Three friends tie three ropes in a knot and pull on the ropes in different direc
ID: 1487968 • Letter: T
Question
Three friends tie three ropes in a knot and pull on the ropes in different directions. Adrienne (rope 1) exerts a 100-N force F AonK that points 30 below the positive x-axis and Jim (rope 2) exerts a 150-N force in the negative y-direction.
A) How hard does Luis now have to pull the knot so that it remains in equilibrium?
B) In what direction does Luis now have to pull the knot so that it remains in equilibrium (clockwise from the negative x-axis)?
I think I'm confused on which become negative based on the direction of the rope. If someone could explain step by step for this I would really appreciate it!
Explanation / Answer
Force applied by Adrienne, FA = 100[cos(-30o) x + sin(-30o) y] = 86.6 i - 50 j
Force applied by Jim, FJ = -150 j
To the knot to remain in equilibrium, net force on the knot should be zero.
=> FL + FA + FJ = 0
=> FL + (86.6 i - 50 j) + (-150 j) = 0
=> FL = -86.6 i + 200 j
A) Magnitude of force applied by Luis, |FL| = [(-86.6)2 + 2002]1/2 = 217.9 N
B) Direction, = tan-1(200 / 86.6) = 66.6o (clockwise from the negative x-axis)