Question

At a family picnic, there’s a strange tug of war that involves three ropes. Team 1 pulls with F1 = 1100N at 65◦ above the horizontal and Team 2 pulls with 1300N at 145circ from the x-axis (horizontal). If the center of the rope doesn’t move, how much must Team 3 be pulling and in what direction relative to the x-axis?

Answer 1

here,

force applied by team 1 , T1 = 1100 N * (cos(65) i + sin(65) j)

T1 = ( 464.89i N + 996.94 j N)

force applied by team 2 , T2 = 1300 N * (cos(145) i + sin(145) j)

T2 = ( - 1064.9 i N + 745.65 j N)

let the force applied by team 3 be T3

as the center will not move

the net force is zero

T1 + T2 + T3 = 0

( 464.89i N + 996.94 j N) + ( - 1064.9 i N + 745.65 j N) + T3 = 0

T3 = (- 600.01 i N - 1742.59 j N)

the magnitude of force applied by team 3 , |T3| = sqrt(600.01^2 + 1742.59^2)

|T3| = 1843 N

the direction of force , theta = arctan((-1742.59 )/(-600.01))

theta = 51.06 degree counterclockwise from +X axis