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

Question

n 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 7860 N and is at the angle

? = 17

n 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 7860 N and is at the angle? = 17 degree 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 degree , 180 degree ].

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) * 7860= 2298.04159912 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) * 7860 in the same direction. find the difference between the two to find the force exerted by the water.

cos(17)(7860) = 7516- 1140 N = 6376.55538187N

so the water is giving a resistance force of 6376.55538187N opposite the direction of travel(-x) direction, and 2298 N perpendicular to the path of travel. we can use pythagorean theorum now:

total force =? 6376.52 + 2298^2 =6777.99841679N

find the angle by taking cos-1(-6376.55/6777.99) = 160.181545263 degrees

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