In the figure, a horse pulls a barge along a canal by means of a rope. The force

Question

In the figure, a horse pulls a barge along a canal by means of a rope. The force on the barge from the rope has a magnitude of 7690 N and is at the angle ? = 17° from the barge's motion, which is in the positive direction of an x axis extending along the canal. The mass of the barge is 9500 kg, and the magnitude of its acceleration is 0.12 m/s2. What are (a) the magnitude and (b) the direction (measured from the positive direction of the x axis) of the force on the barge from the water? Give your answer for (b) in the range of (-180°, 180°].

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Explanation / Answer

the boat is moving parallel to the wall of the canal. therefore the sin component of the rope's force must be counteracted. that is sin(17) * 7690 = 2248 N

now the boat is being accelerated at .12 m/s2

the force required to do that is 9500 kg * .12 m/s2 = 1140 N

the rope is giving force of cos(17) * 7690 in the same direction. find the difference between the two to find the force exerted by the water.

cos(17)(7690) = 7354 N - 1140 N = 6214N



so the water is giving a resistance force of 6214N opposite the direction of travel(-x) direction, and 2248 N perpendicular to the path of travel. we can use pythagorean theorum now:

total force = 62142 + 22482 = 6608N

find the angle by taking cos-1(6214/6608) = 160.1 degrees from the x axis. since both the x and the y components are negative, its going to be 160.1 degrees clockwise which is -160.1 degrees

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