Answer:
T₁ = 71.7 N
T₂ = 50.7 N
Step-by-step explanation:
Sum of forces in the y direction:
∑F = ma
T₁ sin 60° + T₂ sin 45° − mg = 0
T₁ sin 60° + T₂ sin 45° = mg
T₁ (√3 / 2) + T₂ (√2 / 2) = mg
Sum of forces in the x direction:
∑F = ma
-T₁ cos 60° + T₂ cos 45° = 0
T₁ cos 60° = T₂ cos 45°
T₁ / 2 = T₂ (√2 / 2)
T₁ = T₂ √2
Substitute:
(T₂ √2) (√3 / 2) + T₂ (√2 / 2) = mg
T₂ (√6 / 2) + T₂ (√2 / 2) = mg
T₂ (√6 / 2 + √2 / 2) = mg
1.932 T₂ = (10 kg) (9.8 m/s²)
T₂ = 50.7 N
T₁ = T₂ √2
T₁ = 71.7 N