Three people pull simultaneously on a stubborn donkey. Jack pulls eastward with

Question

Three people pull simultaneously on a stubborn donkey. Jack pulls eastward with a force of 78.5 N, Jill pulls with 71.7 N in the northeast direction, and Jane pulls to the southeast with 143 N. (Since the donkey is involved with such uncoordinated people, who can blame it for being stubborn?) Find the magnitude of the net force the people exert on the donkey.What is the direction of the net force? Express this as the angle from the east direction between 0° and 90°, with a positive sign for north of east and a negative sign for south of east.

Explanation / Answer

Forces f = 71.7 i

           f ' = 71.7cos 45 i + 71.7 sin 45 j

              = 50.7 i +50.7 j

          f" = 143 cos 45 i + 143 sin 45 ( -j)

              = 101.12 i – 101.12 j

Net force F = f + f ' + f "

                    = 78.5 i + 50.7 i +50.7 j + 101.12 i – 101.12 j

                    = 230.32 i -50.42 j

Magnitude of F

       F = [ 230.32 2 + (-50.42) 2 ]

          = 235.77 N

Let F makes an angle with east along south then,

tan = 50.42/ 230.32

                  = 12.35 o

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