EQUILIBRIUM The sum of the forces is zero. The acceleration is zero. ΣF = 0 a=0

A 150kg traffic signal is hanging from two wires. If the wire on the left makes a 21 o angle to the horizontal, and the wire on the right makes a 32 o angle, what is the tension in each wire? θ1θ1 θ2θ2

Show forces and angles on a force diagram. T1T1 T2T2 T3T3 θ1θ1 θ2θ2 =mg

Draw and find components of forces. T1T1 T2T2 T 3 =mg θ1θ1 θ2θ2 T 1x T 1y T 2x T 2y

T 1x = -T 1 cos θ 1 T 1y = T 1 sin θ 1 T 2x = T 2 cosθ 2 T 2y = T 2 sinθ 2 T 3x =0 T 3y =-mg T1T1 T2T2 T 3 =mg θ1θ1 θ2θ2 T 1x T 1y T 2x T 2y

Equilibrium conditions: Write component equations in terms of the FBD. ΣF x = 0 -T 1 cos θ 1 + T 2 cos θ 2 =0 ΣF y = 0 T 1 sin θ 1 + T 2 sin θ 2 -mg=0 Solve for T 1 and T 2.

With numbers…

Find the tension in the rope.