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 7920 N and is at the angle ? = 22° 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

Using Fnet = ma

Fcos22 + Fcos22 - F1 = ma

2(7920)cos22 - F1 = 9500 x 0.12

F1 = 13546.59 N opposite to the direction of acceleration.

a) magnitude = 13546.59 N

b) direction = 180 deg

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