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 7830 N and is at the angle θ = 14° 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°].
1.
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 7830 N and is at the angle θ = 14° 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°].
2. Holding onto a tow rope moving parallel to a frictionless ski slope, a 47.0 kg skier is pulled up the slope, which is at an angle of 9.7° with the horizontal. What is the magnitude Frope of the force on the skier from the rope when (a) the magnitude v of the skier's velocity is constant at 2.38 m/s and (b) v = 2.38 m/s as v increases at a rate of 0.128 m/s2?
3. In the figure, a crate of mass m = 118 kg is pushed at a constant speed up a frictionless ramp (θ = 31°) by a horizontal force F→. The positive direction of an x axis is up the ramp, and the positive direction of a y axis is perpendicular to the ramp. (a) What is the magnitude of F→? (b) What is the magnitude of the normal force on the crate?
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