A tugboat pulls two barges down the river. The barge connected to the tugboat, c

Question

A tugboat pulls two barges down the river. The barge connected to the tugboat, carrying coal, has an inertia of2.4 × 105 kg, and the other barge, carrying pig iron, has an inertia of 3.5 × 105 kg. The resistive force between the coal barge and the water is 8.0 × 103 N, and the resistive force between the pig iron barge and the water is 1.0 × 104 N . The common acceleration of all three boats is 0.40 m/s2.Even though the ropes are huge, the gravitational force exerted on them is much smaller than the pulling forces.

A) What is the tension in the rope that connects the tugboat to the coal barge?

B) What is the tension in the rope that connects the two barges?

C) What is the tension in the rope that connects the tugboat to the coal barge if the order of the barges is reversed?

D) What is the tension in the rope that connects the two barges if the order of the barges is reversed?

Explanation / Answer

A)

The force acting on the coal barge is

= 2.4 × 105 N

B)

This rope accounts for the motion of the pig iron barge:

T = 3.5e5kg * 0.40m/s² + 1e4N = 1.5 x 10^5 N

c) If the order of the barges is reversed, then the tugboat is connected to the pig iron barge, not the coal barge. In any event, the tension in the rope connecting the tugboat to either barge is 2.4 × 105 N.

That's because the total mass is accelerating at the same rate and the same drag forces are involved.

D)

Same

1.5 x 10^5 N

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