Answer:
T₁ = 296 N
T₂ = 163 N
T₃ = 325 N
Explanation:
Draw a free body diagram of the bag. There are two forces:
Weight force mg pulling down,
Tension force T₃ pulling up.
Sum of forces in the y direction:
∑F = ma
T₃ − mg = 0
T₃ = mg
T₃ = 325 N
Draw a free body diagram of the connection between the wires. There are three forces, T₁, T₂, and T₃.
Sum of forces in the y direction:
∑F = ma
T₁ sin θ₁ + T₂ sin θ₂ − T₃ = 0
Sum of forces in the x direction:
∑F = ma
T₂ cos θ₂ − T₁ cos θ₁ = 0
T₂ cos θ₂ = T₁ cos θ₁
T₂ = T₁ cos θ₁ / cos θ₂
Substitute:
T₁ sin θ₁ + T₁ cos θ₁ tan θ₂ − T₃ = 0
T₁ (sin θ₁ + cos θ₁ tan θ₂) = T₃
T₁ = T₃ / (sin θ₁ + cos θ₁ tan θ₂)
T₁ = 325 N / (sin 60° + cos 60° tan 25°)
T₁ = 296 N
T₂ = T₁ cos θ₁ / cos θ₂
T₂ = 296 N cos 60° / cos 25°
T₂ = 163 N
