Three people located at A B and C pull on rupes tied to a ri

Three people located at A, B, and C pull on rupes tied to a ring. Find the magnitude and direction of the force with which C must pull so that no one moves (the system is at equilibrium). The magnitude of the force with which C must pull is lb. (Round to the nearest integer as needed.)

Solution

As system is in equilibrium, so Fnet = 0

Fnet = F1 + F2 + F3 = 0

[ 114(-sin45i + cos45j)] + [ 50(sin30i + cos30j)] + F3 = 0

F3 = 55.61i - 123.91j

magnitude of force = sqrt(55.61^2 + 123.91^2) = 135.82 N