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 8070 N and is at the angle  = 14° 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 xaxis) of the force on the barge from the water? Give your answer for (b) in the range of (-180°, 180°].

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(14) * 8070 = 1952 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(14) * 8070 in the same direction. find the difference between the two to find the force exerted by the water.

cos(14)(8070) = 7830 N - 1140 N = 6690N

so the water is giving a resistance force of 6690N opposite the direction of travel(-x) direction, and 1952 N perpendicular to the path of travel. we can use pythagorean theorum now:

total force = 66902 + 1952 = 6969 N find the angle by taking cos-1(-6690/6969) = 163.7 degrees

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