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 8010 N and is at the angle ? = 19° 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

Fy=m.ay.sin(?)= 7830sin(18)= 2419.6N Fx= (9500kg)(0.12m/s2)= 1140 N Fxrope= 7830cos?= 7830cos(18)= 7446.8N Fxwater= Fx - Fxrope= (1140-7446.8)N= -6306.8 N (which makes sense since the water is flowing in the -x direction) Then the angle ? would be arctan (Fy/Fx)= ? arctan(2419.6/-6306.8)= -21 ?= -21

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