A barge is hauled along a straight-line section of canal by two horses harnessed to tow ropes and walking along the tow paths on either side of the canal. Each horse pulls with a force of 505 N at an angle of 11.5° with the centerline of the canal. Find the sum of the two forces exerted by the horses on the barge.
Question
A barge is hauled along a straight-line section of canal by two horses harnessed to tow ropes and walking along the tow paths on either side of the canal. Each horse pulls with a force of 505 N at an angle of 11.5° with the centerline of the canal. Find the sum of the two forces exerted by the horses on the barge.
Solution
The forces exerted by the two horses can be resolved into two components: one along the direction of the canal (horizontal) and the other perpendicular to the canal (vertical).
Step 1: Calculate the horizontal and vertical components of the force exerted by one horse.
The horizontal component (Fh) is given by Fh = F * cos(θ), where F is the force exerted by the horse and θ is the angle of the force. Substituting the given values, we get Fh = 505 N * cos(11.5°) = 495.5 N.
The vertical component (Fv) is given by Fv = F * sin(θ). Substituting the given values, we get Fv = 505 N * sin(11.5°) = 102.3 N.
Step 2: Calculate the total force exerted by the two horses.
Since the horses are on either side of the canal, their vertical forces cancel each other out. Therefore, the total vertical force is 0.
The horizontal forces, however, add up. Therefore, the total horizontal force is 2 * Fh = 2 * 495.5 N = 991 N.
So, the sum of the two forces exerted by the horses on the barge is 991 N.
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