1. A 2.0 x 10^3 kg sailboat experiences an eastward force of 3.0 x 10^3 N by the

Question

1. A 2.0 x 10^3 kg sailboat experiences an eastward force of 3.0 x 10^3 N by the ocean tide and a wind force against its sails with magnitude of 6.0 x 10^3 N directed toward the northwest (45 degrees N of W). What is the resultant acceleration (magnitude and direction)?
2. A girl is using a rope to pull a box that weighs 3.00 x 10^2 N across a level surface with constant velocity. The rope makes an angle of 30.0 degrees above the horizontal, and the tension in the rope is 1.00 x 10^2 N. What is the normal force of the floor on the box (magnitude and direction)?

Explanation / Answer

mass m = 2 * 10^ 3 kg eastward force F = 3 * 10^3 N i force aginst its sails F ' = (6*10^ 3 * cos 45 ) *-i + (6*10^3 * sin 45) j                                     = -4.242*10^ 3 i + 4.242 *10^3 j resultant force F " = F + F '                              = -1.242*10^3 i +4.242*10^3 j magnitude of F " = [ (-1.242*10^3 )^ 2 + (4.242*10^3 ) ^ 2]                           = 4.42 *10^3 N resultant accleration a = F " / m                                   = 2.21 m / s^ 2 (2). box weight W = 300 N angle = 30.0 degrees tension in the rope T= 1.00 x 10^2 N the normal force of the floor on the box = mg - T sin                                                              = W - T sin                                                              = 300 - 50                                                              = 250 N

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