In earlier days, horses pulled barges down canals in the manner shown below. Sup
ID: 1599023 • Letter: I
Question
In earlier days, horses pulled barges down canals in the manner shown below. Suppose that the horse pulls on the rope with a force of 7900 N at an angle of 18° to the direction of motion of the barge, which is headed straight along the positive direction of an x axis. The mass of the barge is 9100 kg, and its acceleration is 0.10 m/s2. What are the magnitude and the direction of the force on the barge from the water?
magnitudeN direction ° (counterclockwise from the +x axis is positive)
Explanation / Answer
Component of applied force in the direction of travel = (cos 18) x 7,900, = 7,513.35N.
Component perpendicular to direction of travel = (sin 19) x 7,900 = 2,571.99N.
Force, no friction, to accelerate mass = (ma) = 9,100 x 0.10, = 910N.
Friction force = (7,153.35 - 910) =6243.35N.
Force on barge = sqrt.(6243.35^2 + 2,571.99^2) = 6,334N., and direction = arctan (2,571.99/5,788.35),
= 23.96 degrees from travel direction, towards the bank opposite that which the horse is on.