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 8130 N and is at the angle ? = 17

Explanation / Answer

Two force act on the barge in the horizontal direction: i) Horizontal component of tension, T in the rope = 8130 cos 17° = 7774.757 N and ii) Opposing drag force from water on the barge = F Under the effect of these two forces, the barge has acceleration of 0.10 m/s^2. So, (9500) * (0.12) = 7774.757 - F => F = 6634.757 N There is another vertical reactive force, F', on the barge from water which is in the downward direction opposite to the upward component of tension T in the rope = T sin 18° = 8130 * sin 17° = 2376.98 N Net force from water is the resultant of F and F' Magnitude of net force from water = v[ (6634.757)^2 + (2376.98)^2 ] = 7047.697 N If ? is the angle made by this force with the horizontal, then ? = - arctan (2376.98) / (6634.757) = - 19.71°

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