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 7660 N and is at the angle = 15° 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°].

Explanation / Answer

Forward Force on the barge is 7660 x cos(15) = 7399 N

Force accelerating barge = 9500 x 0.12 = 1140 N

Force resisting barge = 7399 – 1140 = 6259 N

Sideways pull of horse ( towards the bank ) = 7660 x sin(15) = 1983 N

The water must exert the same but opposite force ( against the boat's rudder ) so the total force on the boat

F = sqrt(6259^2 + 1983^2) = 6566 N

theta = tan^-1(1983/6259) = 16.8

the direction will be 16.8 to the line of the bank. Which is 163.2 from the positive x direction

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