# Calculating tension in a rope

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1. Nov 18, 2015

### ecsthetic

1. The problem statement, all variables and given/known data
A tugboat pulls two barges down the river. The barge connected to the tugboat, carrying coal, has an
inertia of 2.2 × 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 is1.0 × 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?

2. Relevant equations:
f=ma

3. Attempt:
a.) I know the force acting on the coal barge is the pulling force minus water resistance
(2.2 x 10^5)(0.4) - (8.0 x 10^3) = 8 x 10^4 N
so is this tension of the rope equal to 8 x 10^4 N?

b.) For the tension caused by two barges, I sum the force on coal barge and iron barge
(8 x 10^4) + ( 1.4 x 10^5 - 1.0 x 10^4 ) = 2.1 x 10^5 N

can anyone verify my work and need hints on c and d, thanks in advance

2. Nov 18, 2015

### BvU

MAke a drawing and see that the coal barge pulls the pig iron barge, not the other way around ... (but you can use your (a) answer later on ... )