Question

2-1. If θ= 30° and T = 6kN, determine the magnitude of the resultant force acting on the eyebolt and its direction measured clockwise from the positive x axis.

 2-2. If θ = 60° and T = 5 kN, determine the magnitude of the resultant force acting on the eyebolt and its direction measured clockwise from the positive x axis.

 2-3. If the magnitude of the resultant force is to be 9 kN directed along the positive x axis, determine the magnitude of force T acting on the eyebolt and its angle θ.

Answer 1

2.1

X-Component of Resultant force

F_Rx=6Cos(90-30)+8Cos(45)=8.66 KN

Y-Component of resultant force

F_Ry=6Sin(90-30)-8Sin(45)=-0.46 KN

Magnitude

|F_R|=sqrt[8.66²+(-0.46)²]=8.67 KN

Direction

o=tan^-1(-0.46/8.66)=-3.05^o

o=3.05 below the +x-axis

or 360-3.05=356.95^o counterclockwise from +x-axis