Two ropes attached to a young tree are pulled by two landscapers. Rope 1 is pulled with 267 N of force at an angle of 23 degrees north of east and Rope 2 is pulled with 377 N of force due west.

Question

a) Determine the magnitude and direction of the resultant force acting on the tree

b) Determine magnitude and direction of a third cable installed to produce equilibrium.

Answer 1

Unless otherwise stated, all angles are measured CCW from +x-axis.

a. F=267[23o] - 377=245.8+104.3i - 377 = -131.2 + 104.3i = 168N[38.5o]N. of W.

b. F3 and F should be equal in magnitude and 180o out of phase:

Therefore, F3 = 168N[38.5o]S. of E.