretty much challenging..really appreciate any help ^o^

A tugboat is towing a barge with a flexible cable. After towing steadily at constant speed for sometime, the tug propeller thrust T(t) is decreased from 100kN at a steady rate (dT/dt = constant).

given: mass of tug, m1 = 10,000 kg

mass of barge, m2 = 100,000 kg

tug drag characteristic, D1 = 2000.(v1)^2 N

barge drag charateristic, D2 = 6700.(v2)^2 N

cable stiffness 800 kN/m

vb = 0.4904 m/s

1) Determine the maximum magnitude of the 'steady rate' that ensures the tow cable is always in tension during the deceleration from the constant speed to a barge velocity, vb m/s (ignore the cable mass and its sag).

2) Can the non-linear differential equations be solved numerically. how will v1 and v2 behave with respect to time, t?

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# Homework Help: Mechanics is hard need help

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